,,! ,,sci5ce ,,( ,,beauty4 ,,ed9burgh3 ,,pr9t$ ,,by ,,ballantyne ,,& ,,company1 ,,paul',s ,,"w4 ,,! ,,sci5ce ,,( ,,beauty1 ,,z ,,develop$ ,,9 ,,nature ,,& ,,appli$ ,,9 ,,art4 ,,by ,d4 ,r4 ,,hay1 ,f4,r4,s4,e4 8,! irregul> comb9ations ( fanciful inv5tion may delight a:ile1 by t novelty ( :i* ! common satiety ( life s5ds u all 9 que/2 ! pleasures ( sudd5 wond] are soon exhau/$1 & ! m9d c only repose on ! /ability ( tru?40 ,,dr ,,johnson4 ,,william ,,blackwood ,,& ,,sons1 ,,ed9burgh ,,& ,,london4 ,,mdccclvi4 ,,to ,,john ,,goodsir1 ,,esq41 ,f4,r4,s ,s4 ,l4 ,e41 ,,pr(essor ,,( ,,anatomy ,,9 ,,! ,,univ]sity ,,( ,,ed9burgh1 ,,z ,,an ,,expression ,,( ,,gratitude ,,= ,,valuable ,,assi/ance1 ,,z ,,also ,,( ,,high ,,e/eem ,,& ,,s9c]e ,,reg>d1 ,,?is ,,volume ,,is ,,d$icat$1 ,,by ,,! ,,au?or4 ,,preface4 ,my !ory ( beauty 9 =m & col\r be+ n[ admitt$ by ! be/ au?orities to be bas$ on tru?1 ,i h ( late be5 (t5 ask$1 by ^? :o wi%$ to become acqua9t$ ) its nature1 & ! mann] ( its be+ appli$ 9 art1 :i* ( my publications ,i w\ld recomm5d = _! p]usal4 ,?is "q ,i h always f\nd difficulty 9 answ]+2 = al?\gh ! law ^u :i* my !ory is bas$ is *>act]is$ by unity1 yet ! subjects 9 :i* x is appli$1 & ! modes ( its application1 are equally *>act]is$ by v>iety1 & consequ5tly occupy sev]al volumes4 ,"u ^! circum/ances1 ,i consult$ a highly respect$ fri5d1 ^: ma!matical tal5ts & good ta/e are well kn[n1 & to :om ,i h be5 greatly indebt$ = mu* valuable assi/ance dur+ ! c\rse ( my inve/igations4 ,! advice ,i receiv$ on ?is occasion1 0 to publi% a rsum ( my =m] works1 ( su* a "* z n only to expla9 ! nature ( my !ory1 b to exhibit to ! g5]al read]1 by ! mo/ simple modes ( illu/ration & description1 h[ x is develop$ 9 nature1 & h[ x may be ext5sively & ) ease appli$ 9 ^? arts 9 :i* beauty =ms an ess5tial elem5t4 ,! foll[+ pages1 ) _! illu/rations1 are ! results ( an attempt to accompli% ?is object4 ,to ^? :o are already acqua9t$1 ?r\gh my =m] works1 ) ! nature1 scope1 & t5d5cy ( my !ory1 ,i h ! satisfaction to intimate t ,i h be5 enabl$ to include 9 ?is rsum mu* orig9al matt]1 ) ref]5ce bo? to =m & col\r4 ,d4 ,r4 ,,hay4 ,,cont5ts4 ,,page ,,introduction #a ,,! ,,sci5ce ,,( ,,beauty1 ,,evolv$ ,,f ,,! ,,h>monic ,,law ,,( ,,nature1 ,,agreeably ,,to ,,! ,,py?agorean ,,sy/em ,,( ,,num]ical ,,ratio #ae ,,! ,,sci5ce ,,( ,,beauty1 ,,z ,,appli$ ,,to ,,s\nds #bh ,,! ,,sci5ce ,,( ,,beauty1 ,,z ,,appli$ ,,to ,,=ms #cd ,,! ,,sci5ce ,,( ,,beauty1 ,,z ,,develop$ ,,9 ,,! ,,=m ,,( ,,! ,,human ,,head ,,& ,,c\nt5ance #ed ,,! ,,sci5ce ,,( ,,beauty1 ,,z ,,develop$ ,,9 ,,! ,,=m ,,( ,,! ,,human ,,figure #fa ,,! ,,sci5ce ,,( ,,beauty1 ,,z ,,develop$ ,,9 ,,col\rs #fg ,,! ,,sci5ce ,,( ,,beauty ,,appli$ ,,to ,,! ,,=ms ,,& ,,proportions ,,( ,,anci5t ,,grecian ,,vases ,,& ,,ornam5ts #hb ,,app5dix1 ,,no4 ,i4 #ia ,,app5dix1 ,,no4 ,,ii4 #ii ,,app5dix1 ,,no4 ,,iii4 #ajj ,,app5dix1 ,,no4 ,,iv4 #ajj ,,app5dix1 ,,no4 ,v4 #ajd ,,app5dix1 ,,no4 ,,vi4 #aje ,,illu/rations4 ,,plates ,illu/ration3 ,i4 ,?ree ,scales ( ! ,elem5t>y ,rectil9e> ,figures1 viz41 ! ,scal5e ,triangle1 ! ,isosceles ,triangle1 & ! ,rectangle1 compris+ tw5ty-sev5 v>ieties ( ea*1 accord+ to ! h>monic p>ts ( ! ,"r ,angle f to 4 ,d4 ,r4 ,hay del4 ,g4 ,aikman sc4 ,illu/ration3 ,,ii4 ,diagram ( ! ,rectil9e> ,or?ography ( ! ,pr9cipal ,front ( ! ,p>!non ( ,a!ns1 9 :i* its ,proportions are det]m9$ by h>monic p>ts ( ! ,"r ,angle4 ,d4 ,r4 ,hay del4 ,g4 ,aikman sc4 ,illu/ration3 ,,iii4 ,diagram ( ! ,rectil9e> ,or?ography ( ! ,portico ( ! ,temple ( ,!seus at ,a!ns1 9 :i* its ,proportions are det]m9$ by h>monic p>ts ( ! ,"r ,angle4 ,d4 ,r4 ,hay del4 ,g4 ,aikman sc4 ,illu/ration3 ,,iv4 ,diagram ( ! ,rectil9e> ,or?ography ( ! ,ea/ ,end ( ,l9coln ,ca!dral1 9 :i* its ,proportions are det]m9$ by h>monic p>ts ( ! ,"r ,angle4 ,d4 ,r4 ,hay del4 ,g4 ,aikman sc4 ,illu/ration3 ,v4 ,f\r ,ellipses describ$ f ,foci1 det]m9$ by h>monic p>ts ( ! ,"r ,angle1 %ew+ 9 ea* ! ,scal5e ,triangle1 ! ,isosceles ,triangle1 & ! ,rectangle to :i* x belongs4 ,d4 ,r4 ,hay del4 ,g4 ,aikman sc4 ,illu/ration3 ,,vi4 ,! ,composite ,ellipse ( & ( ! ,"r ,angle1 %ew+ its great] & less] ,axis1 its v>i\s ,foci1 & ! ,isosceles ,triangle 9 :i* !y are plac$4 ,d4 ,r4 ,hay del4 ,g4 ,aikman sc4 ,illu/ration3 ,,vii4 ,! ,composite ,ellipse ( & ( ! ,"r ,angle1 %ew+ h[ x =ms ! ,entasis ( ! ,columns ( ! ,p>!non ( ,a!ns4 ,d4 ,r4 ,hay del4 ,g4 ,aikman sc4 ,illu/ration3 ,,viii4 ,sectional ,outl9es ( two ,m\ld+s ( ! ,p>!non ( ,a!ns1 full size1 %ew+ ! h>monic nature ( _! ,curves1 & ! simple mann] ( _! ,con/ruction4 ,d4 ,r4 ,hay del4 ,g4 ,aikman sc4 ,illu/ration3 ,,ix4 ,?ree ,diagrams1 giv+ a ,v]tical1 a ,front1 & a ,side ,aspect ( ! ,geometrical ,con/ruction ( ! ,human ,head & ,c\nt5ance1 9 :i* ! ,proportions are det]m9$ by h>monic p>ts ( ! ,"r ,angle4 ,d4 ,r4 ,hay del4 ,g4 ,aikman sc4 ,illu/ration3 ,x4 ,diagram 9 :i* ! ,symmetrical ,proportions ( ! ,human ,figure are det]m9$ by h>monic p>ts ( ! ,"r ,angle4 ,d4 ,r4 ,hay del4 ,g4 ,aikman sc4 ,illu/ration3 ,,xi4 ,! ,cont\r ( ! ,human ,figure z view$ 9 ,front & 9 ,pr(ile1 its ,curves be+ det]m9$ by ,ellipses1 ^: ,foci are det]m9$ by h>monic p>ts ( ! ,"r ,angle4 ,d4 ,r4 ,hay del4 ,g4 ,aikman sc4 ,illu/ration3 ,,xii4 ,rectil9e> ,diagram1 %ew+ ! ,proportions ( ! ,portl& ,vase1 z det]m9$ by h>monic p>ts ( ! ,"r ,angle1 & ! outl9e ( its =m by an ,elliptic ,curve h>monically describ$4 ,d4 ,r4 ,hay del4 ,g4 ,aikman sc4 ,illu/ration3 ,,xiii4 ,rectil9e> ,diagram ( ! ,proportions & ,curvil9e> ,outl9e ( ! =m ( an anci5t ,grecian ,vase1 ! proportions det]m9$ by h>monic p>ts ( ! ,"r ,angle1 & ! melody ( ! =m by ,curves ( two ,ellipses4 ,d4 ,r4 ,hay del4 ,g4 ,aikman sc4 ,illu/ration3 ,,xiv4 ,rectil9e> ,diagram ( ! ,proportions & ,curvil9e> ,outl9e ( ! =m an anci5t ,grecian ,vase1 ! proportions det]m9$ by h>monic p>ts ( ! ,"r ,angle1 & ! melody ( ! =m by an ,elliptic ,curve4 ,d4 ,r4 ,hay del4 ,g4 ,aikman sc4 ,illu/ration3 ,,xv4 ,two ,diagrams ( ,etruscan ,vases1 ! h>mony ( ,proportions & melody ( ! ,cont\r det]m9$1 respectively1 by p>ts ( ! ,"r ,angle & an ,elliptic ,curve4 ,d4 ,r4 ,hay del4 ,g4 ,aikman sc4 ,illu/ration3 ,,xvi4 ,two ,diagrams ( ,etruscan ,vases1 ^: h>mony ( ,proportion & melody ( ,cont\r are det]m9$ z above4 ,d4 ,r4 ,hay del4 ,g4 ,aikman sc4 ,illu/ration3 ,,xvii4 ,diagram %ew+ ! ,geometric ,con/ruction ( an ,ornam5t belong+ to ! ,p>!non at ,a!ns4 ,d4 ,r4 ,hay del4 ,g4 ,aikman sc4 ,illu/ration3 ,,xviii4 ,diagram ( ! ,geometrical ,con/ruction ( ! anci5t ,grecian ,ornam5t call$ ! ,honeysuckle4 ,d4 ,r4 ,hay del4 ,g4 ,aikman sc4 ,illu/ration3 ,,xix4 ,an additional ,illu/ration ( ! ,cont\r ( ! ,human ,figure1 z view$ 9 ,front & 9 ,pr(ile4 ,d4 ,r4 ,hay del4 ,g4 ,aikman sc4 ,illu/ration3 ,,xx4 ,diagram %ew+ ! mann] 9 :i* ! ,elliptic ,curves are arrang$ 9 ord] to produce an ,outl9e ( ! ,=m ( ! ,human ,figure z view$ 9 ,front4 ,d4 ,r4 ,hay del4 ,g4 ,aikman sc4 ,illu/ration3 ,,xxi4 ,diagram ( a v>iation on ! ,=m ( ! ,portl& ,vase4 ,d4 ,r4 ,hay del4 ,g4 ,aikman sc4 ,illu/ration3 ,,xxii4 ,diagram ( a second v>iation on ! ,=m ( ! ,portl& ,vase4 ,d4 ,r4 ,hay del4 ,g4 ,aikman sc4 ,illu/ration3 ,,xxiii4 ,diagram ( a ?ird v>iation on ! ,=m ( ! ,portl& ,vase4 ,d4 ,r4 ,hay del4 ,g4 ,aikman sc4 ,,introduction4 ,twelve ye>s ago1 "o ( our mo/ em95t philosoph]s1#a ?r\gh ! m$ium ( ! ,ed9burgh ,review1#b gave ! foll[+ acc\nt ( :at 0 !n ! /ate ( ! f9e arts z connect$ ) sci5ce3--8,! disposition to introduce into ! intellectual community ! pr9ciples ( free int]c\rse1 is by no means g5]al2 b we are confid5t t ,art w n suffici5tly develop h] p[]s1 nor ,sci5ce atta9 h] mo/ comm&+ position1 till ! practical k ( ! "o is tak5 9 return = ! s\nd d$uctions ( ! o!r4444 ,x is 9 ! f9e arts1 pr9cipally1 & 9 ! speculations ) :i* !y are associat$1 t ! controll+ p[] ( sci5tific tru? has n ex]cis$ its legitimate influ5ce4 ,9 discuss+ ! pr9ciples ( pa9t+1 sculpture1 ar*itecture1 & l&scape g>d5+1 philosoph]s h r5\nc$ sci5ce z a guide1 & ev5 z an auxili>y2 & a s*ool has aris5 ^: speculations w brook no re/ra9t1 & ^: decisions /& 9 opposition to ! /ronge/ convictions ( our s5ses4 ,t ! ext]nal _w1 9 its gay col\rs & lovely =ms1 is exhibit$ to ! m9d only z a t9t$ mass1 nei!r )9 nor )\t ! eye1 nei!r t\*+ x nor di/ant f x--an ubiquit\s *aos1 :i* exp]i5ce only c analyse & trans=m into ! realities :i* compose x2 t ! beautiful & sublime 9 nature & 9 art d]ive _! p[] ov] ! m9d f association alone1 are among ! philosophical doctr9es ( ! pres5t day1 :i*1 if x be safe1 x is sc>cely prud5t to "q4 ,nor are ^! op9ions ! emanations ( poetical or ill-tra9$ m9ds1 :i* +5uity has elaborat$1 & :i* fa%ion su/a9s4 ,!y are conclusions at :i* mo/ ( our di/+ui%$ philosoph]s h arriv$4 ,!y h be5 giv5 to ! _w ) all ! au?ority ( demon/rat$ tru?2 & 9 proportion to ! hold :i* !y h tak5 ( ! public m9d1 h !y op]at$ z a *eck ^u ! progress ( k40 ,su*1 !n1 0 ! /ate ( art z connect$ ) sci5ce twelve ye>s ago4 ,b al?\gh ! causes :i* !n plac$ sci5ce & ! f9e arts at v>iance h s9ce be5 gradually dim9i%+1 yet !y are /ill f> f be+ remov$4 ,9 pro( ( ?is ,i may ref] to :at took place at ! annual di/ribution ( ! prizes to ! /ud5ts att5d+ our ,scotti% ,metropolitan ,s*ool ( ,design1 9 #ahed1 ! pupils 9 :i* am\nt to upw>ds ( two hundr$4 ,! meet+ on t occasion includ$1 besides ! pupils1 a num]\s & highly respectable assemblage ( arti/s & m5 ( sci5ce4 ,! *airman1 a ,pr(essor 9 our ,univ]sity1 & editor ( "o ( ! mo/ volum9\s works on art1 sci5ce1 & lit]ature ev] produc$ 9 ?is c\ntry1 aft] extoll+ ! g5]al progress ( ! pupils1 s f> z ev9c$ by ! draw+s exhibit$ on ! occasion1 drew ! att5tion ( ! meet+ to a discov]y made by ! head ma/] ( ! ar*itectural & ornam5tal dep>tm5t ( ! s*ool1 viz4--,t ! gr\nd-plan ( ! ,p>!non at ,a!ns _h be5 con/ruct$ by ! application ( ! my/]i\s ovoid or ,vesica ,piscis ( ! middle ages1 subdivid$ by ! my?ic numb]s #c & #g1 & _! int]m$iate odd numb] #e4 ,n[1 x may be rem>k$1 t ! figure ?us ref]r$ to is n an ovoid1 nei!r is x 9 any way ( a my/]i\s nature1 be+ produc$ simply by two equal circles cutt+ ea* o!r 9 _! c5tres4 ,nei!r c x be %ewn t ! numb]s #c & #g are 9 any way m my?ic ?an o!r numb]s4 ,9 fact1 ! t]ms my/]i\s & my?ic s appli$1 c only be reg>d$ z a remnant ( an anci5t t]m9ology1 calculat$ to obscure ! simplicity ( sci5tific tru?1 & :5 us$ by ^? employ$ to tea*--= d\btless ! *airman only gave ! description he receiv$--mu/ t5d to ret>d ! connexion ( t tru? ) ! arts ( design4 ,i %all n[ give a specim5 ( ! mann] 9 :i* a k ( ! philosophy ( ! f9e arts is at pres5t inculcat$ ^u ! public m9d g5]ally4 ,9 ! same metropolis !re has likewise exi/$ = upw>ds ( t5 ye>s a ,philosophical ,in/itution ( great importance & utility1 ^: memb]s am\nt to ne>ly ?ree ?\s&1 embrac+ a l>ge proportion ( ! high] classes ( society1 bo? 9 respect to tal5t & weal?4 ,at ! close ( ! session ( ?is ,in/itution1 9 #ahed1 a le>n$ & eloqu5t philologus1 :o occasionally lectures ^u beauty1 0 appo9t$ to deliv] ! clos+ address1 & t\*+ ^u ! subject ( ! beautiful1 he ?us conclud$-- 8,9 ! wor%ip ( ! beautiful1 & 9 t alone1 we are inf]ior to ! ,greeks4 ,let u !re=e be glad to borr[ f !m2 n slavi%ly1 b ) a wise adaptation--n exclusively1 b ) a cunn+ selection2 9 art1 z 9 religion1 let u le>n to prove all ?+s1 & hold fa/ t :i* is good--n m]ely "o ?+ :i* is good1 b all good ?+s--,classicalism1 ,m$ivalism1 ,mod]nism--let u h & hold !m all 9 "o wide & lu/y embrace4 ,:y %\ld ! _w ( art be m n>r[1 m monoton\s1 ?an ! _w ( nature8 ,did ,god make all ! fl[]s ( "o patt]n1 to please ! devotees ( ! rose or ! lily2 & did ,he make all ! hills1 ) ! gre5 folds ( _! que5ly mantles1 all at "o slope1 to suit ! angleomet] ( ! mo/ ma!matical ( decorators8 ,i tr[ n4 ,let u g & d likewise40 ,i "h take = grant$1 t :at ! lectur] meant by 8! wor%ip ( ! beautiful10 is ! production & appreciation ( works ( art 9 :i* beauty %\ld be a prim>y elem5t2 & judg+ f ! rema9s :i* we possess ( su* works z 7 produc$ by ! anci5t ,grecians1 our inf]iority to !m 9 ^! respects _c c]ta9ly be d5i$4 ,b ,i mu/ reit]ate :at ,i h (t5 be=e ass]t$1 t x is n by borr[+ f !m1 h[ev] cunn+ our selection1 or h[ev] wise our adaptations1 t ?is inf]iority is to be remov$1 b by a re-discov]y ( ! sci5ce :i* ^! anci5t arti/s mu/ h employ$ 9 ! production ( t symmetrical beauty & *a/e elegance :i* p]vad$ all _! works = a p]iod ( ne>ly ?ree hundr$ ye>s4 ,& ,i hold1 t z 9 religion1 s 9 art1 !re is only "o tru?1 a gra9 ( :i* is wor? any am\nt ( philological eloqu5ce4 ,i also take = grant$1 t :at is meant by ,classicalism 9 ! above quotation1 is ! anci5t ,grecian /yle ( art2 by ,m$ivalism1 ! semi-b>b>ic /yle ( ! middle ages2 & by ,mod]nism1 t *aotic jumble ( all previ\s /yles & fa%ions ( art1 :i* is ! peculi> *>act]i/ic ( our pres5t s*ool1 & :i* is1 d\btless1 ! result ( a sy/em ( education bas$ ^u plagi>ism & m]e imitation4 ,!re=e a recomm5dation to embrace ) equal f]v\r 8z good ?+s10 ^! v opposite articisms mu/ be a doctr9e z mis*iev\s 9 art z x w\ld be 9 religion to recomm5d z equally good ?+s ! v>i\s isms into :i* x has also be5 split 9 mod]n times4 ,n[1 8! _w ( nature0 & 8! _w ( art0 h n t equality ( scope :i* ?is lectur] on beauty ascribes to !m1 b diff] v decid$ly 9 t p>ticul>4 ,nei!r w x be difficult to %ew :y 8! _w ( art %\ld be m n>r[ ?an ! _w ( nature0--t x %\ld be !reby r5d]$ m monoton\s does n foll[4 ,x is well kn[n1 t ! 8_w ( nature0 consi/s ( productions1 includ+ objects ( e degree ( beauty f ! v l[e/ to ! highe/1 & calculat$ to suit n only ! ta/es aris+ f v>i\s degrees ( intellect1 b ^? aris+ f ! natural in/9cts ( ! l[] animals4 ,on ! o!r h&1 8! _w ( art10 be+ devot$ to ! gratification & improvem5t ( intellig5t m9ds only1 is !re=e n>r[$ 9 its scope by ! exclusion f its productions ( ! l[] degrees ( beauty--ev5 m$iocrity is inadmissible2 & we "k t ! sci5ce ( ! anci5t ,greek arti/s enabl$ !m to excel ! highe/ individual productions ( nature 9 ! p]fection ( symmetrical beauty4 ,consequ5tly1 all objects 9 nature are n equally well adapt$ = arti/ic /udy1 & x !re=e requires1 on ! "p ( ! arti/1 besides true g5ius1 mu* exp]i5ce & c>e to enable him to *oose prop] subjects f nature2 & x is 9 ! *oice ( su* subjects1 & n 9 plagi>ism f ! anci5ts1 t he %\ld select ) k & adapt ) wisdom4 ,h5ce1 all su* latitud9>ian doctr9es z ^? ,i h quot$ mu/ act z a *eck ^u ! progress ( k 9 ! sci5tific tru? ( art4 ,i h obs]v$ 9 "s ( my works1 t 9 ?is c\ntry a c\rse _h be5 foll[$ 9 our se>* = ! true sci5ce ( beauty n diff]+ f t by :i* ! al*ymi/s ( ! middle ages conduct$ _! inve/igations2 = our ideas ( visible beauty are /ill undef9$1 & our attempts to produce x 9 ! v>i\s bran*es ( art are left dep5dant1 9 a great measure1 ^u *ance4 ,our s*ools are conduct$ )\t ref]5ce to any fir/ pr9ciples or def9ite laws ( beauty1 & f ! draw+ ( a simple ar*itectural m\ld+ to ! intricate comb9ations ( =m 9 ! human figure1 ! pupils tru/ to _! h&s & eyes alone1 s]vilely & me*anically copy+ ! works ( ! anci5ts1 in/ead ( be+ in/ruct$ 9 ! un]r+ pr9ciples ( sci5ce1 ^u :i* ! beauty ( ^? works normally dep5ds4 ,! in/ruction !y receive is imp>t$ )\t ref]5ce to ! judgm5t or und]/&+1 & !y are !reby l$ to imitate effects )\t inve/igat+ causes4 ,d\btless1 m5 ( great g5ius sometimes arrive at excell5ce 9 ! arts ( design )\t a k ( ! pr9ciples ^u :i* beauty ( =m is bas$2 b x %\ld be kept 9 m9d1 t true g5ius includes an intuitive p]ception ( ^? pr9ciples along ) its creative p[]4 ,x is1 !re=e1 to ! g5]ality ( mank9d t in/ruction 9 ! def9ite laws ( beauty w be ( mo/ s]vice1 n only 9 improv+ ! practice ( ^? :o foll[ ! arts pr(essionally1 b 9 enabl+ all ( u to di/+ui% ! true f ! false1 & to ex]cise a s\nd & discrim9at+ ta/e 9 =m+ our judgm5t ^u arti/ic productions4 /hetic culture %\ld consequ5tly sup]s$e s]vile copy+1 z ! basis ( in/ruction 9 our s*ools ( art4 ,_m tea*]s ( draw+1 h[ev]1 /ill ass]t1 t1 by copy+ ! great works ( ! anci5ts1 ! m9d ( ! pupil w become imbu$ ) ideas simil> to !irs--t he w imbibe _! feel+ = ! beautiful1 & !reby become inspir$ ) _! g5ius1 & ?9k z !y ?\ght4 ,to /udy c>efully & to inve/igate ! pr9ciples :i* con/itute ! excell5ce ( ! works ( ! anci5ts1 is no d\bt ( mu* b5efit to ! /ud5t2 b x w\ld be z unreasonable to suppose t he %\ld become inspir$ ) arti/ic g5ius by m]ely copy+ !m1 z x w\ld be to imag9e1 t1 9 lit]ature1 poetic inspiration c\ld be creat$ by mak+ boys transcribe or repeat ! works ( ! anci5t poets4 ,sir ,jo%ua ,reynolds consid]$ copy+ z a delusive k9d ( indu/ry1 & has obs]v$1 t 8,nature h]self is n to be too closely copi$10 ass]t+ t 8!re are excell5ces 9 ! art ( pa9t+ beyond :at is commonly call$ ! imitation ( nature10 & t 8a m]e copi] ( nature c nev] produce any ?+ great40 ,proclus1 an em95t philosoph] & ma!matician ( ! lat] ,platoni/ s*ool 7,a4,d4 #dhe71 says1 t 8he :o takes = 8 model su* =ms z nature produces1 & conf9es himself to an exact imitation ( ^!1 w nev] atta9 to :at is p]fectly beautiful4 ,= ! works ( nature are full ( disproportion1 & fall v %ort ( ! true /&>d ( beauty40 ,x is rem>k$ by ,mr4 ,j4 ,c4 ,daniel1 9 ! introduction to 8 translation ( ,m4 ,victor ,c\s9's 8,philosophy ( ! ,beautiful10 t 8! ,engli% writ]s h advocat$ no !ory :i* all[s ! beautiful to be univ]sal & absolute2 nor h !y pr(ess$ly f\nd$ _! views on orig9al & ultimate pr9ciples4 ,?us ! doctr9e ( ! ,engli% s*ool has = ! mo/ "p be51 t beauty is mutable & special1 & ! inf]5ce t has be5 drawn f ?is tea*+ is1 t all ta/es are equally j1 provid$ t ea* man speaks ( :at he feels40 ,he !n obs]ves1 t ! ,g]man1 & "s ( ! ,fr5* writ]s1 h ?\ght f> diff]5tly2 = ) !m ! beautiful is 8simple1 immutable1 absolute1 ?\gh its =ms are manifold40 ,s f> back z ! ye> #agbe1 ! same tru?s advanc$ by ! mod]n ,g]man & ,fr5* writ]s1 & s eloqu5tly illu/rat$ by ,m4 ,c\s91 7 giv5 to ! _w by ,hut*ison 9 8 8,inquiry into ! ,orig9al ( our ,ideas ( ,beauty & ,virtue40 ,?is au?or says--8,we1 by absolute beauty1 und]/& only t beauty :i* we p]ceive 9 objects1 )\t comp>ison to any ?+ ext]nal1 ( :i* ! object is suppos$ an imitation or picture1 su* z ! beauty p]ceiv$ f ! works ( nature1 artificial =ms1 figures1 !orems4 ,comp>ative or relative beauty is t :i* we p]ceive 9 objects commonly consid]$ z imitations or resemblances ( some?+ else40 ,dr4 ,reid also1 9 8 8,intellectual ,p[]s ( ,man10 says--8,t ta/e1 :i* we may call rational1 is t "p ( our con/itution by :i* we are made to receive pleasure f ! contemplation ( :at we conceive to be excell5t 9 its k9d1 ! pleasure be+ annex$ to ?is judgm5t1 & regulat$ by x4 ,?is ta/e may be true or false1 accord+ z x is f\nd$ on a true or false judgm5t4 ,& if x may be true or false1 x mu/ h fir/ pr9ciples40 ,m4 ,victor ,c\s9's op9ion ^u ?is subject is1 h[ev]1 /ill m conclusive4 ,he obs]ves--8,if ! idea ( ! beautiful is n absolute1 l ! idea ( ! true--if x is no?+ m ?an ! expression ( individual s5tim5t1 ! reb\nd ( a *ang+ s5sation1 or ! result ( ea* p]son's fancy--!n ! discussions on ! f9e arts wav] )\t support1 & w nev] end4 ,= a !ory ( ! f9e arts to be possible1 !re mu/ be some?+ absolute 9 beauty1 j z !re mu/ be some?+ absolute 9 ! idea ( goodness1 to r5d] morals a possible sci5ce40 ,! basis ( ! sci5ce ( beauty mu/ ?us be f\nd$ ^u fix$ pr9ciples1 & :5 ^! pr9ciples are evolv$ ) ! same c>e :i* has *>act]is$ ! lab\rs ( inve/igators 9 natural sci5ce1 & are appli$ 9 ! f9e arts z ! natural sci5ces h be5 9 ! useful arts1 a solid f\ndation w be laid1 n only = correct practice1 b also = a j appreciation ( productions 9 e bran* ( ! arts ( design4 ,we "k t ! m9d receives pleasure ?r\gh ! s5se ( he>+1 n only f ! music ( nature1 b f ! euphony ( prosaic composition1 ! rhy?m ( poetic measure1 ! arti/ic composition ( successive h>mony 9 simple melody1 & ! comb9$ h>mony ( c\nt]po9t 9 ! m complex works ( t art4 ,we "k1 also1 t ! m9d is simil>ly gratifi$ ?r\gh ! s5se ( see+1 n only by ! visible beauties ( nature1 b by ^? ( art1 :e!r 9 symmetrical or picturesque compositions ( =ms1 or 9 h>moni\s arrangem5ts ( gay or sombre col\r+4 ,n[1 9 respect to ! fir/ ( ^! modes ( s5sation1 we "k1 t f ! "t ( ,py?agoras1 ! fact has be5 e/abli%$1 t 9 :atev] mann] nature or art may address ! e>1 ! degree ( ob$i5ce paid to ! fundam5tal law ( h>mony w det]m9e ! pres5ce & degree ( t beauty ) :i* a p]fect organ c impress a well-con/itut$ m9d2 & x is my object 9 ?is1 z x has be5 9 =m] attempts1 to prove x consi/5t ) sci5tific tru?1 t t beauty :i* is address$ to ! m9d by objects ( nature & art1 ?r\gh ! eye1 is simil>ly gov]n$4 ,9 %ort1 to %ew t1 z 9 compositions ( s\nds1 !re c be no true beauty 9 ! abs5ce ( a /rict ob$i5ce to ?is great law ( nature1 nei!r c !re exi/1 9 compositions ( =ms or col\rs1 t pr9ciple ( unity 9 v>iety :i* con/itutes beauty1 unless su* compositions are gov]n$ by ! same law4 ,al?\gh 9 ! songs ( birds1 ! gurgl+ ( brooks1 ! sigh+ ( ! g5tle summ] w9ds1 & all ! o!r beautiful music ( nature1 no analysis might be able to detect ! op]ation ( any precise sy/em ( h>mony1 yet ! pleasure ?us af=d$ to ! human m9d we "k to arise f its respond+ to e developm5t ( an ob$i5ce to ?is law4 ,:51 9 l mann]1 we f9d ev5 9 ^? compositions ( =ms & col\rs :i* con/itute ! wilde/ & mo/ rugg$ ( ,nature's sc5]y1 a species ( picturesque gr&eur & beauty to :i* ! m9d z readily responds z to h] m mild & pleas+ aspects1 or to h] sweete/ music1 we may re/ assur$ t ?is beauty is simply ano!r developm5t (1 & response to1 ! same h>monic law1 al?\gh ! precise nature ( its op]ation may be too subtle to be easily detect$4 ,! rsum ( ! v>i\s works ,i h already publi%$ ^u ! subject1 along ) ! additional illu/rations ,i am ab\t to lay be=e my read]s1 w1 ,i tru/1 po9t out a sy/em ( h>mony1 :i*1 9 =mative art1 z well z 9 t ( col\r+1 w rise sup]ior to ! idiosyncracies ( diff]5t arti/s1 & br+ back to "o common type ! s5sations ( ! eye & ! e>1 !reby improv+ t k ( ! laws ( ! univ]se :i* x is z mu* ! bus9ess ( sci5ce to comb9e ) ! ornam5tal z ) ! useful arts4 ,9 attempt+ ?is1 h[ev]1 ,i beg x may be und]/ood1 t ,i d n believe any sy/em1 bas$ ev5 ^u ! laws ( nature1 capable ( =m+ a royal road to ! p]fection ( art1 or ( 8mapp+ ! mighty maze ( a creative m9d40 ,at ! same "t1 h[ev]1 ,i mu/ cont9ue to reit]ate ! fact1 t ! diffusion ( a g5]al k ( ! sci5ce ( visible beauty w af=d lat5t arti/ic g5ius j su* a vantage gr\nd z t :i* ! g5]al k ( philology diffus$ ?r\gh\t ?is c\ntry af=ds its lat5t lit]>y g5ius4 ,al?\gh m]e le>n+ & true g5ius diff] z mu* 9 ! practice ( art z !y d 9 ! practice ( lit]ature1 yet a precise & sy/ematic education 9 ! true sci5ce ( beauty mu/ c]ta9ly be z useful 9 promot+ ! practice & appreciation ( ! "o1 z a precise & sy/ematic education 9 ! sci5ce ( philology is 9 promot+ ! practice & appreciation ( ! o!r4 ,z all beauty is ! result ( h>mony1 x w be requisite "h to rem>k1 t h>mony is n a simple quality1 b1 z ,ari/otle def9es x1 8! union ( contr>y pr9ciples hav+ a ratio to ea* o!r40 ,h>mony ?us op]ates 9 ! production ( all t is beautiful 9 nature1 :e!r 9 ! comb9ations1 9 ! motions1 or 9 ! aff9ities ( ! elem5ts ( matt]4 ,! contr>y pr9ciples to :i* ,ari/otle alludes1 are ^? ( uni=mity & v>iety2 =1 accord+ to ! pr$om9ance ( ! "o or ! o!r ( ^! pr9ciples1 e k9d ( beauty is *>act]is$4 ,h5ce ! diff]5ce betwe5 symmetrical & picturesque beauty3--! fir/ alli$ to ! pr9ciple ( uni=mity1 9 be+ bas$ ^u precise laws t may be taught s z to enable m5 ( ord9>y capacity to produce x 9 _! works--! second alli$ to ! pr9ciple ( v>iety (t5 to s great a degree t !y yield an ob$i5ce to ! precise pr9ciples ( h>mony s subtilely1 t !y _c be detect$ 9 its con/itution1 b are only felt 9 ! response by :i* true g5ius ackn[l$ges _! pres5ce4 ,! g5]ality ( mank9d may be capable ( p]ceiv+ ?is latt] k9d ( beauty1 & ( feel+ its effects ^u ! m9d1 b m5 ( g5ius1 only1 c imp>t x to works ( art1 :e!r address$ to ! eye or ! e>4 ,?r\gh\t ! s\nds1 =ms1 & col\rs ( nature1 ^! two k9ds ( beauty are f\nd n only 9 di/9ct developm5ts1 b 9 e degree ( amalgamation4 ,we f9d 9 ! songs ( "s birds1 su* z ^? ( ! *aff9*1 ?ru%1 c41 a rhy?mical division1 resembl+ 9 "s measure ! symmetrically precise arrangem5ts ( p>ts :i* *>act]ises all arti/ic musical composition2 :ile 9 ! songs ( o!r birds1 & 9 ! o!r num]\s melodies ) :i* nature *>ms & soo!s ! m9d1 !re is no di/9ct regul>ity 9 ! division ( _! p>ts4 ,9 ! =ms ( nature1 too1 we f9d among/ ! innum]able fl[]s ) :i* ! surface ( ! e>? is s pr(usely decorat$1 an almo/ endless v>iety ( sy/ematic arrangem5ts ( beautiful figures1 (t5 s p]fectly symmetrical 9 _! comb9ation1 t ! mo/ c>eful application ( ! angleomet] c\ld sc>cely detect ! slighte/ deviation f geometrical precision2 :ile1 among/ ! masses ( foliage by :i* ! =ms ( _m trees are divid$ & subdivid$ into p>ts1 z also among/ ! hills & valleys1 ! m\nta9s & rav9es1 :i* divide ! e>?'s surface1 we f9d 9 e possible v>iety ( aspect ! beauty produc$ by t irregul> species ( symmetry :i* *>act]ises ! picturesque4 ,9 l mann]1 we f9d 9 wild z well z cultivat$ fl[]s ! mo/ symmetrical di/ributions ( col\rs accompany+ an equally precise species ( h>mony 9 _! v>i\s k9ds ( contra/s1 (t5 z ma!matically regul> z ! geometric diagrams by :i* writ]s ^u col\r sometimes illu/rate _! works2 :ile 9 ! g5]al col\r+ ( ! picturesque beauties ( nature1 !re is an endless v>iety 9 its di/ributions1 its bl5d+s1 & its modifications4 ,9 ! =ms & col\r+ ( animals1 too1 ! same endless v>iety ( regul> & irregul> symmetry is to be f\nd4 ,b ! highe/ degree ( beauty 9 nature is ! result ( an equal balance ( uni=mity ) v>iety4 ,( ?is ! human figure is an example2 because1 :5 x is ( ^? proportions univ]sally ackn[l$g$ to be ! mo/ p]fect1 its uni=mity be>s to its v>iety an app>5tly equal ratio4 ,! h>mony ( comb9ation 9 ! normal proportions ( its p>ts1 & ! beautifully simple h>mony ( succession 9 ! normal melody ( its s(tly undulat+ outl9e1 are ! p]fection ( symmetrical beauty1 :ile ! innum]able *anges ^u ! cont\r :i* arise f ! actions & attitudes occasion$ by ! v>i\s emotions ( ! m9d1 are calculat$ to produce e species ( picturesque beauty1 f ! s(te/ & mo/ pleas+ to ! gr&e/ & mo/ sublime4 ,among/ ! purely picturesque objects ( inanimate nature1 ,i may1 z 9 a =m] "w1 in/ance an anci5t oak tree1 = its beauty is enhanc$ by want ( app>5t symmetry4 ,?us1 ! m fanta/ically crook$ its bran*es1 & ! great] ! dissimil>ity & v>iety x exhibits 9 its masses ( foliage1 ! m beautiful x appe>s to ! arti/ & ! amateur2 &1 z 9 ! human figure1 any attempt to produce v>iety 9 ! proportions ( its lat]al halves w\ld be de/ructive ( its symmetrical beauty1 s 9 ! oak tree any attempt to produce palpable simil>ity betwe5 any ( its opposite sides w\ld equally det]iorate its picturesque beauty4 ,b picturesque beauty is n ! result ( ! total abs5ce ( symmetry2 =1 z none ( ! irregul>ly con/ruct$ music ( nature c\ld be pleas+ to ! e> unless !re exi/$ 9 ! arrangem5t ( its notes an ob$i5ce1 h[ev] subtle1 to ! great h>monic law ( ,nature1 s nei!r c\ld any object be picturesquely beautiful1 unless ! arrangem5t ( its p>ts yields1 al?\gh x may be obscurely1 an ob$i5ce to ! same law4 ,h[ev] symmetrically beautiful any ar*itectural /ructure may be1 :5 9 a complete & p]fect /ate1 x mu/1 z x proce$s t[>ds ru91 bl5d ! picturesque ) ! symmetrical2 b ! type ( its beauty w cont9ue to be ! latt]1 s long z a suffici5t portion ( x rema9s to convey an idea ( its orig9al p]fection4 ,x is ! same ) ! human =m & c\nt5ance2 = age does n de/roy _! orig9al beauty1 b 9 bo? only less5s t :i* is symmetrical1 :ile x increases t :i* is picturesque4 ,9 %ort1 z a v>iety ( simultane\sly produc$ s\nds1 :i* d n relate to ea* o!r agreeably to ?is law1 c only convey to ! m9d a feel+ ( m]e noise2 s a v>iety ( =ms or col\rs simultane\sly expos$ to ! eye "u simil> circum/ances1 c only convey to ! m9d a feel+ ( *aotic confusion1 or :at may be t]m$ visible discord4 ,z1 !re=e1 ! two pr9ciples ( uni=mity & v>iety1 or simil>ity & dissimil>ity1 are 9 op]ation 9 e h>moni\s comb9ation ( ! elem5ts ( s\nd1 ( =m1 & ( col\r1 we mu/ fir/ h rec\rse to numb]s 9 ! ab/ract be=e we c =m a prop] basis = a univ]sal sci5ce ( beauty4 ,,! ,,sci5ce ,,( ,,beauty ,,evolv$ ,,f ,,! ,,h>monic ,,law ,,( ,,nature1 ,,agreeably ,,to ,,! ,,py?agorean ,,sy/em ,,( ,,num]ical ,,ratio4 ,! sci5tific pr9ciples ( beauty appe> to h be5 well kn[n to ! anci5t ,greeks2 & x mu/ h be5 by ! practical application ( t k to ! arts ( ,design1 t t p cont9u$ = a p]iod ( upw>ds ( ?ree hundr$ ye>s to execute1 9 e dep>tm5t ( ^! arts1 works surpass+ 9 *a/e beauty any t _h ev] be=e appe>$1 & :i* h n be5 equall$ dur+ ! two ?\s& ye>s :i* h s9ce elaps$4 /hetic sci5ce1 z ! sci5ce ( beauty is n[ t]m$1 is bas$ ^u t great h>monic law ( nature :i* p]vades & gov]ns ! univ]se4 ,x is 9 its nature nei!r absolutely physical nor absolutely metaphysical1 b ( an int]m$iate nature1 assimilat+ 9 v>i\s degrees1 m or less1 to "o or o!r ( ^? opposite k9ds ( sci5ce4 ,x specially embodies ! inh]5t pr9ciples :i* gov]n impressions made ^u ! m9d ?r\gh ! s5ses ( he>+ & see+4 ,?us1 ! /hetic pleasure d]iv$ f li/5+ to ! beautiful 9 musical composition1 & f contemplat+ ! beautiful 9 works ( =mative art1 is 9 bo? cases simply a response 9 ! human m9d to arti/ic developm5ts ( ! great h>monic law ^u :i* ! sci5ce is bas$4 ,al?\gh ! eye & ! e> are two diff]5t s5ses1 &1 consequ5tly1 v>i\s 9 _! modes ( receiv+ impressions2 yet ! s5sorium is b "o1 & ! m9d by :i* ^! impressions are p]ceiv$ & appreciat$ is also *>act]is$ by unity4 ,!re appe>s1 likewise1 a /rik+ analogy betwe5 ! natural con/itution ( ! two k9ds ( beauty1 :i* is ?is1 t ! m physically /hetic elem5ts ( ! highe/ works ( musical composition are melody1 h>mony1 & tone1 :il/ ^? ( ! highe/ works ( =mative art are cont\r1 proportion1 & col\r4 ,! melody or !me ( a musical composition & its h>mony are respectively analog\s1--#a/1 ,to ! outl9e ( an arti/ic "w ( =mative art2 & #b;d1 ,to ! proportion :i* exi/s among/ its p>ts4 ,to ! c>eful inve/igator ^! analogies become id5tities 9 _! effect ^u ! m9d1 l ^? ( ! m metaphysically /hetic emotions produc$ by expression 9 ei!r ( ^! arts4 ,agreeably to ! fir/ analogy1 ! outl9e & cont\r ( an object1 suppose t ( a build+ 9 %ade :5 view$ aga9/ a light backgr\nd1 has a simil> effect ^u ! m9d ) t ( ! simple melody ( a musical composition :5 address$ to ! e> unaccompani$ by ! comb9$ h>mony ( c\nt]po9t4 ,agreeably to ! second analogy1 ! v>i\s p>ts into :i* ! surface ( ! suppos$ elevation is divid$ be+ simultane\sly pres5t$ to ! eye1 w1 if arrang$ agreeably to ! same great law1 affect ! m9d l t ( an equally h>moni\s arrangem5t ( musical notes accompany+ ! suppos$ melody4 ,!re is1 h[ev]1 a diff]5ce betwe5 ! con/ruction ( ^! two organs ( s5se1 viz41 t ! e> mu/ 9 a great degree receive its impressions involunt>ily2 :ile ! eye1 on ! o!r h&1 is provid$ by nature ) ! p[] ( ei!r dwell+ ^u1 or in/antly %utt+ out or )draw+ itself f an object4 ,! impression ( a s\nd1 :e!r simple or complex1 :5 made ^u ! e>1 is in/antane\sly convey$ to ! m9d2 b :5 ! s\nd ceases1 ! p[] ( obs]vation also ceases4 ,b ! eye c dwell ^u objects pres5t$ to x s long z !y are all[$ to rema9 pictur$ on ! ret9a2 & ! m9d has !reby ! p[] ( leisurely exam9+ & comp>+ !m4 ,h5ce ! e> guides m z a m]e s5se1 at once & )\t reflection2 :il/ ! eye1 receiv+ its impressions gradually1 & "p by "p1 is m directly "u ! influ5ce ( m5tal analysis1 consequ5tly produc+ a m metaphysically /hetic emotion4 ,h5ce1 also1 ! acquir$ p[] ( ! m9d 9 appreciat+ impressions made ^u x ?r\gh ! organ ( sight "u circum/ances1 su* z p]spective1 c41 :i* to ^? :o take a ha/y view ( ! subject appe> impossible4 ,deal+ z ?is sci5ce !re=e does1 alike ) ! s\rces & ! result+ pr9ciples ( beauty1 x is sc>cely less dep5d5t on ! accuracy ( ! s5ses ?an on ! p[] ( ! und]/&+1 inasmu* z ! effect :i* x produces is z ess5tial a prop]ty ( objects1 z are its laws inh]5t 9 ! human m9d4 ,x necess>ily compreh5ds a k ( ^? fir/ pr9ciples 9 art1 by :i* c]ta9 comb9ations ( s\nds1 =ms1 & col\rs produce an effect ^u ! m9d1 connect$1 9 ! fir/ in/ance1 ) s5sation1 & 9 ! second ) ! reason+ faculty4 ,x is1 !re=e1 n only ! basis ( all true practice 9 art1 b ( all s\nd judgm5t on que/ions ( arti/ic criticism1 & necess>ily includes ^? laws :]eon a correct ta/e mu/ be bas$4 ,d\btless _m eloqu5t & +5i\s treatises h be5 writt5 ^u beauty & ta/e2 b 9 ne>ly e case1 ) no o!r effect ?an t ( involv+ ! subject 9 /ill great] unc]ta9ty4 ,ev5 :5 re/rict$ to ! arts ( design1 !y h fail$ to exhibit any def9ite pr9ciples :]eby ! true may be di/+ui%$ f ! false1 & "s natural & recognis$ laws ( beauty r$uc$ to demon/ration4 ,?is may be attribut$1 9 a great degree1 to ! neglect ( a j discrim9ation betwe5 :at is m]ely agreeable1 or capable ( excit+ pleasurable s5sations1 & :at is ess5tially beautiful2 b /ill m to ! conf\nd+ ( ! op]ations ( ! und]/&+ ) ^? ( ! imag9ation4 ,v slight reflection1 h[ev]1 w suffice to %ew h[ ess5tially di/9ct ^! two faculties ( ! m9d are2 ! =m] be+ regulat$1 9 matt]s ( ta/e1 by irrefragable pr9ciples exi/+ 9 nature1 & respond$ to by an inh]5t pr9ciple exi/+ 9 ! human m9d2 :ile ! latt] op]ates 9 ! production ( ideal comb9ations ( its own creation1 altoge!r indep5d5t ( any imm$iate impression made ^u ! s5ses4 ,! beauty ( a fl[]1 = example1 or ( a dew-drop1 dep5ds on c]ta9 comb9ations ( =m & col\r1 manife/ly ref]able to def9ite & sy/ematic1 ?\gh x may be unrecognis$1 laws2 b :5 ,ob]on1 9 8,midsumm] ,night's ,dream10 is made to exclaim-- 8,& t same dew1 :i* sometimes on ! buds ,0 wont to swell1 l r\nd & ori5t pe>ls1 ,/ood n[ )9 ! pretty fl[]et's eyes1 ,l te>s t did _! own disgrace bewail10-- ! poet introduces a new elem5t ( beauty equally legitimate1 yet altoge!r di/9ct f1 al?\gh accompany+ t :i* con/itutes ! m precise sci5ce ( /hetics z "h def9$4 ,! composition ( ! rhy?m is an op]ation ( ! und]/&+1 b ! beauty ( ! poetic fancy is an op]ation ( ! imag9ation4 ,our physical & m5tal p[]s1 /hetically consid]$1 may !re=e be class$ "u ?ree heads1 9 _! relation to ! f9e arts1 viz41 ! receptive1 ! p]ceptive1 & ! conceptive4 ,! s5ses ( he>+ & see+ are respectively1 9 ! degree ( _! physical p[]1 receptive ( impressions made ^u !m1 & ( ^! impressions ! s5sorium1 9 ! degree ( its m5tal p[]1 is p]ceptive4 ,?is p]ception enables ! m9d to =m a judgm5t :]eby x appreciates ! nature & quality ( ! impression orig9ally made on ! receptive organ4 ,! mode ( ?is op]ation is intuitive1 & ! quickness & accuracy ) :i* ! nature & quality ( ! impression is appreh5d$1 w be 9 ! degree ( ! intellectual vig\r ( ! m9d by :i* x is p]ceiv$4 ,?us we are1 by ! cultivation ( ^! intuitive faculties1 enabl$ to decide ) accuracy z to h>mony or discord1 proportion or de=mity1 & assign s\nd reasons = our judgm5t 9 matt]s ( ta/e4 ,b m5tal conception is ! intuitive p[] ( con/ruct+ orig9al ideas f ^! mat]ials2 = aft] ! receptive p[] has act$1 ! p]ception op]ates 9 e/abli%+ facts1 & !n ! judgm5t is =m$ ^u ^! op]ations by ! reason+ p[]s1 :i* lead1 9 _! turn1 to ! creations ( ! imag9ation4 ,! p[] ( =m+ ^! creations is ! true *>act]i/ic ( g5ius1 & det]m9es ! po9t at :i* art is plac$ beyond all det]m9able canons1--at :i*1 inde$1 /hetics give place to metaphysics4 ,9 ! sci5ce ( beauty1 !re=e1 ! human m9d is ! subject1 & ! effect ( ext]nal nature1 z well z ( works ( art1 ! object4 ,! ext]nal _w1 & ! individual m9d1 ) all t lies )9 ! scope ( its p[]s1 may be consid]$ z two sep>ate exi/5ces1 hav+ a di/9ct relation to ea* o!r4 ,! subject is affect$ by ! object1 ?r\gh t inh]5t faculty by :i* x is enabl$ to respond to e developm5t ( ! all-gov]n+ h>monic law ( nature2 & ! m$ia ( communication are ! s5sorium & its inlets--! organs ( s5se4 ,?is h>monic law ( nature 0 ei!r orig9ally discov]$ by t illu/ri\s philosoph] ,py?agoras1 upw>ds ( five hundr$ ye>s be=e ,*ri/1 or a k ( x obta9$ by him ab\t t p]iod1 f ! ,egyptian or ,*aldean prie/s4 ,= aft] hav+ be5 initiat$ into all ! ,grecian & b>b>ian sacr$ my/]ies1 he w5t to ,egypt1 :]e he rema9$ upw>ds ( tw5ty ye>s1 /udy+ 9 ! colleges ( its prie/s2 & f ,egypt he w5t into ! ,ea/1 & visit$ ! ,p]sian & ,*aldean magi4#c ,by ! g5]ality ( ! biograph]s ( ,py?agoras1 x is said to be difficult to give a cle> idea ( 8 philosophy1 z x is almo/ c]ta9 he nev] committ$ x to writ+1 & t x has be5 disfigur$ by ! fanta/ic dreams & *im]as ( lat] ,py?agoreans4 ,diog5es ,lartius1 h[ev]1 ^: 8,lives ( ! ,philosoph]s0 0 suppos$ to be writt5 ab\t ! end ( ! second c5tury ( our era1 says 8!re are ?ree volumes extant writt5 by ,py?agoras4 ,"o on education1 "o on politics1 & "o on natural philosophy40 ,& adds1 t !re 7 sev]al o!r books extant1 attribut$ to ,py?agoras1 b :i* 7 n writt5 by him4 ,also1 9 8 8,life ( ,philolaus10 t ,plato wrote to ,dion to take c>e & pur*ase ! books ( ,py?agoras4#d ,b :e!r ?is great philosoph] committ$ 8 discov]ies to writ+ or n1 8 doctr9es reg>d+ ! philosophy ( beauty are well-kn[n to be1 t he consid]$ numb]s z ! ess5ce & ! pr9ciple ( all ?+s1 & attribut$ to !m a real & di/9ct exi/5ce2 s t1 9 8 view1 !y 7 ! elem5ts out ( :i* ! univ]se 0 con/ruct$1 & to :i* x ow$ its beauty4 ,diog5es ,lartius gives ! foll[+ acc\nt ( ?is law3--8,t ! monad 0 ! beg9n+ ( ev]y?+4 ,f ! monad proce$s an indef9ite duad1 :i* is subord9ate to ! monad z to its cause4 ,t f ! monad & indef9ite duad proce$s numb]s4 ,t ! "p ( sci5ce to :i* ,py?agoras appli$ himself above all o!rs1 0 ari?metic2 & t he taught #8t f numb]s proce$ signs1 & f ^! latt]1 l9es1 ( :i* plane figures consi/2 t f plane figures are d]iv$ solid bodies2 t ( all plane figures ! mo/ beautiful 0 ! circle1 & ( all solid bodies ! mo/ beautiful 0 ! sph]e4' ,he discov]$ ! num]ical relations ( s\nds on a s+le /r+2 & taught t ev]y?+ owes its exi/5ce & consi/5cy to h>mony4 ,9 s f> z ,i "k1 ! mo/ cond5s$ acc\nt ( all t is kn[n ( ! ,py?agorian sy/em ( numb]s is ! foll[+3--#8,! monad or unity is t quantity1 :i*1 be+ depriv$ ( all numb]1 rema9s fix$4 ,x is ! f\nta9 ( all numb]4 ,! duad is imp]fect & passive1 & ! cause ( increase & division4 ,! triad1 compos$ ( ! monad & duad1 p>takes ( ! nature ( bo?4 ,! tetrad1 tetractys1 or quat]nion numb] is mo/ p]fect4 ,! decad1 :i* is ! sum ( ! f\r =m]1 compreh5ds all ari?metical & musical proportions4'0#e ,^! %ort quotations1 ,i believe1 comprise all t is kn[n1 = c]ta91 ( ! mann] 9 :i* ,py?agoras sy/ematis$ ! law ( numb]s4 ,yet1 f ! tea*+s ( ?is great philosoph] & 8 disciples1 ! h>monic law ( nature1 9 :i* ! fundam5tal pr9ciples ( beauty are embodi$1 became s g5]ally und]/ood & univ]sally appli$ 9 practice ?r\gh\t all ,greece1 t ! fragm5ts ( _! works1 :i* h rea*$ u ?r\gh a p]iod ( two ?\s& ye>s1 are /ill held to be examples ( ! highe/ arti/ic excell5ce ev] atta9$ by mank9d4 ,9 ! pres5t /ate ( art1 !re=e1 a k ( ?is law1 & ( ! mann] 9 :i* x may aga9 be appli$ 9 ! production ( beauty 9 all works ( =m & col\r1 mu/ be ( s+ul> advantage2 & ! object ( ?is "w is to assi/ 9 ! atta9m5t ( su* a k4 ,x has be5 rem>k$1 ) equal compreh5siv5ess & tru?1 by a writ]#f 9 ! ,briti% & ,=eign ,m$ical ,review1 t 8!re is h>mony ( numb]s 9 all nature--9 ! =ce ( gravity--9 ! planet>y movem5ts--9 ! laws ( heat1 light1 electricity1 & *emical aff9ity--9 ! =ms ( animals & plants--9 ! p]ceptions ( ! m9d4 ,! direction1 inde$1 ( mod]n natural & physical sci5ce is t[>ds a g5]alization :i* %all express ! fundam5tal laws ( all by "o simple num]ical ratio4 ,& we ?9k mod]n sci5ce w soon %ew t ! my/icism ( ,py?agoras 0 my/ical only to ! unlett]$1 & t x 0 a sy/em ( philosophy f\nd$ on ! !n exi/+ ma!matics1 :i* latt] seem to h compris$ m ( ! philosophy ( numb]s ?an our pres5t40 ,_m ye>s ( c>eful inve/igation h conv9c$ me ( ! tru? ( ?is rem>k1 & ( ! great advantage d]ivable f an application ( ! ,py?agorean sy/em 9 ! arts ( design4 ,= s simple is its nature1 t any "o ( an ord9>y capacity ( m9d1 & hav+ a k ( ! mo/ simple rules ( ari?metic1 may1 9 a v %ort p]iod1 easily compreh5d its nature1 & be able to apply x 9 practice4 ,! elem5ts ( ! ,py?agorean sy/em ( h>monic numb]1 s f> z c be ga!r$ f ! quotations ,i h giv5 above1 seem to be simply ! indivisible monad 7#a72 ! duad 7#b71 aris+ f ! union ( "o monad ) ano!r2 ! triad 7#c71 aris+ f ! union ( ! monad ) ! duad2 & ! tetrad 7#d71 aris+ f ! union ( "o duad ) ano!r1 :i* tetrad is consid]$ a p]fect numb]4 ,f ! union ( ^! f\r elem5ts arises ! decad 7#aj71 ! numb]1 :i*1 agreeably to ! ,py?agorean sy/em1 compreh5ds all ari?metical & h>monic proportions4 ,if1 !re=e1 we take ^! elem5ts & unite !m progressively 9 ! foll[+ ord]1 we %all f9d ! s]ies ( h>monic numb]s 7#b71 7#c71 7#e71 & 7#g71 :i*1 ) _! multiples1 are ! complete num]ical elem5ts ( all h>mony1 ?us3-- #a #a #b #a #b #c #b #c #e #c #d #g ,9 ord] to r5d] an ext5d$ s]ies ( h>monic numb]s useful1 x mu/ be divid$ into scales2 & x is a rule 9 ! =mation ( ^! scales1 t ! fir/ mu/ beg9 ) ! monad 7#a7 & end ) ! duad 7#b71 ! second beg9 ) ! duad 7#b7 & end ) ! tetrad 7#d71 & t ! beg9n+ & end ( all o!r scales mu/ be cont9u$ 9 ! same ari?metical progression4 ,^! prim>y elem5ts w !n =m ! f\ndation ( a s]ies ( su* scales4 ,i4 7#a7 7#b7 ,,ii4 7#b7 7#c7 7#d7 ,,iii4 7#d7 7#e7 7#f7 7#g7 7#h7 ,,iv4 7#h7 7#i7 7#aj7 7 7 7#ab7 7 7 7#ad7 7#ae7 7#af7 ,! fir/ ( ^! scales has 9 7#a7 & 7#b7 a beg9n+ & an end2 b ! second has 9 7#b71 7#c71 & 7#d7 ! ess5tial requisites dem&$ by ,ari/otle 9 e composition1 viz41 8a beg9n+1 a middle1 & an end20 :ile ! ?ird has n only ^! ess5tial requisites1 b two int]m$iate p>ts 7#e7 & 7#g71 by :i* ! beg9n+1 ! middle1 & ! end are unit$4 ,9 ! f\r? scale1 h[ev]1 ! ari?metical progression is int]rupt$ by ! omission ( numb]s #aa & #ac1 :i*1 n be+ multiples ( ei!r 7#b71 7#c71 7#e71 or 7#g71 are inadmissible4 ,su* is ! nature ( ! h>monic law :i* gov]ns ! progressive scales ( numb]s by ! simple multiplication ( ! monad4 ,i %all n[ use ^! numb]s z divisors 9 ! =mation ( a s]ies ( f\r su* scales ( p>ts1 :i* has = its prim>y elem5t1 in/ead ( ! indivisible monad1 a quantity :i* may be indef9itely divid$1 b :i* _c be add$ to or multipli$4 ,l ! monad1 h[ev]1 ?is quantity is repres5t$ by 7#a74 ,! foll[+ is ?is s]ies ( f\r scales ( h>monic p>ts3-- ,i4 7#a7 77 ,,ii4 77 77 77 ,,iii4 77 77 77 77 77 ,,iv4 77 77 77 7 7 77 7 7 77 77 77 ,! scales ,i41 ,,ii41 & ,,iii4 may n[ be r5d]$ z complete z scale ,,iv41 simply by multiply+ upw>ds by #b f 771 771 771 771 & 771 ?us3-- ,i4 7#a7 77 77 77 77 77 77 ,,ii4 77 77 77 77 77 77 77 ,,iii4 77 77 77 77 77 77 77 ,,iv4 77 77 77 7 7 77 7 7 77 77 77 ,we n[ f9d betwe5 ! beg9n+ & ! end ( scale ,i4 ! quantities 771 771 771 771 & 774 ,! ?ree fir/ ( ^! quantities we f9d to be ! rema9d]s ( ! :ole indef9ite quantity conta9$ 9 7#a71 aft] subtract+ f x ! prim>y h>monic quantities 771 771 & 772 we1 h[ev]1 f9d also among/ ^! h>monic quantities t ( 771 :i* be+ subtract$ f 7#a7 leaves 771 a quantity ! mo/ suitable :]eby to fill up ! hiatus betwe5 77 & 77 9 scale ,i41 :i* arises f ! omission ( 77 9 scale ,,iv4 ,9 l mann] we f9d ! two la/ ( ^! quantities1 77 & 771 are respectively ! l>ge/ ( ! two p>ts into :i* #g & #ae are susceptible ( be+ divid$4 ,f9d+ ! numb] #e to be divisible into p>ts m unequal ?an 7#b7 to 7#c7 & less unequal ?an 7#d7 to 7#g71 77 naturally fills up ! hiatus betwe5 ^! quantities 9 scale ,i41 :i* hiatus arises f ! omission ( 77 9 scale ,,iv4 ,?us3-- ,i4 7#a7 77 77 77 77 77 77 77 77 ,,ii4 77 77 77 7 7 77 7 7 77 77 77 ,,iii4 77 77 77 7 7 77 7 7 77 77 77 ,,iv4 77 77 77 7 7 77 7 7 77 77 77 ,scale ,i4 be+ n[ complete1 we h only to divide ^! latt] quantities by 7#b7 d[nw>ds 9 ord] to complete ! o!r ?ree4 ,?us3-- ,i4 7#a7 77 77 77 77 77 77 77 77 ,,ii4 77 77 77 77 77 77 77 77 77 ,,iii4 77 77 77 77 77 77 77 77 77 ,,iv4 77 77 77 77 77 77 77 77 77 ,! h>mony exi/+ among/ ^! numb]s or quantities consi/s ( ! num]ical relations :i* ! p>ts be> to ! :ole & to ea* o!r2 & ! m simple ^! relations are1 ! m p]fect is ! h>mony4 ,! foll[+ are ! num]ical h>monic ratios :i* ! p>ts be> to ! :ole3-- ,i4 7#a3a7 7#h3i7 7#d3 #e7 7#c3 #d7 7#b3 #c7 7#c3 #e7 7#d3 #g7 7#h3ae7 7#a3 #b7 ,,ii4 7#a3b7 7#d3i7 7#b3 #e7 7#c3 #h7 7#a3 #c7 7#c3aj7 7#b3 #g7 7#d3ae7 7#a3 #d7 ,,iii4 7#a3d7 7#b3i7 7#a3 #e7 7#c3af7 7#a3 #f7 7#c3bj7 7#a3 #g7 7#b3ae7 7#a3 #h7 ,,iv4 7#a3h7 7#a3i7 7#a3aj7 7#c3cb7 7#a3ab7 7#c3dj7 7#a3ad7 7#a3ae7 7#a3af7 ,! foll[+ are ! pr9cipal num]ical relations :i* ! p>ts 9 ea* scale be> to "o ano!r3-- 77377 7#g3h7 77377 7#i3aj7 77377 7#e3f7 77377 7#f3g7 77377 7#ad3ae7 77377 7#ae3af7 ,al?\gh ^! relations are exemplifi$ by p>ts ( scale ,i41 ! same ratios exi/ betwe5 ! relative p>ts ( scales ,,ii41 ,,iii41 & ,,iv41 & w\ld exi/ betwe5 ! p>ts ( any o!r scales t might be add$ to t s]ies4 ,^! are ! simple elem5ts ( ! sci5ce ( t h>mony :i* p]vades ! univ]se1 & by :i* ! v>i\s k9ds ( beauty /hetically impress$ ^u ! s5ses ( he>+ & see+ are gov]n$4 ,,! ,,sci5ce ,,( ,,beauty ,,z ,,appli$ ,,to ,,s\nds4 ,x is well-kn[n t all s\nds arise f a peculi> action ( ! air1 & t ?is action may be excit$ by ! concussion result+ f ! sudd5 displacem5t ( a portion ( ! atmosph]e itself1 or by ! rapid motions ( bodies1 or ( conf9$ columns ( air2 9 all :i* cases1 :5 ! motions are irregul>1 & ! =ce great1 ! s\nd convey$ to ! s5sorium is call$ a noise4 ,b t musical s\nds are ! result ( equal & regul> vibratory motions1 ei!r ( an ela/ic body1 or ( a column ( air 9 a tube1 excit+ 9 ! surr\nd+ atmosph]e a regul> & equal pulsation4 ,! e> is ! m$ium ( communication betwe5 ^? v>ieties ( atmosph]ic action & ! seat ( consci\sness4 ,to describe fully ! beautiful arrangem5t ( ! v>i\s p>ts ( ?is organ1 & _! adaptation to ! purpose ( collect+ & convey+ ^! undulatory motions ( ! atmosph]e1 is z mu* beyond ! scope ( my pres5t attempt z x is beyond my anatomical k2 b ,i may simply rem>k1 t )9 ! e>1 & mo/ c>efully protect$ 9 ! con/ruction ( t organ1 !re is a small cavity conta9+ a pellucid fluid1 9 :i* ! m9ute extremities ( ! auditory n]ve float2 & t ?is fluid is ! la/ ( ! m$ia ?r\gh :i* ! action produc+ ! s5sation ( s\nd is convey$ to ! n]ve1 & !nce to ! s5sorium1 :]e its nature becomes p]ceptible to ! m9d4 ,! impulses :i* produce musical notes mu/ arrive at a c]ta9 frequ5cy be=e ! e> loses ! int]vals ( sil5ce betwe5 !m1 & is impress$ by only "o cont9u$ s\nd2 & z !y increase 9 frequ5cy ! s\nd becomes m acute ^u ! e>4 ,! pit* ( a musical note is1 !re=e1 det]m9$ by ! frequ5cy ( ^! impulses2 b1 on ! o!r h&1 its int5sity or l\dness w dep5d ^u ! viol5ce & ! quality ( its tone on ! mat]ial employ$ 9 produc+ !m4 ,all su* s\nds1 !re=e1 :atev] be _! l\dness or ! quality ( _! tone 9 :i* ! impulses occur ) ! same frequ5cy are 9 p]fect unison1 hav+ ! same pit*4 ,^u ?is ! :ole doctr9e ( h>monies is f\nd$1 & by ?is ! laws ( num]ical ratio are f\nd to op]ate 9 ! production ( h>mony1 & ! !ory ( music r5d]$ susceptible ( exact reason+4 ,! me*anical means by :i* su* s\nds c be produc$ are extremely v>i\s2 b1 z x is my purpose simply to %ew ! nature ( h>mony ( s\nd z relat$ to1 or z evolv+ num]ical h>monic ratio1 ,i %all conf9e myself to ! mo/ simple mode ( illu/ration--namely1 t ( ! mono*ord4 ,?is is an in/rum5t consi/+ ( a /r+ ( a giv5 l5g? /ret*$ betwe5 two bridges /&+ ^u a graduat$ scale4 ,suppose ?is /r+ to be /ret*$ until its t5sion is su* t1 :5 drawn a little to a side & sudd5ly let g1 x w\ld vibrate at ! rate ( #fd vibrations 9 a second ( "t1 produc+ to a c]ta9 di/ance 9 ! surr\nd+ atmosph]e a s]ies ( pulsations ( ! same frequ5cy4 ,^! pulsations w communicate ?r\gh ! e> a musical note :i* w\ld1 !re=e1 be ! fundam5tal note ( su* a /r+4 ,n[1 ! ph5om5on said to be discov]$ by ,py?agoras is well kn[n to ^? acqua9t$ ) ! sci5ce ( ac\/ics1 namely1 t imm$iately aft] ! /r+ is ?us put into vibratory motion1 x spontane\sly divides itself1 by a node1 into two equal p>ts1 ! vibrations ( ea* ( :i* occur ) a d\ble frequ5cy--namely1 #abh 9 a second ( "t1 &1 consequ5tly1 produce a note d\bly acute 9 pit*1 al?\gh mu* weak] z to int5sity or l\dness2 t x !n1 :ile p]=m+ ^! two s]ies ( vibrations1 divides itself1 by two nodes1 into ?ree p>ts1 ea* ( :i* vibrates ) a frequ5cy triple t ( ! :ole /r+2 t is1 p]=ms #aib vibrations 9 a second ( "t1 & produces a note correspond+ 9 increase ( acut5ess1 b /ill less int5se ?an ! =m]1 & t ?is cont9ues to take place 9 ! ari?metical progression ( #b1 #c1 #d1 c4 ,simultane\s vibrations1 agreeably to ! same law ( progression1 :i*1 h[ev]1 seem to admit ( no o!r primes ?an ! numb]s #b1 #c1 #e1 & #g1 are easily excit$ ^u any /r+$ in/rum5t1 ev5 by ! lighte/ possible t\* ( any ( its /r+s :ile 9 a /ate ( vibratory motion1 & ! notes ?us produc$ are di/+ui%$ by ! "n ( h>monics4 ,x foll[s1 !n1 t "o-half ( a musical /r+1 :5 divid$ f ! :ole by ! pressure ( ! f+]1 or any o!r means1 & put into vibratory motion1 produces a note d\bly acute to t produc$ by ! vibratory motion ( ! :ole /r+2 ! ?ird "p1 simil>ly sep>at$1 a note trebly acute2 & ! same ) e "p into :i* any musical /r+ may be divid$4 ,?is is ! fundam5tal pr9ciple by :i* all /r+$ in/rum5ts are made to produce h>mony4 ,x is ! same ) w9d in/rum5ts1 ! s\nds ( :i* are produc$ by ! frequ5cy ( ! pulsations occasion$ 9 ! surr\nd+ atmosph]e by agitat+ a column ( air conf9$ )9 a tube z 9 an organ1 9 :i* ! frequ5cy ( pulsation becomes great] 9 an inv]se ratio to ! l5g? ( ! pipes4 ,b ! foll[+ s]ies ( f\r successive scales ( musical notes w give ! read] a m compreh5sive view ( ! mann] 9 :i* !y foll[ ! law ( num]ical ratio j expla9$ ?an any m l5g!n$ exposition4 ,x is "h requisite to m5tion1 t 9 ! con/ruction ( ^! scales1 ,i h n only adopt$ ! old ,g]man or lit]al mode ( indicat+ ! notes1 b h includ$1 z ! ,g]mans d1 ! note t]m$ by u ,b flat z ,b natural1 & ! note we t]m ,b natural z ,h4 ,n[1 al?\gh ?is arrangem5t diff]s f t foll[$ 9 ! con/ruction ( our mod]n ,diatonic scale1 yet z ! ratio ( #d3g is m closely relat$ to t ( #a3b ?an t ( #h3ae1 & z x is (f]$ by nature 9 ! spontane\s division ( ! mono*ord1 ,i consid]$ x q admissible4 ,! figures give ! p>ts ( ! mono*ord :i* w\ld produce ! notes4 ,i4 7#a7 77 77 77 77 77 77 77 7799 ,c ,d ,e ,f ,g ,a ,b ,h c ,,ii4 7799 77 77 77 7799 77 77 77 7799 c d e f g a b h c ,,iii4 7799 77 7799 77 7799 77 7799 77 7799 c d e f g a b h c ,,iv4 7799 7799 7799 77 7799 77 7799 7799 7799 c d e f g a b h c ,! notes m>k$ 7997 are ! h>monics :i* naturally arise f ! division ( ! /r+ by #b1 #c1 #e1 & #g1 & ! multiples ( ^! primes4 ,?us e musical s\nd is compos$ ( a c]ta9 numb] ( p>ts call$ pulsations1 & ^! p>ts mu/ 9 e scale relate h>monically to "s fundam5tal numb]4 ,:5 ^! p>ts are multiples ( ! fundam5tal numb] by #b1 #d1 #h1 c41 l ! pulsations ( ! s\nds indicat$ by c1 c1 c1 c1 !y are call$ tonic notes1 be+ ! mo/ consonant2 :5 ! pulsations are simil> multiples by #c1 #f1 #ab1 c41 l ^? ( ! s\nds indicat$ by g1 g1 g1 !y are call$ dom9ant notes1 be+ ! next mo/ consonant2 & multiples by #e1 #aj1 c41 l ^? ( ! s\nds indicat$ by e1 e1 e1 !y are call$ m$iant notes1 f a simil> cause4 ,9 h>monic comb9ations ( musical s\nds1 ! /hetic feel+ produc$ by _! agreem5t dep5ds ^u ! relations !y be> to ea* o!r ) ref]5ce to ! numb] ( pulsations produc$ 9 a giv5 "t by ! fundam5tal note ( ! scale to :i* !y belong2 & x w be obs]v$1 t ! m simple ! num]ical ratios are among/ ! pulsations ( any numb] ( notes simultane\sly produc$1 ! m p]fect _! agreem5t4 ,h5ce ! orig9 ( ! common *ord or fundam5tal concord 9 ! unit$ s\nds ( ! tonic1 ! dom9ant1 & ! m$iant notes1 ! ratios & co9cid5ces ( ^: pulsations #b3a1 #c3b1 #e3d1 may ?us be exemplifi$3-- ,illu/ration ,9 musical composition1 ! law ( numb] also gov]ns its division into p>ts1 9 ord] to produce ^u ! e>1 along ) ! beauty ( h>mony1 t ( rhy?m4 ,?us a piece ( music is divid$ into p>ts ea* ( :i* conta9s a c]ta9 numb] ( o!r p>ts call$ b>s1 :i* may be divid$ & subdivid$ into any numb] ( notes1 & ! p]=mance ( ea* b> is und]/ood to occupy ! same portion ( "t1 h[ev] num]\s ! notes x conta9s may be2 s t ! music ( art is regul>ly symmetrical 9 its /ructure2 :ile t ( nature is 9 g5]al z irregul> & indef9ite 9 its rhy?m z x is 9 its h>mony4 ,?us ,i h endeav\r$ briefly to expla9 ! mann] 9 :i* ! law ( num]ical ratio op]ates 9 t species ( beauty p]ceiv$ ?r\gh ! e>4 ,! def9ite pr9ciples ( ! art ( music f\nd$ ^u ?is law h be5 = ages s sy/ematis$ t ^? :o are in/ruct$ 9 !m advance /eadily 9 proportion to _! natural end[m5ts1 :ile ^? :o refuse ?is in/ruction r>ely atta9 to any excell5ce4 ,9 ! si/] arts ( =m & col\r1 h[ev]1 a sy/em ( tuition1 f\nd$ ^u ?is law1 is /ill a desid]atum1 & a k ( ! sci5tific pr9ciples by :i* ^! arts are gov]n$ is conf9$ to a v few1 & sc>cely ackn[l$g$ among/ ^? ^: pr(essions mo/ require _! practical application4 ,,! ,,sci5ce ,,( ,,beauty ,,z ,,appli$ ,,to ,,=ms4 ,x is ju/ly rem>k$1 9 ! 8,illu/rat$ ,record ( ! ,new ,york ,exhibition ( #ahec10 t 8x is a "q wor?y ( consid]ation h[ f> ! m$iocrity ( ! pres5t day is attributable to an ov]we5+ reliance on natural p[]s & a neglect ( ! lights ( sci5ce20 & !re is express$ a ?or\gh conviction ( ! fact t1 besides ! evils ( ! copy+ sy/em1 8mu* g5ius is n[ wa/$ 9 ! acquirem5t ( rudim5t>y k 9 ! sl[ s*ool ( practical exp]im5t1 & t ! excell5ce ( ! anci5t ,greek s*ool ( design arose f a ?or\ghly dige/$ canon ( =m1 & ! use ( geometrical =mulas1 :i* make ! works ev5 ( ! second & ?ird-rate g5ius ( t p]iod ! wond] & admiration ( ! pres5t day40 ,t su* a canon ( =m1 & t ! use ( su* geometrical =mula1 ent]$ into ! education1 & !reby facilitat$ ! practice ( anci5t ,greek art1 ,i h 9 a =m] "w express$ my firm belief1 :i* is f\nd$ on ! rem>kable fact1 t = a p]iod ( ne>ly ?ree c5turies1 & ?r\gh\t a :ole c\ntry politically divid$ into /ates (t5 at w> ) ea* o!r1 works ( sculpture1 ar*itecture1 & ornam5tal design 7 execut$1 :i* surpass 9 symmetrical beauty any works ( ! k9d produc$ dur+ ! two ?\s& ye>s t h s9ce elaps$4 ,s decid$ is ?is sup]iority1 t ! arti/ic rema9s ( ! extraord9>y p]iod ,i allud$ to are1 9 all civilis$ nations1 /ill held to be ! mo/ p]fect specim5s ( =mative art 9 ! _w2 & ev5 :5 s fragm5t>y z to be d5ud$ ( ev]y?+ t c convey an idea ( expression1 !y /ill excite admiration & wond] by ! purity ( _! geometric beauty4 ,& s univ]sal 0 ?is excell5ce1 t x seems to h *>act]is$ e production ( =mative art1 h[ev] humble ! use to :i* x 0 appli$4 ,! common supposition1 t ?is excell5ce 0 ! result ( an extraord9>y am\nt ( g5ius exi/+ among ! ,greek p dur+ t p>ticul> p]iod1 is n consi/5t ) :at we "k ( ! progress ( mank9d 9 any o!r direction1 & is1 9 ! pres5t /ate ( art1 calculat$ to ret>d its progress1 inasmu* z su* an idea w\ld sugge/ t1 in/ead ( mak+ any ex]tion to arrive at a l g5]al excell5ce1 ! _w mu/ wait = x until a simil> suppos$ psy*ological ph5om5on %all occur4 ,b hi/ory t5ds to prove t ! long p]iod ( univ]sal arti/ic excell5ce ?r\gh\t ,greece c\ld only be ! result ( an e>ly inculcation ( "s well-dige/$ sy/em ( correct elem5t>y pr9ciples1 by :i* ! ord9>y am\nt ( g5ius allott$ to mank9d 9 e age 0 prop]ly nurtur$ & cultivat$2 & by :i*1 also1 a correct k & appreciation ( art 7 dissem9at$ among/ ! p g5]ally4 ,inde$1 ,mll]1 9 8 8,anci5t ,art & its ,rema9s10 %ews cle>ly t "s c]ta9 fix$ pr9ciples1 con/itut+ a sci5ce ( proportions1 7 kn[n 9 ,greece1 & t !y =m$ ! basis ( all arti/s' education & practice dur+ ! p]iod ref]r$ to2 also1 t art began to decl9e1 & its brighte/ p]iod to close1 z ?is sci5ce fell into disuse1 & ! ,greek arti/s1 in/ead ( work+ = an enlight5$ community1 :o und]/ood ! nature ( ! pr9ciples :i* guid$ !m1 7 call$ ^u to gratify ! impati5t :ims ( pamp]$ & tyrannical rul]s4 ,by be+ in/ruct$ 9 ?is sci5ce ( proportion1 ! ,greek arti/s 7 enabl$ to imp>t to _! repres5tations ( ! human figure a ma!matically correct species ( symmetrical beauty2 :e!r accompany+ ! sl5d] & delicately undulat$ =m ( ! ,v5us1--its opposite1 ! massive & p[]ful m\ld ( ! ,h]cules1--or ! *>act]i/ic repres5tation ( any o!r deity 9 ! hea!n my?ology4 ,& ?is seems to h be5 done ) equal ease 9 ! m9ute figure cut on a preci\s gem1 & 9 ! mo/ colossal /atue4 ,! same in/ruction likewise enabl$ ! ar*itects ( ,greece to in/itute ^? v>ieties ( proportions 9 /ructure call$ ! ,classical ,ord]s ( ,ar*itecture2 :i* are s p]fect t1 s9ce ! sci5ce :i* gave !m bir? has be5 buri$ 9 oblivion1 classical ar*itecture has be5 little m ?an an imitative art2 = all :o h s9ce writt5 ^u ! subject1 f ,vitruvius d[nw>ds1 h arriv$ at no?+1 9 s f> z ! great elem5t>y pr9ciples 9 "q are conc]n$1 beyond ! mo/ vague & unsatisfactory conjectures4 ,= a m cle> und]/&+ ( ! nature ( ?is application ( ! ,py?agorean law ( numb] to ! h>mony ( =m1 x w be requisite to repeat ! fact1 t mod]n sci5ce has %ewn t ! cause ( ! impression1 produc$ by ext]nal nature ^u ! s5sorium1 call$ light1 may be trac$ to a molecul> or e!real action4 ,?is action is excit$ naturally by ! sun1 artificially by ! combu/ion ( v>i\s sub/ances1 & sometimes physically )9 ! eye4 ,l ! atmosph]ic pulsations :i* produce s\nd1 ! action :i* produces light is capable1 )9 a limit$ sph]e1 ( be+ reflect$ f "s bodies & transmitt$ ?r\gh o!rs2 & by ?is reflection & transmission ! visible nature ( =ms & figures is communicat$ to ! s5sorium4 ,! eye is ! m$ium ( ?is communication2 & its /ructural beauty1 & p]fect adaptation to ! purpose ( convey+ ?is action1 mu/1 l ^? ( ! e>1 be left to ! anatomi/ fully to describe4 ,x is "h only necess>y to rem>k1 t ! optic n]ve1 l ! auditory n]ve1 ends 9 a c>efully protect$ fluid1 :i* is ! la/ ( ! m$ia int]pos$ betwe5 ?is peculi>ly subtle action & ! n]ve ^u :i* x impresses ! pres5ce ( ! object f :i* x is reflect$ or ?r\gh :i* x is transmitt$1 & ! nature ( su* object made p]ceptible to ! m9d4 ,! eye & ! e> are ?us1 9 "o ess5tial po9t1 simil> 9 _! physiology1 relatively to ! means provid$ = receiv+ impressions f ext]nal nature2 x is1 !re=e1 b reasonable to believe t ! eye is capable ( appreciat+ ! exact subdivision ( spaces1 j z ! e> is capable ( appreciat+ ! exact subdivision ( int]vals ( "t2 s t ! division ( space into exact numb]s ( equal p>ts w /hetically affect ! m9d ?r\gh ! m$ium ( ! eye4 ,we assume1 !re=e1 t ! /&>d ( symmetry1 s e/imat$1 is d$uc$ f ! simple/ law t c\ld h be5 conceiv$--! law t ! angles ( direction mu/ all be> to "s fix$ angle ! same simple relations :i* ! diff]5t notes 9 a *ord ( music be> to ! fundam5tal note2 t is1 relations express$ ari?metically by ! smalle/ natural numb]s4 ,?us ! eye1 be+ guid$ 9 its e/imate by direction r ?an by di/ance1 j z ! e> is guid$ by numb] ( vibrations r ?an by magnitude1 bo? x & ! e> convey simplicity & h>mony to ! m9d )\t ef=t1 & ! m9d ) equal facility receives & appreciates !m4 ,on ! ,rectil9e> ,=ms & ,proportions ( ,ar*itecture4 ,z we are accu/om$ 9 all cases to ref] direction to ! horizontal & v]tical l9es1 & z ! meet+ ( ^! l9es makes ! "r angle1 x naturally con/itutes ! fundam5tal angle1 by ! h>monic division ( :i* a sy/em ( proportion may be e/abli%$1 & ! !ory ( symmetrical beauty1 l t ( music1 r5d]$ susceptible ( exact reason+4 ,let !re=e ! "r angle be ! fundam5tal angle1 & let x be divid$ ^u ! quadrant ( a circle into ! h>monic p>ts already expla9$1 ?us3-- ,sup]- ,sub- ,sub- ,sub- ,semi-sub- ,"r tonic ,m$iant dom9ant ,dom9ant m$iant tonic tonic ,tonic ,angle4 ,angles4 ,angles4 ,angles4 ,angles4 ,angles4 ,angles4 ,angles4 ,angles4 ,i4 7#a7 77 77 77 77 77 77 77 77 ,,ii4 77 77 77 77 77 77 77 77 77 ,,iii4 77 77 77 77 77 77 77 77 77 ,,iv4 77 77 77 77 77 77 77 77 77 ,9 ord] t ! analogy may be kept 9 view1 ,i h giv5 to ! p>ts ( ea* ( ^! f\r scales ! appropriate nom5clature ( ! notes :i* =m ! diatonic scale 9 music4 ,:5 a "r angl$ triangle is con/ruct$ s t its two smalle/ angles are equal1 ,i t]m x simply ! triangle ( 771 because ! small] angles are ea* "o-half ( ! "r angle4 ,b :5 ! two angles are unequal1 ! triangle may be nam$ aft] ! smalle/4 ,= in/ance1 :5 ! small] angle1 :i* we %all "h suppose to be "o-?ird ( ! "r angle1 is made ) ! v]tical l9e1 ! triangle may be call$ ! v]tical scal5e triangle ( 772 & :5 made ) ! horizontal l9e1 ! horizontal scal5e triangle ( 774 ,z e rectangle is made up ( two ( ^! "r angl$ triangles1 ! same t]m9ology may also be appli$ to ^! figures4 ,?us1 ! equilat]al rectangle or p]fect squ>e is simply ! rectangle ( 771 be+ compos$ ( two simil> "r angl$ triangles ( 772 & :5 two v]tical scal5e triangles ( 771 & ( simil> dim5sions1 are unit$ by _! hypo!nuses1 !y =m ! v]tical rectangle ( 771 & 9 l mann] ! horizontal triangles ( 77 simil>ly unit$ w\ld =m ! horizontal rectangle ( 774 ,z ! isosceles triangle is 9 l mann] compos$ ( two "r angl$ scal5e triangles jo9$ by "o ( _! sides1 ! same t]m9ology may be appli$ to e v>iety ( t figure4 ,all ! angles ( ! fir/ ( ! above scales1 except t ( 771 give rectangles ^: longe/ sides are 9 ! horizontal l9e1 :ile ! o!r ?ree give rectangles ^: longe/ sides are 9 ! v]tical l9e4 ,i h illu/rat$ 9 ,plate ,i4 ! mann] 9 :i* ?is h>monic law acts ^u ^! elem5t>y rectil9e> figures by con/ruct+ a s]ies agreeably to ! angles ( scales ,,ii41 ,,iii41 ,,iv4 ,?r\gh\t ?is s]ies a b c is ! prim>y scal5e triangle1 ( :i* ! rectangle a b c e is compos$2 d c e ! v]tical isosceles triangle2 & :5 ! plate is turn$1 d e a ! horizontal isosceles triangle1 bo? ( :i* are compos$ ( ! same prim>y scal5e triangle4 ,sid5ote3 ,plate ,i4 ,?us ! mo/ simple elem5ts ( symmetry 9 rectil9e> =ms are ! ?ree foll[+ figures3-- ,! equilat]al rectangle or p]fect squ>e1 ,! oblong rectangle1 & ,! isosceles triangle4 ,x has be5 %ewn t 9 h>monic comb9ations ( musical s\nds1 ! /hetic feel+ produc$ by _! agreem5t dep5ds ^u ! relation !y be> to ea* o!r ) ref]5ce to ! numb] ( pulsations produc$ 9 a giv5 "t by ! fundam5tal note ( ! scale to :i* !y belong2 & t ! m simply !y relate to ea* o!r 9 ?is way ! m p]fect ! h>mony1 z 9 ! common *ord ( ! fir/ scale1 ! relations ( ^: p>ts are 9 ! simple ratios ( #b3a1 #c3b1 & #e3d4 ,x is equally consi/5t ) ?is law1 t :5 appli$ to =m 9 ! composition ( an assortm5t ( figures ( any k9d1 _! respective proportions %\ld be> a v simple ratio to ea* o!r 9 ord] t a def9ite & pleas+ h>mony may be produc$ among/ ! v>i\s p>ts4 ,n[1 ?is is z effectually done by =m+ !m ^u ! h>monic divisions ( ! "r angle z musical h>mony is produc$ by s\nds result+ f h>monic divisions ( a vibratory body4 ,hav+ 9 previ\s works#g giv5 ! requisite illu/rations ( ?is fact 9 full detail1 ,i %all "h conf9e myself to ! mo/ simple k9d1 tak+ = my fir/ example "o ( ! f9e/ specim5s ( classical ar*itecture 9 ! _w--! front portico ( ! ,p>!non ( ,a!ns4 ,! angles :i* gov]n ! proportions ( ?is beautiful elevation are ! foll[+ h>monic p>ts ( ! "r angle-- ,tonic ,dom9ant ,m$iant ,subtonic ,sup]tonic ,angles4 ,angles4 ,angles4 ,angle4 ,angles4 77 77 77 77 77 77 77 77 77 77 77 ,sid5ote3 ,plate ,,ii4 ,9 ,plate ,,ii4 ,i give a diagram ( its rectil9e> or?ography1 :i* is simply con/ruct$ by l9es drawn1 ei!r horizontally1 v]tically1 or obliquely1 :i* latt] make ) ei!r ( ! =m] l9es "o or o!r ( ! h>monic angles 9 ! above s]ies4 ,= example1 ! horizontal l9e ,,ab repres5ts ! l5g? ( ! base or surface ( ! upp] /ep ( ! sub/ructure ( ! build+4 ,! l9e ,,ae1 :i* makes an angle ( 77 ) ! horizontal1 det]m9es ! height ( ! colonnade4 ,! l9e ,,ad1 :i* makes an angle ( 77 ) ! horizontal1 det]m9es ! height ( ! portico1 exclusive ( ! p$im5t4 ,! l9e ,,ac1 :i* makes an angle ( 77 ) ! horizontal1 det]m9es ! height ( ! portico1 includ+ ! p$im5t4 ,! l9e ,,gd1 :i* makes an angle ( 77 ) ! horizontal1 det]m9es ! =m ( ! p$im5t4 ,! l9es ,,ez & ,,ly1 :i* respectively make angles ( 77 & 77 ) ! horizontal1 det]m9e ! bread? ( ! ar*itrave1 frieze1 & cornice4 ,! l9e v n u1 :i* makes an angle ( 77 ) ! v]tical1 det]m9es ! bread? ( ! triglyphs4 ,! l9e t d1 :i* makes an angle ( 771 det]m9es ! bread? ( ! metops4 ,! l9es c b r f1 & a i1 :i* make ea* an angle ( 77 ) ! v]tical1 det]m9e ! wid? ( ! five c5tre int]columniations4 ,! l9e z k1 :i* makes an angle ( 77 ) ! v]tical1 det]m9es ! wid? ( ! two rema9+ int]columniations4 ,! l9es c s1 q x1 & y h1 ea* ( :i* makes an angle ( 77 ) ! v]tical1 det]m9e ! diamet]s ( ! ?ree columns on ea* side ( ! c5tre4 ,! l9e w l1 :i* makes an angle ( 77 ) ! v]tical1 det]m9es ! diamet] ( ! two rema9+ or corn] columns4 ,9 all ?is1 ! l5g? & bread? ( ! p>ts are det]m9$ by horizontal & v]tical l9es1 :i* are necess>ily at "r angles ) ea* o!r1 & ! position ( :i* are det]m9$ by "o or o!r ( ! l9es mak+ ! h>monic angles above enum]at$4 ,n[1 ! l5g?s & bread?s ?us s simply det]m9$ by ^! few angles1 h be5 prov$ to be correct by _! agreem5t ) ! mo/ c>eful measurem5ts :i* c\ld possibly be made ( ?is exquisite specim5 ( =mative art4 ,^! measurem5ts 7 obta9$ by ! 8,society ( ,dilettanti10 ,london1 :o1 expressly = t purpose1 s5t ,mr ,f4 ,c4 ,p5rose1 a highly educat$ ar*itect1 to ,a!ns1 :]e he rema9$ = ab\t five mon?s1 engag$ 9 ! execution ( ?is int]e/+ commission1 ! results ( :i* are n[ publi%$ 9 a magnific5t volume by ! ,society4#h ,! agreem5t 0 s /rik+1 t ,mr ,p5rose has be5 publicly ?ank$ by an em95t man ( sci5ce = be>+ te/imony to ! tru? ( my !ory1 :o 9 do+ s obs]ves1 8,! dim5sions :i* he 7,mr ,p5rose7 gives are to me ! sure/ v]ification ( ! !ory ,i c\ld h desir$4 ,! m9ute discrepancies =m t v elem5t ( practical inc]titude1 bo? z to execution & direct measurem5t1 :i* always prevails 9 mat]ialis+ a ma!matical calculation made "u su* conditions40#i ,al?\gh ! measurem5ts tak5 by ,mr ,p5rose are und5iably correct1 z all :o exam9e ! great "w j ref]r$ to mu/ ackn[l$ge1 & al?\gh !y h af=d$ me ! be/ possible means ( te/+ ! accuracy ( my !ory z appli$ to ! ,p>!non1 yet ! ideas ( ,mr ,p5rose z to ! pr9ciples !y evolve are f\nd$ ^u ! fallaci\s doctr9e :i* has s long prevail$1 & /ill prevails1 9 ! /hetics ( ar*itecture1 viz41 t h>mony may be imp>t$ by ratios betwe5 ! l5g?s & bread?s ( p>ts4 ,i h tak5 = my second example an elevation :i*1 al?\gh ( small] dim5sions1 is no less celebrat$ = ! beauty ( its proportions ?an ! ,p>!non itself1 viz41 ! front portico ( ! temple ( ,!seus1 :i* has also be5 measur$ by ,mr ,p5rose4 ,! angles :i* gov]n ! proportions ( ?is elevation are ! foll[+ h>monic p>ts ( ! "r angle3-- ,tonic ,dom9ant ,m$iant ,angles4 ,angles4 ,angles4 77 77 77 77 77 77 77 ,sid5ote3 ,plate ,,iii4 ,a diagram ( ! rectil9e> or?ography ( ?is portico is giv5 9 ,plate ,,iii4 ,its con/ruction is simil> to t ( ! ,p>!non 9 respect to ! h>monic p>ts ( ! "r angle1 & ,i h !re=e only to obs]ve1 t ! l9e ,a ,e makes an angle ( 772 ! l9e ,a ,d an angle ( 772 ! l9e ,a ,c an angle ( 772 ! l9e ,g ,d an angle ( 772 & ! l9es ,e ,z & ,l ,y angles ( 77 ) ! horizontal4 ,z to ! colonnade or v]tical "p1 ! l9e a b1 :i* det]m9es ! ?ree middle int]columniations1 makes an angle ( 772 ! l9e c d1 :i* det]m9es ! two out] int]columniations1 makes an angle ( 772 & ! l9e e f1 :i* det]m9es ! less] diamet] ( ! columns1 makes an angle ( 77 ) ! v]tical4 ,i ne$ give no fur!r details "h1 z my int5tion is to %ew ! simplicity ( ! me?od by :i* ?is !ory may be r$uc$ to practice1 & because ,i h giv5 9 my o!r works ample details1 9 full illu/ration ( ! or?ography ( ^! two /ructures1 especially ! fir/4#aj ,! =ego+ examples be+ bo? horizontal rectangul> compositions1 ! proportions ( _! pr9cipal p>ts h necess>ily be5 det]m9$ by l9es drawn f ! extremities ( ! base1 mak+ angles ) ! horizontal l9e1 & =m+ !reby ! diagonals ( ! v>i\s rectangles into :i*1 9 _! lead+ features1 !y are necess>ily resolv$4 ,b ! example ,i am n[ ab\t to give is ( ano!r "*1 be+ a v]tical pyramidal composition1 & consequ5tly ! proportions ( its pr9cipal p>ts are det]m9$ by ! angles :i* ! oblique l9es make ) ! v]tical l9e repres5t+ ! height ( ! elevation1 & =m+ a s]ies ( isosceles triangles2 = ! isosceles triangle is ! type ( all pyramidal composition4 ,?is ?ird example is ! ea/ end ( ,l9coln ,ca!dral1 a ,go?ic /ructure1 :i* is ackn[l$g$ to be "o ( ! f9e/ specim5s ( t /yle ( ar*itecture exi/+ 9 ?is c\ntry4 ,! angles :i* gov]n ! proportions ( ?is elevation are ! foll[+ h>monic p>ts ( ! "r angle3-- ,tonic4 ,dom9ant4 ,m$iant4 ,subtonic4 ,sup]tonic4 77 77 77 77 77 77 77 77 77 77 ,sid5ote3 ,plate ,,iv4 ,9 ,plate ,,iv4 ,i give a diagram ( ! v]tical1 horizontal1 & oblique l9es1 :i* compose ! or?ography ( ?is beautiful elevation4 ,! l9e ,a ,b repres5ts ! full height ( ?is /ructure4 ,! l9e ,a ,c1 :i* makes an angle ( 77 ) ! v]tical1 det]m9es ! wid? ( ! design1 ! tops ( ! aisle w9d[s1 & ! bases ( ! p$im5ts on ! inn] buttresses2 ,a ,g1 77 ) ! v]tical1 t ( ! out] buttress2 ,a ,f1 77 ) ! v]tical1 t ( ! space betwe5 ! out] & inn] buttresses & ! wid? ( ! great c5tre w9d[2 & ,a ,e1 77 ) v]tical1 t ( bo? ! inn] buttresses & ! space betwe5 ^!4 ,a ,h1 :i* makes 77 ) ! v]tical1 det]m9es ! =m ( ! p$im5t ( ! c5tre1 & ! full height ( ! base & surbase4 ,a ,i1 :i* makes 77 ) ! v]tical1 det]m9es ! =m ( ! p$im5t ( ! small] gables1 ! base ( ! p$im5t on ! out] buttress1 ! base ( ! ornam5tal recess betwe5 ! out] & inn] buttresses1 ! spr+ ( ! ar* ( ! c5tre w9d[1 ! tops ( ! p$im5ts on ! inn] buttresses1 & ! spr+ ( ! ar* ( ! upp] w9d[4 ,a ,k1 :i* makes 771 det]m9es ! height ( ! out] buttress2 & ,a ,z1 :i* makes 77 ) ! horizontal1 det]m9es t ( ! inn] buttresses4 ,= ! reasons already giv51 ,i ne$ n "h g into fur!r detail4#aa ,x is1 h[ev]1 wor?y ( rem>k 9 ?is place1 t not)/&+ ! great diff]5ce :i* exi/s betwe5 ! /yle ( composition 9 ?is ,go?ic design1 & 9 t ( ! ea/ end ( ! ,p>!non1 ! h>monic elem5ts ^u :i* ! or?ographic beauty ( ! "o dep5ds1 are almo/ id5tical ) ^? ( ! o!r4 ,on ! ,curvil9e> ,=ms & ,proportions ( ,ar*itecture4 ,ea* regul> rectil9e> figure has a curvil9e> figure t exclusively belongs to x1 & to :i* may be appli$ a correspond+ t]m9ology4 ,= in/ance1 ! circle belongs to ! equilat]al rectangle2 t is1 ! rectangle ( 771 an ellipse to e o!r rectangle1 & a composite ellipse to e isosceles triangle4 ,?us ! mo/ simple elem5ts ( beauty 9 ! curvil9e> =ms ( ar*itectural design are ! foll[+ ?ree figures3-- ,! circle1 ,! ellipse1 & ,! composite ellipse4 ,i f9d x necess>y 9 ?is place to g into "s details reg>d+ ! specific "* ( ! two latt] figures1 because ! prop] mode ( describ+ ^! beautiful curves1 & _! high value 9 ! practice ( ! ar*itectural draughtsman & ornam5tal design]1 seem z yet unkn[n4 ,9 pro( ( ?is ass]tion1 ,i mu/ aga9 ref] to ,mr ,p5rose's great "w publi%$ by ! 8,society ( ,dilettanti40 ,at page #eb ( t "w x is obs]v$1 t 8by :atev] means an ellipse is to be con/ruct$ me*anically1 x is a "w ( "t 7if n ( absolute difficulty7 s to arrange ! foci1 c41 z to produce an ellipse ( any exact l5g? & bread? :i* may be desir$40 ,n[1 ?is is f> f be+ ! case1 = ! me?od ( arrang+ ! foci ( an ellipse ( any giv5 l5g? & bread? is extremely simple1 be+ z foll[s3-- ,let ,a ,b ,c 7figure #a7 be ! l5g?1 & ,d ,b ,e ! bread? ( ! desir$ ellipse4 ,illu/ration3 ,fig4 #a4 ,take ,a ,b ^u ! compasses1 & place ! po9t ( "o leg ^u ,e & ! po9t ( ! o!r ^u ! l9e ,a ,b1 x w meet x at ,f1 :i* is "o focus3 keep+ ! po9t ( ! "o leg ^u ,e1 remove ! po9t ( ! o!r to ! l9e ,b ,c1 & x w meet x at ,g1 :i* is ! o!r focus4 ,b1 :5 ! proportions ( an ellipse are to be imp>t$ by means ( "o ( ! h>monic angles1 suppose ! angle ( 771 !n ! foll[+ is ! process3-- ,let ,a ,b ,c 7figure #b7 repres5t ! l5g? ( ! int5d$ ellipse4 ,?r\gh ,b draw ,b e indef9itely1 at "r angles ) ,a ,b ,c2 ?r\gh ,c draw ! l9e ,c f indef9itely1 mak+1 ) ,b ,c1 an angle ( 774 ,take ,b ,c ^u ! compasses1 & place ! po9t ( "o leg ^u ,d :]e ,c f int]sects ,b e1 & ! po9t ( ! o!r ^u ! l9e ,a ,b1 x w meet x at ,f1 :i* is "o focus4 ,keep+ ! po9t ( "o leg /ill ^u ,d1 remove ! po9t ( ! o!r to ! l9e ,b ,c1 & x w meet x at ,g1 :i* is ! o!r focus4 ,illu/ration3 ,fig4 #b4 ,! foci be+ 9 ei!r case ?us simply asc]ta9$1 ! me?od ( describ+ ! curve on a small scale is equally simple4 ,sid5ote3 ,plate ,v4 ,a p9 is fix$ into ea* ( ! two foci1 & ano!r into ! po9t ,d4 ,ar\nd ^! ?ree p9s a wax$ ?read1 flexible b n ela/ic1 is ti$1 c>e be+ tak5 t ! knot be ( a k9d t w n slip4 ,! p9 at ,d is n[ remov$1 & a h>d black lead p5cil introduc$ )9 ! ?read b&4 ,! p5cil is !n mov$ ar\nd ! p9s fix$ 9 ! foci1 keep+ ! ?read b& at a full & equal t5sion2 ?us simply ! ellipse is describ$4 ,:51 h[ev]1 ! gov]n+ angle is acute1 say less ?an 771 x is requisite to adopt a m accurate me?od ( description1#ab z ! ar*itectural examples :i* foll[ w %ew4 ,b ar*itectural draughtsm5 & ornam5tal design]s w\ld d well to supply !mselves1 = ord9>y practice1 ) half a doz5 s]ies ( ellipses1 v>y+ 9 ! proportions ( _! axes f 77 to 77 ( ! scale1 & ! l5g? ( _! major axes f #a to #f in*es4 ,^! %\ld be describ$ by ! above simple process1 ^u v /rong draw+ pap]1 & c>efully cut out1 ! edge ( ! pap] be+ kept smoo?1 & ea* ellipse hav+ its great] & less] axes1 its foci1 & ! hypo!nuse ( its scal5e triangle drawn ^u x4 ,to exemplify ?is1 ,i give ,plate ,v41 :i* exhibits ! ellipses ( 771 771 771 & 771 inscrib$ 9 _! rectangles1 on :i* a b & c d are respectively ! great] & less] axes1 o o ! foci1 & d b ! angle ( ea*4 ,su* a s]ies ( ^! beautiful figures w\ld be f\nd p>ticul>ly useful 9 draw+ ! m\ld+s ( ,grecian ar*itecture2 =1 to describe ! curvil9e> cont\r ( su* m\ld+s f s+le po9ts1 z has be5 done ) ^? :i* embelli% ev5 our mo/ pret5d+ attempts at ! re/oration ( t classical /yle ( ar*itecture1 is to give ! resemblance ( an ext]nal =m )\t ! h>mony :i* con/itutes its real beauty4 ,mr ,p5rose1 ow+ to ! suppos$ difficulty reg>d+ ! description ( ellipses j allud$ to1 endeav\rs to %ew t ! curves ( all ! m\ld+s ?r\gh\t ! ,p>!non 7 ei!r p>abolic or hyp]bolic2 b ,i believe su* curves c h no connexion ) ! elem5t>y =ms ( ar*itecture1 = !y are curves :i* repres5t motion1 & d n1 by cont9u$ production1 =m clos$ figures4 ,b ,i h %ewn1 9 a =m] "w1#ac t ! cont\rs ( ^! m\ld+s are compos$ ( curves ( ! composite ellipse1--a figure :i* ,i s "n because x is compos$ simply ( arcs ( v>i\s ellipses h>monically fl[+ into ea* o!r4 ,! composite ellipse1 :5 drawn sy/ematically ^u ! isosceles triangle1 resembles closely p>abolic & hyp]bolic curves--only diff]+ f ^! inasmu* z x possesses ! ess5tial quality ( circumscrib+ h>monically "o ( ! elem5t>y rectil9e> figures employ$ 9 ar*itecture1 :ile ^? ( ! p>abola & hyp]bola1 z ,i h j obs]v$1 are m]ely curves ( motion1 &1 consequ5tly1 nev] c h>monically circumscribe or be resolv$ into any regul> figure4 ,! composite ellipse may be ?us describ$4 ,sid5ote3 ,plate ,,vi4 ,let ,a ,b ,c 7,plate ,,vi47 be a v]tical isosceles triangle ( 771 bisect ,a ,b 9 ,d1 & ?r\gh ,d draw indef9itely ,d f p]p5dicul> to ,a ,b1 & ?r\gh ,b draw indef9itely ,b g1 mak+ ! angle ,d ,b g 771 ,d f & ,b g int]sect+ ea* o!r 9 ,m4 ,take ,b ,d & ,d ,m z semi-axes ( an ellipse1 ! foci ( :i* w be at p & q1 9 ea* ( ^!1 & 9 ea* ( ! foci h t & k r 9 ! l9es ,a ,c & ,b ,c1 fix a p91 & "o also 9 ! po9t ,m1 tie a ?read ar\nd ^! p9s1 )draw ! p9 f ,m1 & trace ! composite ellipse 9 ! mann] already describ$ ) respect to ! simple ellipse4 ,9 "s ( my e>li] works ,i describ$ ?is figure by tak+ ! angles ( ! isosceles triangle z foci2 b ! above me?od is mu* m correct4 ,z ! elem5t>y angle ( ! triangle is 771 & t ( ! elliptic curve describ$ ar\nd x 771 ,i call x ! composite ellipse ( 77 & 771 _! h>monic ratio be+ #d3c2 & s on ( all o!rs1 accord+ to ! diff]5ce t may ?us exi/ betwe5 ! elem5t>y angles4 ,! visible curves :i* s(t5 & beautify ! melody ( ! outl9e ( ! front ( ! ,p>!non1 z giv5 9 ,mr ,p5rose's great "w1 ,i h c>efully analys$1 & h f\nd !m 9 z p]fect agreem5t ) ?is sy/em1 z its rectil9e> h>mony has be5 %ewn to be4 ,?is ,i demon/rat$ 9 ! "w j ref]r$ to#ad by a s]ies ( twelve plates1 %ew+ t ! entasis ( ! columns 7a subject ^u :i* !re has be5 mu* speculation7 is simply an arc ( an ellipse ( 771 ^: great] axis makes ) ! v]tical an angle ( 772 or simply1 ! =m ( "o ( ^! columns is ! fru/rum ( an elliptic-sid$ or prolate-sph]oidal cone1 ^: section is a composite ellipse ( 77 & 771 ! h>monic ratio ( ^! two angles be+ #d3c1 ! same z t ( ! angles ( ! composite ellipse j exemplifi$4 ,sid5ote3 ,plate ,,vii4 ,sid5ote3 ,plate ,,viii4 ,9 ,plate ,,vii4 is repres5t$ ! section ( su* a cone1 ( :i* ,a ,b ,c is ! isosceles triangle ( 771 & ,b ,d & ,d ,m ! semi-axes ( an ellipse ( 774 ,m ,n & ,o ,p are ! entases ( ! column1 & d e f ! normal con/ruction ( ! capital4 ,all ^! are fully illu/rat$ 9 ! "w above ref]r$ to1#ae 9 :i* ,i h also %ewn t ! curve ( ! neck ( ! column is t ( an ellipse ( 772 ! curve ( ! capital or e*9us1 t ( an ellipse ( 772 ! curve ( ! m\ld+ "u ! cymatium ( ! p$im5t1 t ( an ellipse ( 772 & ! curve ( ! b$-m\ld+ ( ! cornice ( ! p$im5t1 t ( an ellipse ( 774 ,! curve ( ! cavetto ( ! s(fit ( ! corona is compos$ ( ellipses ( 77 & 772 ! curve ( ! cymatium :i* surm\nts ! corona1 is t ( an ellipse ( 772 ! curve ( ! m\ld+ ( ! capital ( ! ant ( ! po/icum1 t ( an ellipse ( 772 ! curves ( ! l[] m\ld+ ( ! same capital are compos$ ( ^? ( an ellipse ( 77 & ( ! circle 772 ! curve ( ! m\ld+ :i* is plac$ betwe5 ! two latt] is t ( an ellipse ( 772 ! curve ( ! upp] m\ld+ ( ! b& "u ! beams ( ! ceil+ ( ! p]i/yle1 t ( an ellipse ( 772 ! curve ( ! l[] m\ld+ ( ! same b&1 t ( an ellipse ( 772 & ! curves ( ! m\ld+ at ! bottom ( ! small /ep or podium betwe5 ! columns1 are ^? ( ! circle 77 & ( an ellipse ( 774 ,i h also %ewn ! curve ( ! flut+ ( ! columns to be t ( 774 ,! great] axis ( ea* ( ^! ellipses1 :5 n 9 ! v]tical or horizontal l9es1 makes an h>monic angle ) "o or o!r ( !m4 ,9 ,plate ,,viii41 sections ( ! two la/-nam$ m\ld+s are repres5t$ full size1 :i* w give ! read] an idea ( ! simple mann] 9 :i* ! ellipses are employ$ 9 ! production ( ^? h>monic curves4 ,?us we f9d t ! sy/em "h adopt$ = apply+ ?is law ( nature to ! production ( beauty 9 ! ab/ract =ms employ$ 9 ar*itectural composition1 s f> f involv+ u 9 any?+ complicat$1 is *>act]is$ by extreme simplicity4 ,9 conclud+ ?is "p ( my treatise1 ,i may "h repeat :at ,i h advanc$ 9 a late "w1#af viz41 my conviction ( ! probability t a sy/em ( apply+ ?is law ( nature 9 ar*itectural con/ruction 0 ! only great practical secret ( ! ,freemasons1 all _! o!r secrets be+ connect$1 n ) _! art1 b ) ! social con/itution ( _! society4 ,?is valuable secret1 h[ev]1 seems to h be5 lo/1 z its practical application fell into disuse2 b1 z t anci5t society consi/$ ( speculative z well z practical masons1 ! secrets connect$ ) _! social union h /ill be5 pres]v$1 along ) ! excell5t laws by :i* ! bro!rhood is gov]n$4 ,x c sc>cely be d\bt$ t !re 0 "s su* practically useful secret among/ ! ,freemasons or e>ly ,go?ic ar*itects2 = we f9d 9 all ! v5]able rema9s ( _! art :i* exi/ 9 ?is c\ntry1 symmetrical elegance ( =m p]vad+ ! g5]al design1 h>moni\s proportion among/ all ! p>ts1 beautiful geometrical arrangem5ts ?r\gh\t all ! trac]y1 z well z 9 ! elegantly symmetris$ foliat$ decorations :i* belong to t /yle ( ar*itecture4 ,b x is at ! same "t wor?y ( rem>k1 t :5ev] !y div]g$ f ar*itecture to sculpture & pa9t+1 & attempt$ to repres5t ! human figure1 or ev5 any ( ! l[] animals1 _! productions are su* z to conv9ce u t 9 ?is c\ntry ^! arts 7 9 a v degrad$ /ate ( b>b>ism--! figures are (t5 mu* disproportion$ 9 _! p>ts & di/ort$ 9 _! attitudes1 :ile _! repres5tations ( animals & *im]as are :imsically absurd4 ,x w\ld1 !re=e1 appe> t ar*itecture1 z a f9e art1 mu/ h be5 pres]v$ by "s peculi> influ5ce f p>tak+ ( ! b>b>ism s app>5t 9 ! si/] arts ( t p]iod4 ,al?\gh its practical secrets h be5 long lo/1 ! ,freemasons ( ! pres5t day trace ! orig9al possession ( !m to ,moses1 :o1 !y say1 8modell$ masonry into a p]fect sy/em1 & circumscrib$ its my/]ies by l&-m>ks significant & unalt]able40 ,n[1 z ,moses receiv$ 8 education 9 ,egypt1 :]e ,py?agoras is said to h acquir$ 8 fir/ k ( ! h>monic law ( numb]s1 x is highly probable t ?is p]fect sy/em ( ! great ,jewi% legislator 0 bas$ ^u ! same law ( nature :i* con/itut$ ! f\ndation ( ! ,py?agorean philosophy1 & ultimately l$ to t excell5ce 9 art :i* is /ill ! admiration ( ! _w4 ,py?agoras1 x w\ld appe>1 =m$ a sy/em mu* m p]fect & compreh5sive ?an t practis$ by ! ,freemasons 9 ! middle ages ( ,*ri/ianity2 = x 0 z applicable to sculpture1 pa9t+1 & music1 z x 0 to ar*itecture4 ,?is p]fection 9 ar*itecture is /rik+ly exemplifi$ 9 ! ,p>!non1 z comp>$ ) ! ,go?ic /ructures ( ! middle ages2 = x w be f\nd t ! :ole six elem5t>y figures ,i h enum]at$ z belong+ to ar*itecture1 are requir$ 9 complet+ ! or?ographic beauty ( t noble /ructure4 ,& among/ ^!1 none conduce m to t beauty ?an ! simple & composite ellipses4 ,n[1 9 ! ar*itecture ( ! be/ p]iods ( ,go?ic1 or1 inde$1 9 t ( any aft] p]iod 7,roman ar*itecture includ$71 ^! beautiful curves seem to h be5 ignor$1 & t ( ! circle alone employ$4 ,be ^? matt]s z !y may1 h[ev]1 ! great law ( num]ical h>monic ratio rema9s unalt]able1 & a prop] application ( x 9 ! sci5ce ( art w nev] fail to be z productive ( effect1 z its op]ation 9 nature is univ]sal1 c]ta91 & cont9ual4 ,,! ,,sci5ce ,,( ,,beauty1 ,,z ,,develop$ ,,9 ,,! ,,human ,,head ,,& ,,c\nt5ance4 ,! mo/ rem>kable *>act]i/ics ( ! human head & c\nt5ance are ! globul> =m ( ! cranium1 unit$ z x is ) ! prolate sph]oidal =m produc$ by ! p>ts :i* con/itute ! face1 & ! approximation ( ! pr(ile to ! v]tical2 = 9 none ( ! l[] animals does ! skull pres5t s ne> a resemblance to a comb9ation ( ^! geometric =ms1 nor ! plane ( ! face to ?is direction4 ,we also f9d t al?\gh ^! peculi> *>act]i/ics are v>i\sly modifi$ among ! num]\s races ( mank9d1 yet "o law appe>s to gov]n ! beauty ( ! :ole4 ,! highe/ & mo/ cultivat$ ( ^! races1 h[ev]1 pres5t only an approximation to ! p]fect developm5t ( ^? di/+ui%+ m>ks ( humanity2 & !re=e ! beauty ( =m & proportion :i* 9 nature *>act]ises ! human head & c\nt5ance1 exhibits only a p>tial developm5t ( ! h>monic law ( visible beauty4 ,on ! o!r h&1 we f9d t1 9 _! sculpture1 ! anci5t ,greeks surpass$ ord9>y nature1 & produc$ 9 _! beau ideal a species ( beauty free f ! imp]fections & peculi>ities t con/itute ! individuality by :i* ! c\nt5ances ( m5 are di/+ui%$ f ea* o!r4 ,x may be requisite "h to rem>k1 t ?is species ( beauty is indep5d5t ( ! m intellectual quality ( expression4 ,= z ,sir ,*>les ,bell has said1 8,beauty ( c\nt5ance may be def9$ 9 words1 z well z demon/rat$ 9 art4 ,a face may be beautiful 9 sleep1 & a /atue )\t expression may be highly beautiful4 ,b x w be said !re is expression 9 ! sleep+ figure or 9 ! /atue4 ,is x n r t we see 9 ^! ! capacity = expression8--t our m9ds are active 9 imag9+ :at may be ! motions ( ^! features :5 awake or animat$8 ,?us1 we speak ( an expressive face be=e we h se5 a movem5t grave or *e]ful1 or any indication 9 ! features ( :at prevails 9 ! he>t40 ,?is capacity = expression c]ta9ly enhances our admiration ( ! human c\nt5ance2 b x is m a concomitant ( ! prim>y cause ( its beauty ?an ! cause itself4 ,?is cause re/s on t simple & secure basis--! h>monic law ( nature2 = ! ne>] ! c\nt5ance approximates to an h>moni\s comb9ation ( ! mo/ p]fect figures 9 geometry1 or r ! m its g5]al =m & ! relation ( its individual p>ts are arrang$ 9 ob$i5ce to t law1 ! high] its degree ( beauty1 & ! great] its capacity = ! expression ( ! passions4 ,v>i\s attempts h be5 made to def9e geometrically ! diff]5ce betwe5 ! ord9>y & ! ideal beauty ( ! human head & c\nt5ance1 ! mo/ prom95t ( :i* is t ( ,camp]4 ,he trac$1 ^u a pr(ile ( ! skull1 a l9e 9 a horizontal direction1 pass+ ?r\gh ! =am5 ( ! e> & ! ext]ior m>g9 ( ! sockets ( ! front tee? ( ! upp] jaw1 ^u :i* he rais$ an oblique l9e1 tang5tial to ! m>g9 ( ^! sockets1 & to ! mo/ prom95t "p ( ! =ehead4 ,agreeably to ! obliquity ( ?is l9e1 he det]m9$ ! relative proportion ( ! areas occupi$ by ! bra9 & by ! face1 & h5ce inf]r$ ! degree ( intellect4 ,:5 he appli$ ?is measurem5t to ! heads ( ! antique /atues1 he f\nd ! angle mu* great] ?an 9 ord9>y nature2 b t ?is simple fact af=d$ no rule = ! reproduction ( ! ideal beauty ( anci5t ,greek art1 is v evid5t f ! heads & c\nt5ances by :i* 8 treatise is illu/rat$4 ,sir ,*>les ,bell ju/ly rem>ks1 t al?\gh1 by ,camp]'s me?od1 ! =ehead may be ?r[n =w>d1 yet1 :ile ! features ( common nature are pres]v$1 we refuse to ackn[l$ge a simil>ity to ! beautiful =ms ( ! antique m>bles4 8,x is true10 he says1 8t1 by advanc+ ! =ehead1 x is rais$1 ! face is %ort5$1 & ! eye br\ght to ! c5tre ( ! head4 ,b ) all ?is1 !re is mu* want+--t :i* measurem5t1 or a m]e l9e1 w n %ew u40--8,! tru? is1 t we are m mov$ by ! features ?an by ! =m ( ! :ole head4 ,unless !re be a con=mity 9 e feature to ! g5]al %ape ( ! head1 ?r[+ ! =ehead =w>d on ! face produces de=mity2 & ! "q returns ) full =ce--,h[ is x t we are l$ to conc$e t ! antique head ( ! ,apollo1 or ( ! ,jupit]1 is beautiful :5 ! facial l9e makes a hundr$ degrees ) ! horizontal l9e8 ,9 o!r words--,h[ d we admit t to be beautiful :i* is n natural8 ,simply = ! same reason t1 if we discov] a brok5 portion ( an antique1 a nose1 or a *9 ( m>ble1 we c say1 )\t delib]ation--,?is mu/ h belong$ to a "w ( antiquity2 :i* proves t ! "* is di/+ui%able 9 e "p--9 ea* feature1 z well z 9 ! :ole head40 ,dr ,ok5 says ^u ?is subject3#ag--8,! face is beautiful ^: nose is p>allel to ! sp9e4 ,no human face has gr[n into ?is e/ate2 b e nose makes an acute angle ) ! sp9e4 ,! facial angle is1 z is well kn[n1 #hj4 ,:at1 z yet1 no man has rem>k$1 & :at is n to be rem>k$1 ei!r1 )\t our view ( ! cranial signification1 ! old ma/]s h felt ?r\gh inspiration4 ,!y h n only made ! facial angle a "r angle1 b h ev5 /epp$ beyond ?is--! ,romans go+ up to #if1 ! ,greeks ev5 to #ajj4 ,:5ce comes x t ?is unnatural face ( ! ,grecian works ( art is /ill m beautiful ?an t ( ! ,roman1 :5 ! latt] comes ne>] to nature8 ,! reason !re( resides 9 ! fact ( ! ,grecian arti/ic face repres5t+ nature's design m ?an t ( ! ,roman2 =1 9 ! =m]1 ! nose is plac$ q p]p5dicul>1 or p>allel to ! sp9al cord1 & ?us returns :i!r x has be5 d]iv$40 ,o!r v>i\s & conflict+ op9ions ^u ?is subject h be5 giv5 to ! _w2 b we f9d t ! pr9ciple f :i* arose ! ideal beauty ( ! head & c\nt5ance1 z repres5t$ 9 works ( anci5t ,greek art1 is /ill a matt] ( dispute4 ,:51 h[ev]1 we exam9e c>efully a f9e specim51 we f9d its beauty & gr&eur to dep5d m ^u ! degree ( h>mony among/ its p>ts1 z to _! relative proportions & mode ( arrangem5t1 ?an ^u _! excell5ce tak5 individually4 ,x is1 !re=e1 cle> t ^? 7& !y are _m7 :o attribute ! beauty ( anci5t ,greek sculpture m]ely to a selection ( p>ts f v>i\s models1 mu/ be 9 error4 ,no assemblage ( p>ts f ord9>y nature c\ld h produc$ its pr9cipal *>act]i/ic1 ! excess 9 ! angle ( ! facial l9e1 mu* less c\ld x h l$ to t exquisite h>mony ( p>ts by :i* x is s em95tly di/+ui%$2 nei!r c we reasonably agree ) ,dr ,ok5 & o!rs1 :o ass]t t x 0 produc$ by an exclusive degree ( ! inspiration ( g5ius among/ ! ,greek p dur+ a c]ta9 p]iod4 ,t ! inspiration ( g5ius1 comb9$ ) a c>eful /udy ( nature1 7 ess5tial elem5ts 9 ! production ( ! great works :i* h be5 h&$ d[n to u1 no "o w d5y2 b ^! elem5ts h exi/$ 9 all ages1 :il/ ! ideal head belongs exclusively to ! ,greeks dur+ ! p]iod 9 :i* ! s*ools ( ,py?agoras & ,plato 7 op54 ,is x n1 !re=e1 reasonable to suppose1 t1 besides g5ius & ! /udy ( nature1 ano!r elem5t 0 employ$ 9 ! production ( ?is excell5ce1 & t ?is elem5t arose f ! precise ma!matical doctr9es taught 9 ! s*ools ( ^! philosoph]s8 ,an application ( ! great h>monic law seems to prove t !re is no object 9 nature 9 :i* ! sci5ce ( beauty is m cle>ly develop$ ?an 9 ! human head & c\nt5ance1 nor to ! repres5tations ( :i* ! same sci5ce is m easily appli$2 & x is to ! mode 9 :i* ?is is done t ! v>ieties ( sex & "* may be imp>t$ to works ( art4 ,hav+ gone into full detail1 & giv5 ample illu/rations 9 a =m] "w1#ah x is unnecess>y = me to ent] ^u t "p ( ! subject 9 ?is rsum2 b only to %ew ! typical /ructure ( beauty by :i* ?is noble "w ( creation is di/+ui%$4 ,! angles :i* gov]n ! =m & proportions ( ! human head & c\nt5ance are1 ) ! "r angle1 a s]ies ( sev51 :i*1 f ! simplicity ( _! ratios to ea* o!r1 are calculat$ to produce ! mo/ p]fect concord4 ,x consi/s ( ! "r angle & its foll[+ p>ts-- ,tonic4 ,dom9ant4 ,m$iant4 ,subtonic4 77 77 77 77 77 77 ,^! angles1 & ! figures :i* belong to !m1 are ?us arrang$3-- ,sid5ote3 ,plate ,,ix4 ,! v]tical l9e ,a ,b 7,plate ,,ix4 fig4 #b7 repres5ts ! full l5g? ( ! head & face4 ,tak+ ?is l9e z ! great] axis ( an ellipse ( 771 su* an ellipse is describ$ ar\nd x4 ,?r\gh ,a ! l9es ,a ,g1 ,a ,k1 ,a ,l1 ,a ,m1 & ,a ,n1 are drawn on ea* side ( ! l9e ,a ,b1 mak+1 ) ! v]tical1 respectively ! angles ( 771 771 771 771 & 774 ,?r\gh ! po9ts ,g1 ,k1 ,l1 ,m1 & ,n1 :]e ^! /raight l9es meet ! curv$ l9e ( ! ellipse1 horizontal l9es are drawn by :i* ! foll[+ isosceles triangles are =m$1 ,a ,g ,g1 ,a ,k ,k1 ,a ,l ,l1 ,a ,m ,m1 & ,a ,n ,n4 ,f ! c5tre ,x ( ! equilat]al triangle ,a ,g ,g ! curvil9e> figure ( 771 viz41 ! circle1 is describ$ circumscrib+ t triangle4 ,! curvil9e> plane figures ( 77 & 771 respectively1 repres5t ! solid bodies ( :i* !y are sections1 viz41 a sph]e & a prolate sph]oid4 ,^! bodies1 f ! mann] 9 :i* !y are "h plac$1 are p>tially amalgamat$1 z %ewn 9 figures #a & #c ( ! same plate1 ?us repres5t+ ! =m ( ! human head & c\nt5ance1 bo? 9 _! ext]nal appe>ance & osse\s /ructure1 m correctly ?an !y c\ld be repres5t$ by any o!r geometrical figures4 ,?us1 ! angles ( 77 & 77 det]m9e ! typical =m4 ,f ea* ( ! po9ts u & n1 :]e ,a ,m cuts ,g ,g on bo? sides ( ,a ,b1 a circle is describ$ ?r\gh ! po9ts p & q1 :]e ,a ,k cuts ,g ,g on bo? sides ( ,a ,b1 & ) ! same radius a circle is describ$ f ! po9t a1 :]e ,k ,k cuts ,a ,b4 ,! circles u & n det]m9e ! position & size ( ! eyeballs1 & ! circle a ! wid? ( ! nose1 z also ! horizontal wid? ( ! m\?4 ,! l9es ,g ,g & ,k ,k also det]m9e ! l5g? ( ! jo9+s ( ! e> to ! head4 ,! l9es ,l ,l & ,m ,m det]m9e ! v]tical wid? ( ! m\? & lips :5 at p]fect repose1 & ! l9e ,n ,n ! sup]ior edge ( ! *94 ,?us simply are ! features arrang$ & proportion$ on ! facial surface4 ,x mu/1 h[ev]1 be borne 9 m9d1 t 9 treat+ simply ( ! /hetic beauty ( ! human head & c\nt5ance1 we h only to d ) ! ext]nal appe>ance4 ,9 ?is rese>*1 !re=e1 ! sy/em ( ,dr ,camp]1 ,dr ,ow51 & o!rs1 ^: inve/igations 7 m ( a physiological ?an an /hetic "*1 c be ( little s]vice2 because1 accord+ to t sy/em1 ! facial angle is det]m9$ by draw+ a l9e tang5tial to ! ext]ior m>g9 ( ! sockets ( ! front tee? ( ! upp] jaw1 & ! mo/ prom95t "p ( ! =ehead4 ,n[1 z ^! sockets are1 :5 ! skull is naturally clo!d1 & ! features 9 repose1 entirely conceal$ by ! upp] lip1 we mu/ take ! prom95t "p ( x1 in/ead ( ! sockets "u x1 9 ord] to det]m9e prop]ly ?is di/+ui%+ m>k ( humanity4 ,& ,i believe x w be f\nd1 t :5 ! head is prop]ly pois$1 ! ne>] ! angle :i* ?is l9e makes ) ! horizontal approa*es #ij1 ! m symmetrically beautiful w be ! g5]al arrangem5t ( ! p>ts 7see l9e y z1 figure #c1 ,plate ,,ix474 ,,! ,,sci5ce ,,( ,,beauty1 ,,z ,,develop$ ,,9 ,,! ,,=m ,,( ,,! ,,human ,,figure4 ,! mann] 9 :i* ?is sci5ce is develop$ 9 ! symmetrical proportions ( ! entire human figure1 is z rem>kable = its simplicity z x has be5 %ewn to be 9 ^? ( ! head & c\nt5ance4 ,hav+ gone into v full details1 & giv5 ample illu/ration 9 two =m] works#ai ^u ?is subject1 ,i may "h conf9e myself to ! illu/ration ( "o description ( figure1 & to a reit]ation ( "s facts /at$ 9 ^! works4 ,^! facts are1 #a/1 ,t on a giv5 l9e ! human figure is develop$1 z to its pr9cipal po9ts1 entirely by l9es drawn ei!r f ! extremities ( ?is l9e1 or f "s obvi\s or det]m9$ localities4 #b;d1 ,t ! angles :i* ^! l9es make ) ! giv5 l9e1 are all simple sub-multiples ( "s giv5 fundam5tal angle1 or be> to x a proportion expressible "u ! mo/ simple relations1 su* z ^? :i* con/itute ! scale ( music4 #c;d1 ,t ! cont\r is resolv$ into a s]ies ( ellipses ( ! same simple angles4 ,&1 #d?1 ,t ^! ellipses1 l ! l9es1 are incl9$ to ! fir/ giv5 l9e by angles :i* are simple sub-multiples ( ! giv5 fundam5tal angle4 ,f :i* f\r facts1 & agreeably to ! hypo!sis ,i h adopt$1 x results z a natural consequ5ce t ! only ef=t :i* ! m9d ex]cises ?r\gh ! eye1 9 ord] to put itself 9 possession ( ! data = =m+ its judgm5t1 is ?is1 t x comp>es ! angles ab\t a po9t1 & !reby appreciates ! simplicity ( _! relations4 ,9 select+ ! prom95t features ( a figure1 ! eye is n seek+ to comp>e _! relative di/ances--x is occupi$ solely ) _! relative positions4 ,9 trac+ ! cont\r1 9 l mann]1 x is n left 9 vague unc]ta9ty z to :at is ! curve :i* is pres5t$ to x2 unconsci\sly x feels ! complete ellipse develop$ be=e x2 & if t ellipse & its position are bo? =m$ by angles ( ! same simple relative value z ^? :i* aid$ its det]m9ation ( ! positions ( ! prom95t features1 x is satisfi$1 & f9ds ! symmetry p]fect4 ,mll]1 & o!r inve/igators into ! ar*ology ( art1 ref] to ! great difficulty :i* exi/s 9 discov]+ ! pr9ciples :i* ! anci5ts foll[$ 9 reg>d to ! proportions ( ! human figure1 f ! diff]5t sexes & *>act]s to :i* !y require to be appli$4 ,b 9 ! sy/em ?us f\nd$ ^u ! h>monic law ( nature1 no su* difficulty is felt1 = x is z applicable to ! massive proportions :i* *>act]ise ! anci5t repres5tations ( ! ,h]cules1 z to ! delicate & p]fectly symmetrical beauty ( ! ,v5us4 ,?is *ange is effect$ simply by an increase 9 ! fundam5tal angle4 ,= in/ance1 9 ! con/ruction ( a figure ( ! exact proportions ( ! ,v5us1 ! "r angle is adopt$4 ,b 9 ! con/ruction ( a figure ( ! massive proportions ( ! ,h]cules1 x is requisite to adopt an angle :i* be>s to ! "r angle ! ratio ( #f3e4 ,! adoption ( ?is angle ,i h %ewn 9 ano!r "w#bj to produce 9 ! ,h]cules ^? proportions :i* are s *>act]i/ic ( physical p[]4 ,! ellipses :i* gov]n ! outl9e1 be+ also =m$ ^u ! same l>g] class ( angles1 give ! cont\r ( ! muscles a m massive "*4 ,9 comp>+ ! male & female =ms ?us geometrically con/ruct$1 x w be f\nd t t ( ! female is m h>moni\sly symmetrical1 because ! "r angle is ! fundam5tal angle = ! trunk & ! limbs z well z = ! head & c\nt5ance2 :ile 9 t ( ! male1 ! "r angle is ! fundam5tal angle = ! head only4 ,x may also be obs]v$1 t1 f ! great] proportional wid? ( ! pelvis ( ! female1 ! c5tres ( t motion :i* ! heads ( ! ?igh bones p]=m 9 ! cotyloid cavities1 & ! c5tres ( t /ill m ext5sive range ( motion :i* ! arm is capable ( p]=m+ at ! %\ld] jo9ts1 are ne>ly 9 ! same l9e :i* det]m9es ! c5tral motion ( ! v]tebral column1 :ile ^? ( ! male are n2 consequ5tly all ! motions ( ! female are m graceful ?an ^? ( ! male4 ,?is diff]5ce betwe5 ! fundam5tal angles1 :i* imp>t to ! human figure1 on ! "o h&1 ! beauty ( fem99e proportion & cont\r1 & on ! o!r1 ! gr&eur ( mascul9e /r5g?1 be+ 9 ! ratio ( #e3f1 all[s ample latitude = ^? int]m$iate classes ( proportions :i* ! anci5ts imp>t$ to _! v>i\s o!r deities 9 :i* ^! two qualities 7 bl5d$4 ,i !re=e conf9e myself to an illu/ration ( ! ext]nal cont\r ( ! =m1 & ! relative proportions ( all ! p>ts ( a female figure1 su* z ^? ( ! /atues ( ! ,v5us ( ,melos & ,v5us ( ,m$ici4 ,! angles :i* gov]n ! =m & proportions ( su* a figure are1 ) ! "r angle1 a s]ies ( twelve1 z foll[s3-- ,tonic4 ,dom9ant4 ,m$iant4 ,subtonic4 ,sup]tonic4 77 77 77 77 77 77 77 77 77 77 77 ,^! angles are employ$ 9 ! con/ruction ( a diagram1 :i* det]m9es ! proportions ( ! p>ts ?r\gh\t ! :ole figure4 ,?us3-- ,sid5ote3 ,plate ,x4 ,let ! l9e ,a ,b 7fig4 #a1 plate ,x47 repres5t ! height ( ! figure to be con/ruct$4 ,at ! po9t ,a1 make ! angles ( ,c ,a ,d 771 ,f ,a ,g 771 ,h ,a ,i 771 ,k ,a ,l 771 & ,m ,a ,n 774 ,at ! po9t ,b1 make ! angles ,k ,b ,l 771 ,u ,b ,a 771 & ,o ,b ,a 774 ,?r\gh ! po9t ,k1 9 :i* ! l9es ,a ,k & ,b ,k int]sect "o ano!r1 draw ,p ,k ,o p>allel to ,a ,b1 & ?r\gh ,c ,f ,h & ,m1 :]e ?is l9e meets ,a ,c1 ,a ,f1 ,a ,h1 & ,a ,m1 draw ,c ,d1 ,f ,g1 ,h ,i1 & ,m ,n1 p]p5dicul> to ,a ,b2 draw also ,k ,l p]p5dicul> to ,a ,b2 jo9 ,b ,f & ,b ,h1 & ?r\gh ,c draw ,c ,e1 mak+ ) ,a ,b ! angle 771 :i* completes ! arrangem5t ( ! elev5 angles ^u ,a ,b2 = ,f ,b ,g is v ne>ly 771 & ,h ,b ,i v ne>ly 774 ,at ! po9t f1 :]e ,a ,c int]sects ,o ,b1 draw f a p]p5dicul> to ,a ,b2 & ?r\gh ! po9t i1 :]e ,b ,o int]sects ,m ,n1 draw ,s i ,t p>allel to ,a ,c4 ,?r\gh m1 :]e ,s i ,t int]sects ,f ,b1 draw m n2 ?r\gh 1 :]e ,s i ,t int]sects ,k ,b1 draw w2 ?r\gh ,t draw ,t g1 mak+ an angle ( 77 ) ,o ,p4 ,jo9 ,n ,p1 ,m ,b1 & g ,p1 & :]e ,n ,p int]sects ,k ,b1 draw ,q ,r p]p5dicul> to ,a ,b4 ,on ,a ,e z a diamet]1 describe a circle cutt+ ,a ,c 9 r1 & draw r o p]p5dicul> to ,a ,b4 ,) ,a o & o r z semi-axes1 describe ! ellipse ,a r e1 cutt+ ,a ,h 9 t2 & draw t u p]p5dicul> to ,a ,b4 ,) ,a u & t u1 z semi-axes describe ! ellipse ,a t d4 ,on a ,l1 z major axis1 describe ! ellipse ( 774 ,= ! side aspect or pr(ile ( ! figure ! diagram is ?us con/ruct$-- ,on "o side ( a l9e ,a ,b 7fig4 #b1 ,plate ,x47 con/ruct ! rectil9e> portion ( a diagram ! same z fig4 #a4 ,?r\gh i draw ,w ,y p>allel to ,a ,b1 & draw ,a z p]p5dicul> to ,a ,b4 ,make ,w a equal to ,a a 7fig4 #a71 & on a l1 z major axis1 describe ! ellipse ( 774 ,?r\gh a draw a p p>allel to ,a ,f1 & ?r\gh p draw p t p]p5dicul> to ,w ,y4 ,?r\gh a draw f a u p]p5dicul> to ,w ,y4 ,^u a diamet] equal to ,a ,e describe a circle ^: circumf]5ce %all t\* ,a ,b & ,a z4 ,) semi-axes equal to ,a o & o r 7fig4 #a71 describe an ellipse ) its major axis p>allel to ,a ,b1 & its circumf]5ce t\*+ ,o ,p & z ,a4 ,sid5ote3 ,plate ,,xi4 ,?us simply are ! diagrams ( ! g5]al proportions ( ! human figure1 z view$ 9 front & 9 pr(ile1 con/ruct$2 & ,plate ,,xi4 gives ! cont\r 9 bo? po9ts ( view1 z compos$ entirely ( ! curvil9e> figures ( 771 771 771 771 & 774 ,fur!r detail "h w\ld be out ( place1 & ,i %all !re=e ref] ^? :o require x to ! ,app5dix1 or ! m elaborate works to :i* ,i h already ref]r$4 ,! beauty d]iv$ f proportion1 imp>t$ by ! sy/em "h po9t$ out1 & f a cont\r ( curves d]iv$ f ! same h>monic angles1 is n conf9$ to ! human figure1 b is f\nd 9 v>i\s m9or degrees ( p]fection 9 all ! organic =ms ( nature1 :e!r animate or inanimate1 ( :i* ,i h 9 o!r works giv5 _m examples4#ba ,,! ,,sci5ce ,,( ,,beauty1 ,,z ,,develop$ ,,9 ,,col\rs4 ,!re is n among/ ! v>i\s ph5om5a ( nature "o t m readily excites our admiration1 or makes on ! m9d a m vivid impression ( ! ord]1 v>iety1 & h>moni\s beauty ( ! creation1 ?an t ( col\r4 ,on ! g5]al l&scape ?is ph5om5on is display$ 9 ! production ( t species ( h>mony 9 :i* col\rs are s v>i\sly bl5d$1 & 9 :i* !y are by light1 %ade1 & di/ance modifi$ 9 su* an inf9ity ( gradation & hue4 ,al?\gh g5ius is cont9ually /ruggl+1 ) b p>tial success1 to imitate ^? effects1 yet1 ?r\gh ! ,div9e b5efic5ce1 all ^: organs ( sight are 9 an ord9>y degree ( p]fection c appreciate & enjoy !m4 ,9 w9t] ?is pleasure is (t5 to a c]ta9 ext5t )drawn1 :5 ! col\rless sn[ alone clo!s ! surface ( ! e>?4 ,b ?is is only a pause 9 ! g5]al h>mony1 :i*1 z ! spr+ returns1 addresses itself ! m pleas+ly to our p]ception 9 its v]nal melody1 :i*1 gradually resolv+ itself into ! full ri* hues ( luxuriant beauty exhibit$ 9 ! foliage & fl[]s ( summ]1 subsequ5tly rises into ! m vivid & p[]ful h>monies ( autumn's col\r+4 ,?us ! eye is prep>$ aga9 to enjoy t re/ :i* su* excit+ causes may be said to h r5d]$ necess>y4 ,:5 we pass f ! g5]al col\r+ ( nature to t ( p>ticul> objects1 we are aga9 wrapt 9 wond] & admiration by ! beauty & h>mony :i* s con/antly1 & 9 su* inf9ite v>iety1 pres5t !mselves to our view1 & :i* are s (t5 f\nd comb9$ 9 ! mo/ m9ute objects4 ,& ! sy/ematic ord] & uni=mity p]ceptible amid/ ?is endless v>iety 9 ! col\r+ ( animate & inanimate nature is ?us ano!r *>act]i/ic ( beauty equally preval5t ?r\gh\t creation4 ,by ?is uni=mity 9 col\r1 v>i\s species ( animals are (t5 di/+ui%$2 & 9 ea* individual ( mo/ ( ^! species1 h[ mu* is ?is beauty enhanc$ :5 ! uni=mity prevails 9 ! resemblance ( _! lat]al halves6 ,! human c\nt5ance exemplifies ?is 9 a /rik+ mann]2 ! slighte/ v>iety ( col\r betwe5 "o & ano!r ( ! d\ble p>ts is at once de/ructive ( its symmetrical beauty4 ,_m ( ! l[] animals1 :e!r inhabitants ( ! e>?1 ! air1 or ! wat]1 owe mu* ( _! beauty to ?is k9d ( uni=mity 9 ! col\r ( ! furs1 fea!rs1 scales1 or %ells1 ) :i* !y are clo!d4 ,9 ! vegetable k+dom1 we f9d a great degree ( uni=mity ( col\r 9 ! leaves1 fl[]s1 & fruit ( ! same plant1 comb9$ ) all ! h>moni\s beauty ( v>iety :i* a little c>eful exam9ation develops4 ,9 ! col\rs ( m9]als1 too1 ! same may be obs]v$4 ,9 %ort1 9 ! beauty ( col\r+1 z 9 e o!r species ( beauty1 uni=mity & v>iety are f\nd to comb9e4 ,an appreciation ( col\r dep5ds1 9 ! fir/ place1 z mu* ^u ! physical p[]s ( ! eye 9 convey+ a prop] impression to ! m9d1 z t ( music on ^? ( ! e>4 ,b an e> = music1 or an eye = col\r1 are1 9 s f> z beauty is conc]n$1 errone\s expressions2 because !y are m]ely applicable to ! impression made ^u ! s5ses1 & d n ref] to ! /hetical pr9ciples ( h>mony1 by :i* beauty c alone be und]/ood4 ,a good eye1 comb9$ ) exp]i5ce1 may enable u to =m a correct idea z to ! purity ( an individual col\r1 or ( ! relative diff]5ce exi/+ betwe5 two sep>ate hues2 b ?is sort ( discrim9ation does n con/itute t k9d ( appreciation ( ! h>mony ( col\r by :i* we admire & enjoy its developm5t 9 nature & art4 ,! p[] ( p]ceiv+ & appreciat+ beauty ( any k9d1 is a pr9ciple inh]5t 9 ! human m9d1 :i* may be improv$ by cultivation 9 ! degree ( ! p]fection ( ! art s5ses4 ,great pa9s h be5 be/[$ on ! education ( ! e>1 9 assi/+ x to appreciate ! melody & h>mony ( s\nd2 b /ill mu* rema9s to be done 9 reg>d to ! cultivation ( ! eye1 9 appreciat+ col\r z well z =m4 ,x is true1 t !re are individuals ^: p[]s ( vision are p]fect1 9 s f> z reg>ds ! appreciation ( light1 %ade1 & configuration1 b :o are totally incapable ( p]ceiv+ effects produc$ by ! int]m$iate ph5om5on ( col\r1 e object appe>+ to !m ei!r :ite1 black1 or neutral gray2 o!rs1 :o are equally bl9d z to ! effect ( "o ( ! ?ree prim>y col\rs1 b see ! o!r two p]fectly1 ei!r s+ly or comb9$2 :ile !re are _m :o1 hav+ ! full physical p[] ( p]ceiv+ all ! v>ieties ( ! ph5om5on1 & :o are ev5 capable ( mak+ nice di/9ctions among/ a v>iety ( v>i\s col\rs1 are yet incapable ( appreciat+ ! /hetic quality ( h>mony :i* exi/s 9 _! prop] comb9ation4 ,x is ! same ) respect to ! effects ( s\nds ^u ! e>--"s h organs s con/itut$1 t notes above or bel[ a c]ta9 pit* are to !m inaudible2 :ile o!rs1 ) physical p[]s o!rwise p]fect1 are incapable ( appreciat+ ei!r melody or h>mony 9 musical composition4 ,b p]ceptions s imp]fectly con/itut$ are1 by ! goodness ( ! ,creator1 ( v r>e occurr5ce2 !re=e all attempts at improvem5t 9 ! sci5ce ( /hetics mu/ be suit$ to ! capacities ( ! g5]ality ( mank9d1 among/ :om ! p]ception ( col\r exi/s 9 a v>iety z great z t by :i* _! c\nt5ances are di/+ui%$4 ,arti/s n[ & !n appe> :o h ?is intuitive p]ception 9 su* p]fection1 t !y are capable ( transf]r+ to _! works ! mo/ beautiful h>monies & mo/ delicate gradations ( col\rs1 9 a mann] t no acquir$ k c\ld h enabl$ !m to imp>t4 ,to ^? :o possess su* a gift1 z well z to ^? to :om ! ord9>y p[]s ( p]ception are d5i$1 x w\ld be equally useless to (f] an explanation ( ! v>i\s modes 9 :i* ! h>mony ( col\r develops itself1 or to attempt a def9ition ( ! _m v>i\s col\rs1 hues1 t9ts1 & %ades1 aris+ out ( ! simple elem5ts ( ?is ph5om5on4 ,b to ^? ^: p[]s lie betwe5 ^! extremes1 be+ nei!r above nor bel[ cultivation1 su* an explanation & def9ition mu/ =m a /ep t[>ds ! improvem5t ( t inh]5t pr9ciple :i* con/itutes ! basis ( /hetical sci5ce4 ,al?\gh ! v>iety & h>mony ( col\r :i* nature is cont9ually pres5t+ to our view1 are app>5t to all ^: visual organs are 9 a natural /ate1 & ?us to ! g5]ality ( mank9d2 yet a k ( ! simplicity by :i* ?is v>iety & beauty are produc$1 is1 aft] ages ( philosophic rese>* & exp]im5tal inquiry1 only beg9n+ to be prop]ly und]/ood4 ,light may be consid]$ z an active1 & d>kness a passive pr9ciple 9 ! economy ( ,nature1 & col\r an int]m$iate ph5om5on aris+ f _! jo9t influ5ce2 & x is 9 ! ratios 9 :i* ^! prim>y pr9ciples act ^u ea* o!r1 by :i* ,i "h int5d to expla9 ! sci5ce ( beauty z evolv$ 9 col\r4 ,x has be5 usual to consid] col\r z an inh]5t quality 9 light1 & to suppose t col\r$ bodies absorb c]ta9 classes ( its rays1 & reflect or transmit ! rema9d]2 b x appe>s to me t col\r is m probably ! result ( c]ta9 modes 9 :i* ! opposite pr9ciples ( motion & re/1 or =ce & resi/ance1 op]ate 9 ! production1 refraction1 & reflection ( light1 & t ea* col\r is mutually relat$1 al?\gh 9 diff]5t degrees1 to ^! active & passive pr9ciples4 ,:ite & black are ! repres5tatives ( light & d>kness1 or activity & re/1 & are !re=e calculat$ z pigm5ts to r$uce col\rs & hues to t9ts & %ades4 ,hav+1 h[ev]1 fully illu/rat$ ! nature ( t9ts & %ades 9 a =m] "w1#bb ,i %all "h conf9e myself to col\rs 9 _! full int5sity--%ew+ ! v>i\s modifications :i* _! union ) ea* o!r produce1 along ) ! h>monic relations :i* ^! modifications be> to ! prim>ies1 & to ea* o!r 9 respect to w>m? & coolness ( tone1 z well z to light & %ade4 ,! prim>y col\rs are r$1 yell[1 & blue4 ,( ^!1 yell[ is mo/ alli$ to light1 & blue to %ade1 :ile r$ is neutral 9 ^! respects1 be+ equally alli$ to bo?4 ,9 respect to tone1 t ( r$ is w>m1 & t ( blue cool1 :ile ! tone ( yell[ is neutral4 ,! ratios ( _! relations to ea* o!r 9 ^! respects w appe> 9 ! h>monic scales to :i*1 = ! fir/ "t1 ,i am ab\t to subject col\rs1 & to sy/ematise _! v>i\s simple & comp\nd relations1 :i* are z foll[3-- ,f ! b9>y union ( ! prim>y col\rs1 ! second>y col\rs arise-- ,orange col\r1 f ! union ( yell[ & r$4 ,gre51 f ! union ( yell[ & blue4 ,purple1 f ! union ( r$ & blue4 ,f ! b9>y union ( ! second>y col\rs1 ! prim>y hues arise-- ,yell[-hue1 f ! union ( orange & gre54 ,r$-hue1 f ! union ( orange & purple4 ,blue-hue1 f ! union ( purple & gre54 ,f ! b9>y union ( ! prim>y hues1 ! second>y hues arise-- ,orange-hue1 f ! union ( yell[-hue & r$-hue4 ,gre5-hue1 f ! union ( yell[-hue & blue-hue4 ,purple-hue1 f ! union ( r$-hue & blue-hue4 ,ea* hue owes its *>act]i/ic di/9ction to ! proportionate pr$om9ance or subord9ation ( "o or o!r ( ! ?ree prim>y col\rs 9 its composition4 ,x foll[s1 t 9 e hue ( r$1 yell[ & blue are subord9ate2 9 e hue ( yell[1 r$ & blue are subord9ate2 & 9 e hue ( blue1 r$ & yell[ are subord9ate4 ,9 l mann]1 9 e hue ( gre51 r$ is subord9ate2 9 e hue ( orange1 blue is subord9ate2 & 9 e hue ( purple1 yell[ is subord9ate4 ,by ! union ( two prim>y col\rs1 9 ! production ( a second>y col\r1 ! nature ( bo? prim>ies is alt]$2 & z !re are only ?ree prim>y or simple col\rs 9 ! scale1 ! two t are unit$ h>monically 9 a comp\nd col\r1 =m ! natural contra/ to ! rema9+ simple col\r4 ,not)/&+ all ! v>iety t ext5ds beyond ! six positive col\rs1 x may be said t !re are only ?ree prop] contra/s ( col\r 9 nature1 & t all o!rs are simply modifications ( ^!4 ,pure r$ is ! mo/ p]fect contra/ to pure gre52 because x is *>act]is$ among/ ! prim>y col\rs by w>m? ( tone1 :ile among/ ! second>y col\rs gre5 is di/+ui%$ by coolness ( tone1 bo? be+ equally relat$ to ! prim>y elem5ts ( light & %ade4 ,pure yell[ is ! mo/ p]fect contra/ to pure purple2 because x is *>act]is$ among/ ! prim>y col\rs z mo/ alli$ to light1 :il/ pure purple is *>act]is$ among/ ! second>ies z mo/ alli$ to %ade1 bo? be+ equally neutral z to tone4 ,pure blue is ! mo/ p]fect contra/ to pure orange2 because x is *>act]is$ among/ ! prim>y col\rs z n only ! mo/ alli$ to %ade1 b z be+ ! coole/ 9 tone1 :il/ pure orange is *>act]is$ among/ ! second>ies z be+ ! mo/ alli$ to light & ! w>me/ 9 tone4 ,! same pr9ciple op]ates ?r\gh\t all ! modifications ( ^! prim>y & second>y col\rs4 ,su* is ! simple nature ( contra/ ^u :i* ! beauty ( col\r+ ma9ly dep5ds4 ,x be+ n[ e/abli%$ z a sci5tific fact1 t ! effect ( light ^u ! eye is ! result ( an e!real action1 simil> to ! atmosph]ic action by :i* ! effect ( s\nd is produc$ ^u ! e>2 also1 t ! v>i\s col\rs :i* light assumes are ! effect ( c]ta9 modifications 9 ?is e!real action2--j z ! v>i\s s\nds1 :i* con/itute ! scale ( musical notes1 are kn[n to be ! effect ( c]ta9 modifications 9 ! atmosph]ic action by :i* s\nds 9 g5]al are produc$3 ,!re=e1 z h>mony may ?us be impress$ ^u ! m9d ?r\gh ei!r ( ^! two art s5ses--he>+ & see+--! pr9ciples :i* gov]n ! modifications 9 ! e!real action ( light1 s z to produce ?r\gh ! eye ! effect ( h>mony1 _c be suppos$ to diff] f ^? pr9ciples :i* we "k gov]n ! modifications ( ! atmosph]ic action ( s\nd1 9 produc+ ?r\gh ! e> a l effect4 ,i %all !re=e endeav\r to illu/rate ! sci5ce ( beauty z evolv$ 9 col\rs1 by =m+ scales ( _! v>i\s modifications agreeably to ! same ,py?agorean sy/em ( num]ical ratio f :i* ! h>monic elem5ts ( beauty 9 s\nds 7 orig9ally evolv$1 & by :i* ,i h endeav\r$ 9 ?is1 z 9 previ\s works1 to sy/ematise ! h>monic beauty ( =ms4 ,illu/ration ,x w be obs]v$1 t ) a view to avoid complexity z mu* z possible1 ,i h1 9 ! arrangem5t ( ! above s]ies ( scales1 n only conf9$ myself to ! m]ely elem5t>y p>ts ( ! ,py?agorean sy/em1 b h left out ! h>monic modifications ^u 77 & 771 9 ord] t ! ari?metical progression might n be int]rupt$4#bc ,! above elem5t>y process w1 ,i tru/1 be f\nd suffici5t to expla9 ! progress1 by h>monic union1 ( a prim>y col\r to a ton$ gray1 & h[ ! simple & comp\nd col\rs naturally arrange !mselves into ! elem5ts ( five scales1 ! p>ts ( :i* cont9ue f prim>y to second>y col\r2 f second>y col\r to prim>y hue2 f prim>y hue to second>y hue2 f second>y hue to prim>y-ton$ gray2 & f prim>y-ton$ gray to second>y-ton$ gray 9 ! simple ratio ( #b3a2 !reby produc+ a s]ies ( ! mo/ beautiful & p]fect contra/s4 ,! natural arrangem5t ( ! prim>y col\rs ^u ! sol> spectrum is r$1 yell[1 blue1 & ,i h !re=e adopt$ ! same arrangem5t on ! pres5t occasion4 ,r$ be+1 consequ5tly1 ! fir/ tonic1 & blue ! second1 ! divisions express ! num]ical ratios :i* ! col\rs be> to "o ano!r1 9 respect to t col\rific p[] = :i* r$ is pre-em95t4 ,?us1 yell[ is to r$1 z #b3c2 blue to yell[1 z #c3d2 purple to orange1 z #e3f2 & gre5 to purple1 z #f3g4 ,! foll[+ s]ies ( complet$ scales are arrang$ ^u ! =ego+ pr9ciple1 ) ! natural connect+ l9ks ( r$-orange1 yell[-orange1 yell[-gre51 & blue-gre51 introduc$ 9 _! prop] places4 ,! appropriate t]m9ology ( musical notes has be5 adopt$1 & ! scales are compos$ z foll[s3-- ,scale ,i4 consi/s ( prim>y & second>y col\rs2 ,scale ,,ii4 ( second>y col\rs & prim>y hues2 ,scale ,,iii4 ( prim>y & second>y hues2 ,scale ,,iv4 ( second>y hues & prim>y-ton$ grays2 & ,scale ,v4 ( prim>y & second>y-ton$ grays2 ,all ! p>ts 9 ea* ( ^! scales1 f ! fir/ tonic to ! second1 relate to ! same p>ts ( ! scale bel[ !m 9 ! simple ratio ( #b3a2 & s]ially to ! fir/ tonic 9 ! foll[+ ratios3-- #h3i1 #d3e1 #c3d1 #b3c1 #c3e1 #d3g1 #h3ae1 #a3b4 ,fir/ ,s]ies ( ,scales4 ---------------------------------------- ------------------------- ,tonic4 ,sup]tonic4 ,m$iant4 ,subdom9ant4 ,dom9ant4 ,subm$iant4 ,subtonic4 ,semi-subtonic4 ,tonic4 ---------------------------------------- ------------------------- ,i4 77 77 77 77 77 77 77 77 77 ,r$4 ,r$- ,orange4,yell[-,yell[4,yell[-,gre54,blue - ,blue4 orange4 orange4 gre54 gre54 ---------------------------------------- ------------------------- ,,ii4 77 77 77 77 77 77 77 77 77 ,gre54,blue- ,blue ,blue- ,purple ,r$- ,r$ ,r$- ,orange4 gre5 hue4 purple hue4 purple hue4 orange hue4 hue4 hue4 hue4 ---------------------------------------- ------------------------- ,,iii477 77 77 77 77 77 7777 77 ,r$ ,r$- ,orange ,yell[-,yell[ ,yell[-,gre5 ,blue- ,blue hue4 orange hue4 orange hue4 gre5 hue4 gre5 hue4 hue4 hue4 hue4 hue4 ---------------------------------------- ------------------------- ,,iv4 7777 77 77 77 77 7777 77 ,gre5 ,blue- ,blue- ,blue- ,purple ,r$- ,r$- ,r$- ,orange hue4 gre5- ton$ purple-hue4 purple-ton$ orange-hue4 ton$ gray4 ton$ ton$ gray4 ton$ gray4 gray4 gray4 gray4 ---------------------------------------- ------------------------- ,v4 7777 77 7777 777777 77 ,r$- ,r$- ,orange-,yell[-,yell[-,yell[-,gre5- ,blue- ,blue- ton$ orange-ton$ orange-ton$ gre5- ton$ gre5-ton$ gray4 ton$ gray4 ton$ gray4 ton$ gray4 ton$ gray4 gray4 gray4 gray4 gray4 ---------------------------------------- ------------------------- ,to ! scales ( *romatic p[] ,i add ano!r s]ies ( scales1 9 :i* yell[1 be+ ! fir/ tonic1 & blue ! second1 ! num]ical divisions express ! ratios :i* ! col\rs 9 ea* scale be> to "o ano!r 9 respect to light & %ade4 ,?us r$ is to yell[1 9 respect to light1 z #b3c2 blue to r$1 z #c3d2 gre5 to orange1 z #e3f1 & purple to gre51 z #f3g4 ,^! scales may !re=e be t]m$ scales = ! col\r-bl9d1 because1 9 comp>+ col\rs1 ^? ^: sight is ?us defective1 naturally comp>e ! ratios ( ! light & %ade ( :i* diff]5t col\rs are prim>ily con/itut$4 ,illu/ration ,! foll[+ is a s]ies ( five complete scales ( ! h>monic p>ts into :i* ! light & %ade 9 col\rs may be divid$ 9 ea* scale accord+ to ! above arrangem5t3-- ,second ,s]ies ( ,scales4 ---------------------------------------- ------------------------- ,tonic4 ,sup]tonic4 ,m$iant4 ,subdom9ant4 ,dom9ant4 ,subm$iant4 ,subtonic4 ,semi-subtonic4 ,tonic4 ---------------------------------------- ------------------------- ,i4 77 77 77 77 77 77 77 77 77 ,yell[4,yell[-,orange4,r$- ,r$4 ,r$- ,purple4,blue- ,blue4 orange4 orange4 purple4 purple4 ---------------------------------------- ------------------------- ,,ii4 77 77 77 77 77 77 77 77 77 ,purple4,blue- ,blue ,blue- ,gre54,yell[-,yell[ ,yell[-,orange purple hue4 gre5 gre5 hue4 orange hue4 hue4 hue4 hue4 ---------------------------------------- ------------------------- ,,iii477 77 77 77 7777 77 77 77 ,yell[ ,yell[-,orange ,r$- ,r$ ,r$- ,purple ,blue- ,blue hue4 orange hue4 orange hue4 purple hue4 purple hue4 hue4 hue4 hue4 hue4 ---------------------------------------- ------------------------- ,,iv4 77 77 77 77 7777 77 77 77 ,purple ,blue- ,blue- ,blue- ,gre5 ,yell[-,yell[-,yell[-,orange hue4 purple-ton$ gre5- hue4 gre5- ton$ orange-hue4 ton$ gray4 ton$ ton$ gray4 ton$ gray4 gray4 gray4 gray4 ---------------------------------------- ------------------------- ,v4 77 77 77 77777777 77 77 ,yell[-,yell[-,orange-,r$- ,r$- ,r$- ,purple-,blue- ,blue- ton$ orange-ton$ orange-ton$ purple-ton$ gre5- ton$ gray4 ton$ gray4 ton$ gray4 ton$ gray4 ton$ gray4 gray4 gray4 gray4 gray4 ---------------------------------------- ------------------------- ,%\ld ,i be correct 9 arrang+ col\rs ^u scales id5tical ) ^? ^u :i* musical notes h be5 arrang$1 & 9 assum+ t col\rs h ! same ratios to ea* o!r1 9 respect to _! h>monic p[] ^u ! eye1 :i* musical notes h 9 respect to _! h>monic p[] ^u ! e>1 ! col\ri/ may yet be enabl$ to imp>t h>monic beauty to 8 works ) z mu* c]ta9ty & ease1 z ! musician imp>ts ! same quality to 8 compositions3 = ! col\ri/ has no m "r to tru/ exclusively to 8 eye 9 ! arrangem5t ( col\rs1 ?an ! musician has to tru/ exclusively to 8 e> 9 ! arrangem5t ( s\nds4 ,we f9d1 9 comp>+ ! dom9ant p>ts 9 ! fir/ & second scales ( ! second s]ies1 t !y are equal z to light & %ade1 s t _! relative p[]s ( contra/ dep5d entirely ^u col\r4 ,h5ce x is t r$ & gre5 are ! two col\rs1 ! diff]5ce betwe5 :i* ! col\r-bl9d are lea/ able to appreciate4 ,pr(essor ,george ,wilson1 9 8 excell5t "w1 8,rese>*es on ,col\r-,bl9dness10 m5tions ! case ( an engrav]1 :i* proves ! p[] ( ! eye 9 be+ able to appreciate ^! orig9al con/itu5ts ( col\r1 irrespective ( ! int]m$iate ph5om5on ( tone4 ,?is engrav]1 in/ead ( express+ regret on acc\nt ( 8 be+ col\r-bl9d1 obs]v$ to ! pr(essor1 8,my defective vision is1 to a c]ta9 ext5t1 a useful & valuable quality4 ,?us1 an engrav] has two negatives to deal )1 i4e41 :ite & black4 ,n[1 :5 ,i look at a picture1 ,i see x only 9 :ite & black1 or light & %ade1 or1 z arti/s t]m x1 ! effect4 ,i f9d at times _m ( my bro!r engrav]s 9 d\bt h[ to translate c]ta9 col\rs ( pictures1 :i* to me are matt]s ( decid$ c]ta9ty & ease4 ,?us to me x is valuable40 ,! col\r-bl9d are !re=e z incapable ( receiv+ pleasure f ! h>moni\s union ( v>i\s col\rs1 z ^? :o1 to use a common t]m1 h no e> = music1 are ( be+ gratifi$ by ! 8melody ( sweet s\nds40 ,! g5]ality ( mank9d are1 h[ev]1 capable ( appreciat+ ! h>mony ( col\r :i*1 l t ( bo? s\nd & =m1 arises f ! simultane\s exhibition ( opposite pr9ciples hav+ a ratio to ea* o!r4 ,^! pr9ciples are 9 cont9ual op]ation ?r\gh\t nature1 & f !m we (t5 d]ive pleasure )\t be+ consci\s ( ! cause4 ,all :o are n col\r-bl9d mu/ h felt !mselves /ruck ) ! h>monic beauty ( a cl\dless sky1 al?\gh 9 x !re is no configuration1 & at fir/ sight app>5tly b "o col\r4 ,n[1 z we "k t !re c be no m impression ( h>mony made ^u ! m9d by look+ ^u a s+le col\r1 ?an !re c\ld be by li/5+ to a s+le cont9u$ musical note1 h[ev] sweet its tone1 we are apt at fir/ to imag9e t ! organ ( vision has1 9 "s measure1 convey$ a false impression to ! m9d4 ,b x has n done s2 = light1 :5 reflect$ f ! atmosph]e1 produces ^? cool tones ( blue1 gray1 & purple1 :i* seem to clo! ! di/ant m\nta9s2 b1 :5 transmitt$ ?r\gh ! same atmosph]e1 x produces ^? num]\s w>m t9ts1 ! mo/ int5se ( :i* give ! gorge\s effects :i* s (t5 accompany ! sett+ sun4 ,we h1 !re=e1 9 ! upp] "p ( a cle> sky1 :]e ! atmosph]e may be said to be illum9at$ pr9cipally by reflection f ! surface ( ! e>?1 a comp>atively cool tone ( blue1 ! result ( reflection1 :i* gradually bl5ds into ! w>m t9ts1 ! result ( transmission ?r\gh ! same atmosph]e4 ,su* a composition ( h>moni\s col\r+ is to ! eye :at ! voice ( ! s(t brea? ( summ] among/ ! trees1 ! hum ( insects on a sultry day1 or ! simple h>mony ( ! olian h>p1 is to ! e>4 ,to su* a composition ( *romatic h>mony mu/ also be ref]r$ ! univ]sal concurr5ce ( mank9d 9 appreciat+ ! peculi> beauty ( :ite m>ble /atu>y4 ,t ! pr9cipal con/itu5t ( beauty 9 su* works ought to be h>mony ( =m1 no "o w d5y2 b ?is is n ! only elem5t1 z appe>s f ! fact1 t a ca/ 9 pla/] ( ,p>is1 ( a f9e :ite m>ble /atue1 al?\gh id5tical 9 =m1 is f> less beautiful ?an ! orig9al4 ,n[ ?is und\bt$ly mu/ be ! consequ5ce ( its hav+ be5 *ang$ f a semi-transluc5t sub/ance1 :i*1 l ! atmosph]e1 c transmit z well z reflect light1 to an opaque sub/ance1 :i* c only reflect x4 ,?us ! opposite pr9ciples ( *romatic w>m? & coolness are equally balanc$ 9 :ite m>ble--! "o be+ ! natural result ( ! p>tial transmission ( light1 & ! o!r t ( its reflection4 ,z a s]ies ( col\r$ illu/rations w\ld be beyond ! scope ( ?is rsum1 ,i may ref] ^? :o wi% to prosecute ! inquiry1 ) ! assi/ance ( su* a s]ies1 to my publi%$ works ^u ! subject4#bd ,,! ,,sci5ce ,,( ,,beauty1 ,,appli$ ,,to ,,! ,,=ms ,,& ,,proportions ,,( ,,anci5t ,,grecian ,,vases ,,& ,,ornam5ts4 ,9 exam9+ ! rema9s ( ! ornam5tal works ( ! anci5t ,greek arti/s1 x appe>s highly probable t ! h>mony ( _! proportions & melody ( _! cont\r are equally ! result ( a sy/ematis$ application ( ! same h>monic law4 ,?is probability n be+ fully elucidat$ 9 any ( my =m] works1 ,i w require to g into "s detail on ! pres5t occasion4 ,i take = my fir/ illu/ration an unexceptionable example1 viz43-- ,! ,portl& ,vase4 ,al?\gh ?is beautiful specim5 ( anci5t art 0 f\nd ab\t ! middle ( ! sixte5? c5tury1 inclos$ 9 a m>ble s>cophagus )9 a sepul*ral *amb] "u ! ,monte del ,grano1 ne> ,rome1 & al?\gh ! date ( its production is unkn[n1 yet its be+ a "w ( anci5t ,grecian art is und\bt$2 & ! exquisite beauty ( its =m has be5 univ]sally ackn[l$g$1 bo? dur+ ! "t x rema9$ 9 ! palace ( ! ,b>b]9i family at ,rome1 & s9ce x 0 add$ to ! treasures ( ! ,briti% ,museum4 ,! =ms & proportions ( ?is gem ( art appe> to me to yield an ob$i5ce to ! great h>monic law ( nature1 simil> to t :i* ,i h in/anc$ 9 ! proportions & cont\r ( ! be/ specim5s ( anci5t ,grecian ar*itecture4 ,sid5ote3 ,plate ,,xii4 ,let ! l9e ,a ,b 7,plate ,,xii47 repres5t ! full height ( ! vase4 ,?r\gh ,a draw ,a a1 & ?r\gh ,b draw ,b b indef9itely1 ,a a mak+ an angle ( 771 & ,b b an angle ( 771 ) ! v]tical4 ,?r\gh ! po9t ,c1 :]e ,a a & ,b b int]sect "o ano!r1 draw ,d ,c ,e v]tical4 ,?r\gh ,a ,c & ,b respectively1 draw ,a ,d1 ,c ,f1 & ,b ,e horizontal4 ,draw simil> l9es on ! o!r side ( ,a ,b1 & ! rectil9e> portion ( ! diagram is complete4 ,! curvil9e> cont\r may be ?us add$3-- ,take a cut-out ellipse ( 771 ^: great] axis is equal to ! l9e ,a ,b1 & #a/4 ,place x ^u ! diagram1 s t its circumf]5ce may be tang5tial to ! l9es ,c ,e & ,c ,f1 & its great] axis m n may make an angle ( 77 ) ! v]tical1 & trace its circumf]5ce4 #b;d4 ,place x ) its circumf]5ce tang5tial to t ( ! fir/ at ! po9t m1 :ile its great] axis 7( :i* o p is a "p7 is 9 ! horizontal1 & trace ! portion ( its circumf]5ce q o r4 #c;d4 ,place x ) its circumf]5ce tang5tial to t ( ! above at v1 :ile its great] axis 7( :i* u v is a "p7 makes an angle ( 77 ) ! v]tical1 & trace ! portion ( its circumf]5ce s v t4 ,?us ! curvil9e> cont\r ( ! body & neck are h>monically det]m9$4 ,! curve ( ! h&le may be det]m9$ by ! same ellipse plac$ s t its great] axis 7( :i* i k is a "p7 makes an angle ( 77 ) ! v]tical4 ,make simil> trac+s on ! o!r side ( ,a ,b1 & ! diagram is complete4 ,! inscrib+ rectangle ,d ,g ,e ,k is t ( 774 ,! outl9e result+ f ?is diagram1 n only is 9 p]fect agreem5t ) my recollection ( ! =m1 b ) ! measurem5ts ( ! orig9al giv5 9 ! 8,p5ny ,cyclopdia20 ( ! accuracy ( :i* !re c be no d\bt4 ,!y are /at$ ?us3--8,x is ab\t t5 in*es 9 height1 & beautifully curv$ f ! top d[nw>ds2 ! diamet] at ! top be+ ab\t ?ree in*es & a-half2 at ! neck or smalle/ "p1 two in*es2 at ! l>ge/ 7mid-height71 sev5 in*es2 & at ! bottom1 five in*es40 ,! h>monic elem5ts ( ?is beautiful =m1 !re=e1 appe> to be ! foll[+ p>ts ( ! "r angle3-- ,tonic4 ,dom9ant4 ,m$iant4 ,subm$iant4 77 77 77 77 77 77 ,:5 we reflect ^u ! v>iety ( h>monic ellipses t may be describ$1 & ! innum]able positions 9 :i* !y may be h>monically plac$ ) respect to ! horizontal & v]tical l9es1 z well z ^u ! v>i\s modes 9 :i* _! circumf]5ces may be comb9$1 ! v>iety :i* may be introduc$ among/ su* =ms z ! =ego+ appe>s almo/ endless4 ,my second example is t (-- ,an ,anci5t ,grecian ,m>ble ,vase ( a ,v]tical ,composition4 ,i %all n[ proce$ to ano!r class ( ! anci5t ,greek vase1 ! =m ( :i* is ( a m complex "*4 ,! specim5 ,i h *os5 = ! fir/ example ( ?is class is "o ( ^? s correctly measur$ & beautifully del9eat$ by ,ta?am 9 8 unequall$ "w4#be ,?is vase is a "w ( anci5t ,grecian art 9 ,p>ian m>ble1 :i* he met ) 9 ! collection at ! ,villa ,albani1 ne> ,rome4 ,its height is #d ft4 #d 94 ,sid5ote3 ,plate ,,xiii4 ,! foll[+ is ! =mula by :i* ,i endeav\r to develop its h>monic elem5ts3-- ,let ,a ,b 7,plate ,,xiii47 repres5t ! full height ( ?is vase4 ,?r\gh ,b draw ,b ,d1 mak+ an angle ( 77 ) ! v]tical4 ,?r\gh ,d draw ,d ,o v]tical1 ?r\gh ,a draw ,a ,c1 mak+ an angle ( 772 ?r\gh ,b draw ,b ,l1 mak+ an angle ( 771 & ,b ,s1 mak+ an angle ( 771 ea* ) ! v]tical4 ,?r\gh ,a draw ,a ,d1 ?r\gh ,b draw ,b ,o1 ?r\gh ,l draw ,l ,n1 ?r\gh ,c draw ,c ,f1 & ?r\gh ,s draw ,s ,p1 all horizontal4 ,?r\gh ,a draw ,a ,h1 mak+ an angle ( 77 ) ! v]tical1 & ?r\gh ,h draw ,h ,m v]tical4 ,draw simil> l9es on ! o!r side ( ,a ,b1 & ! rectil9e> portion ( ! diagram is complete1 & its inscrib+ rectangle t ( 774 ,! curvil9e> portion may ?us be add$-- ,take a cut-out ellipse ( 771 ^: great] axis is ab\t ! l5g? ( ! body ( ! int5d$ vase1 place x ) its less] axis ^u ! l9e ,s ,p1 & its great] axis ^u ! l9e ,d ,o1 & trace ! "p a b ( its circumf]5ce ^u ! diagram4 ,place ! same ellipse ) "o ( its foci ^u ,c1 & its great] axis ^u ,c ,f1 & trace its circumf]5ce ^u ! diagram4 ,take a cut-out ellipse ( 771 ^: great] axis is ne>ly equal to t ( ! ellipse already us$2 place x ) its great] axis ^u ,m ,h1 & its less] axis ^u ,l ,n1 & trace its circumf]5ce ^u ! diagram4 ,make simil> trac+s ^u ! o!r side ( ,a ,b1 & ! diagram is complete4 ,9 ?is1 z 9 ! o!r diagrams1 ! /rong portions ( ! l9es give ! cont\r ( ! vase4 ,! h>monic elem5ts ( ?is classical =m1 !re=e1 appe> to be ! "r angle & its foll[+ p>ts3-- ,tonic4 ,dom9ant4 ,m$iant4 ,subm$iant4 77 77 77 77 77 77 ,my ?ird example is t (-- ,an ,anci5t ,grecian ,vase ( a ,horizontal ,composition4 ,?is example belongs to ! same class z ! la/1 b x is ( a horizontal composition4 ,x 0 c>efully drawn f ! orig9al 9 ! museum ( ! ,vatican by ,ta?am1 9 ^: et*+s x w be f\nd ) its ornam5tal decorations4 ,! diagram ( its h>monic elem5ts may be con/ruct$ z foll[s3-- ,sid5ote3 ,plate ,,xiv4 ,let ,a ,b 7,plate ,,xiv47 repres5t ! full height ( ! vase4 ,?r\gh ,b draw ,b ,d1 mak+ an angle ( 77 ) ! v]tical4 ,?r\gh ,a draw ,a ,h1 ,a ,l1 & ,a ,c1 mak+ respectively ! foll[+ angles1 77 ) ! v]tical1 77 ) ! v]tical1 & 77 ) ! horizontal4 ,^! angles det]m9e ! horizontal l9es ,h ,b1 ,l ,n1 & ,c ,f1 :i* divide ! vase into its p>ts1 & ! inscrib+ rectangle ,d ,g ,k ,o is 774 ,?is completes ! rectil9e> portion ( ! diagram4 ,! ellipse by :i* ! curvil9e> portion is add$ is "o ( 771 ! great] axis ( :i*1 at a b1 z also at c d1 makes an angle ( 77 ) ! v]tical1 & ! same axis at e f an angle ( 77 ) ! horizontal4 ,! h>monic elem5ts ( ?is vase1 !re=e1 appe> to be3-- ,tonic4 ,dom9ant4 ,m$iant4 ,subm$iant4 ,sup]tonic4 ,! ,"r 77 77 77 77 ,angle4 77 ,my rema9+ examples are ^? (-- ,etruscan ,vases4 ,( ^! vases ,i give f\r examples1 by :i* ! simplicity ( ! me?od employ$ 9 apply+ ! h>monic law w be app>5t4 ,sid5ote3 ,plate ,,xv4 ,! inscrib+ rectangle ,d ,g ,e ,k ( fig4 #a1 ,plate ,,xv41 is "o ( 771 )9 :i* are arrang$ trac+s f an ellipse ( 771 ^: great] axis at a b makes an angle ( 771 at c d an angle ( 771 & at e f an angle ( 771 ) ! v]tical4 ,! h>monic elem5ts ( ! cont\r ( ?is vase1 !re=e1 appe> to be3-- ,tonic4 ,dom9ant4 ,subdom9ants4 ,subm$iant4 ,! ,"r 77 77 77 ,angle4 77 ,! inscrib+ rectangle ,l ,m ,n ,o ( fig4 #b is t ( 771 )9 :i* are arrang$ trac+s f an ellipse ( 771 ^: great] axis1 at a b & c d respectively1 makes angles ( 77 & 77 ) ! horizontal1 :ile t at e f is 9 ! horizontal l9e4 ,! h>monic elem5ts ( ! cont\r ( ?is vase1 !re=e1 appe> to be3-- ,tonic4 ,dom9ant4 ,subtonic4 77 77 77 ,sid5ote3 ,plate ,,xvi4 ,! inscrib+ rectangle ,p ,q ,r ,s ( fig4 #a1 ,plate ,,xvi41 is "o ( 771 )9 :i* are arrang$ trac+s f an ellipse ( 771 ^: great] axis1 at a b1 c d1 & e f1 makes respectively angles ( 77 ) ! horizontal1 77 & 77 ) ! v]tical4 ,its h>monic elem5ts1 !re=e1 appe> to be3-- ,tonic4 ,dom9ant4 ,m$iant4 ,sup]tonic4 ,subdom9ant4 ,subm$iant4 ,! ,"r 77 77 77 77 77 ,angle4 ,! inscrib+ rectangle ,t ,u ,v ,x ( fig4 #b is "o ( 771 )9 :i* are arrang$ trac+s f an ellipse ( 77 ^: great] axis at a b is 9 ! v]tical l9e1 & at c d makes an angle ( 774 ,! h>monic elem5ts ( ! cont\r ( ?is vase1 !re=e1 appe> to be3-- ,tonic4 ,subm$iant4 ,sup]tonic4 77 77 77 ,^! f\r ,etruscan vases1 ! cont\rs ( :i* are ?us r$uc$ to ! h>monic law ( nature1 are 9 ! ,briti% ,museum1 & engrav+s ( !m are to be f\nd 9 ! well-kn[n "w ( ,mr ,h5ry ,moses1 ,plates #d1 #f1 #ad1 & #g1 respectively1 :]e !y are repres5t$ ) _! appropriate decorations & col\rs4 ,to ^!1 ,i add two examples (-- ,anci5t ,grecian ,ornam5t4 ,i h else:]e %ewn#bf t ! elliptic curve p]vades ! ,p>!non f ! entases ( ! column to ! smalle/ m\ld+1 & we ne$ n1 !re=e1 be surpris$ to f9d x employ$ 9 ! con/ruction ( ! only two ornam5ts belong+ to t great "w4 ,sid5ote3 ,plate ,,xvii4 ,9 ! diagram 7,plate ,,xvii471 ,i endeav\r to exhibit ! geometric con/ruction ( ! upp] "p ( "o ( ! ornam5tal apices1 t]m$ antefix1 :i* surm\nt$ ! cornice ( ! ,p>!non4 ,! fir/ ellipse employ$ is t ( 771 ^: great] axis a b is 9 ! v]tical l9e2 ! second is also t ( 771 ^: great] axis c d makes1 ) ! v]tical1 an angle ( 772 ! ?ird ellipse is ! same ) its major axis e f 9 ! v]tical l9e4 ,?r\gh "o ( ! foci ( ?is ellipse at ,a ! l9e ,a ,c is drawn1 & ^u ! "p ( ! circumf]5ce ,c e1 ! numb] ( p>ts1 #a1 #b1 #c1 #d1 #e1 #f1 #g1 ( :i* ! surm\nt+ "p ( ?is ornam5t is to consi/1 are set (f4 ,t "p ( ! circumf]5ce ( ! ellipse ^: l>g] axis is c d is divid$ f g to c into a l numb] ( p>ts4 ,! ?ird ellipse employ$ is "o ( 774 ,take a cut-out ellipse ( ?is k9d1 ^: l>g] axis is equal 9 l5g? to ! inscrib+ rectangle4 ,place x ) its v]tex ^u ! same ellipse at g1 s t its circumf]5ce w pass ?r\gh ,c1 & trace x2 remove its apix fir/ to p1 !n to q1 & proce$ 9 ! same way to q1 r1 s1 t1 u1 & v1 s t its circumf]5ce w pass ?r\gh ! sev5 divisions on c g & e ,c3 v o1 u n1 t m1 s i1 r k1 q j1 p l1 & g x1 are p>ts ( ! l>g] axes ( ! ellipses f :i* ! curves are trac$4 ,! small ellipse ( :i* ! ends ( ! p>ts are =m$ is t ( 774 ,sid5ote3 ,plate ,,xviii4 ,9 ! diagram 7,plate ,,xviii471 ,i endeav\r to exhibit ! geometric con/ruction ( ! anci5t ,grecian ornam5t1 commonly call$ ! ,honeysuckle1 f its resemblance to ! fl[] ( t "n4 ,! fir/ "p ( ! process is simil> to t j expla9$ ) ref]5ce to ! antefix ( ! ,p>!non1 al?\gh ! angles 9 "s p>ts diff]4 ,! cont\r is det]m9$ by ! circumf]5ce ( an ellipse ( 771 ^: major axis ,a ,b makes an angle ( 77 ) ! v]tical1 & ! leaves or petals are arrang$ ^u a portion ( ! p]imet] ( a simil> ellipse ^: l>g] axis ,e ,f is 9 ! v]tical l9e1 & ^! p>ts are aga9 arrang$ ^u a simil> ellipse ^: l>g] axis ,c ,d makes an angle ( 77 ) ! v]tical4 ,! fir/ s]ies ( curv$ l9es proce$+ f #a1 #b1 #c1 #d1 #e1 #f1 #g1 & #h1 are betwe5 ,k ,e & ,h ,c1 "p ( ! circumf]5ce ( an ellipse ( 772 & ^? betwe5 ,c ,h & ,a ,g are p>ts ( ! circumf]5ce ( f\r ellipses1 ea* ( 771 b v>y+ z to ! l5g?s ( _! l>g] axes f #e to #c in*es4 ,! *ange f ! convex to ! concave1 :i* produces ! ogie =ms ( :i* ?is ornam5t is compos$1 takes place ^u ! l9e ,c ,h1 & ! l9es a b1 c d1 e f1 g h1 i k1 l m1 n o1 & p q1 are p>ts ( ! l>g] axis ( ! f\r ellipses ! circumf]5ce ( :i* give ! upp] p>ts ( ! petals or leaves4 ,?is peculi> ,grecian ornam5t is (t51 l ! antefix ( ! ,p>!non1 comb9$ ) ! curve ( ! spiral scroll4 ,b ! volute is s well und]/ood t ,i h n r5d]$ my diagrams m complex by add+ t figure4 ,_m v>ieties ( ?is union are to be f\nd 9 ,ta?am's et*+s1 already ref]r$ to4 ,! antefix ( ! ,p>!non1 & its only o!r ornam5t ! honeysuckle1 z repres5t$ on ! s(fit ( ! cornice1 are to be f\nd 9 ,/ew>t's 8,a!ns40 ,,app5dix4 ,no4 ,i4 ,9 pages #cd1 #ce1 & #eh1 ,i h reit]at$ an op9ion advanc$ 9 sev]al ( my =m] works1 viz41 t1 besides g5ius1 & ! /udy ( nature1 an additional cause mu/ be assign$ = ! g5]al excell5ce :i* *>act]ises su* works ( ,grecian art z 7 execut$ dur+ a p]iod comm5c+ ab\t #ejj ,b4,c41 & end+ ab\t #bjj ,b4,c4 ,& t ?is cause mo/ probably 01 t ! arti/s ( t p]iod 7 in/ruct$ 9 a sy/em ( fix$ pr9ciples1 bas$ ^u ! doctr9es ( ,py?agoras & ,plato4 ,?is op9ion has n be5 object$ to by ! g5]ality ( ^? critics :o h review$ my works2 b has1 h[ev]1 met ) an oppon5t1 ^: recondite rese>*es & le>n$ obs]vations are wor?y ( p>ticul> att5tion4 ,^! are giv5 9 an essay by ,mr ,c4 ,knight ,watson1 8,on ! ,classical ,au?orities = ,anci5t ,art10 :i* appe>$ 9 ! ,cambridge ,j\rnal ( ,classical & ,sacr$ ,philology 9 ,june #ahed4 ,z ?is essay is n o!rwise likely to meet ! eyes ( ! g5]ality ( my read]s1 & z ! objections he raises to my op9ion only occupy two out ( ! sixte5 ample p>agraphs :i* con/itute ! fir/ "p ( ! essay1 ,i %all quote !m fully3-- 8,! next "n on our li/ is t ( ! fam\s ,euphranor 7,b4,c4 #cfb74 ,= ! fact t to ! practice ( sculpture & ( pa9t+ he add$ an exposition ( ! !ory1 we are indebt$ to ,pl9y1 :o says 7xxxv4 #aa1 #dj71 #8,volum9a quoque composuit de symmetria et coloribus4' ,:5 we reflect on ! critical position occupi$ by ,euphranor 9 ! hi/ory ( ,greek art1 z a connect+ l9k betwe5 ! idealism ( ,pheidias & ! naturalism ( ,lysippus1 we c sc>cely ov]e/imate ! value ( a treatise on art proce$+ f su* a qu>t]4 ,?is is especially ! case ) ! fir/ ( ! two works "h assign$ to ,euphranor4 ,! inquiries :i* ( late ye>s h be5 in/itut$ by ,mr ,d4 ,r4 ,hay ( ,ed9burgh1 on ! proportions ( ! human figure1 & on ! natural pr9ciples ( beauty z illu/rat$ by works ( ,greek art1 con/itute an epo* 9 ! /udy ( /hetics & ! philosophy ( =m4 ,n[1 9 ! pres5ce ( ^! inquiries1 or ( su* less solid results z ,mr ,hay's pr$ecessors 9 ! same field h elicit$1 x naturally becomes an object ( consid]able int]e/ to asc]ta9 h[ f> ^! laws ( =m & pr9ciples ( beauty 7 consci\sly develop$ 9 ! m9d1 & by ! *isel1 ( ! sculptor3 h[ f> any su* sy/em ( curves & proportions z ,mr ,hay's 0 us$ by ! ,greek z a practical manual ( 8 craft4 ,)\t 9 ! lea/ wi%+ to impugn ! accuracy ( t g5tleman's results--a piece ( presumption ,i %\ld d well to avoid--,i mu/ be p]mitt$ to d\bt :e!r ! #8,symmetria' ( ,euphranor conta9$ any?+ analog\s to !m 9 k9d1 or inde$ equal 9 value4 ,x mu/ n be =gott5 t ! tru? ( ,mr ,hay's !ory is p]fectly compatible ) ! fact1 t ( su* !ory ! ,greek may h be5 utt]ly ignorant4 ,x is on ?is fact ,i insi/3 x is "h t ,i jo9 issue ) ,mr ,hay1 & ) 8 review] 9 a rec5t numb] ( ,blackwood's ,magaz9e4 ,or1 to speak m accurately1--:ile ,i am q prep>$ to f9d t ! ,elg9 m>bles w be/ ( all /& ! te/ :i* ,mr ,hay has hi!rto appli$1 ,i believe1 to works ( a lat] age1 ,i am none ! less conv9c$ t x is precisely t gold5 age ( ,hell5ic art to :i* !y belong1 precisely t fir/ & *ief ( ,hell5ic arti/s by :om !y 7 execut$1 to :i* & to :om any su* l9e ( rese>* on ! laws ( =m w\ld h be5 pre-em95tly ali54 ,pheidias1 rememb]1 by ! "r ( primog5iture1 is ! rul+ _s ( idealism 9 art4 ,( spontaneity 0 t idealism begott5 & nurtur$3 by any su* sy/em z ,mr ,hay's1 t spontaneity w\ld be smo!r$ & p>alys$4 ,pheidias copi$ an idea 9 8 own m9d--#8,ipsius 9 m5te insidebat species pul*ritud9is eximia qudam' 7,cic472--lat] ages copi$ him4 ,he creat$3 !y criticis$4 ,he 0 ! au?or ( ,iliads3 !y ! au?ors ( ,poetics4 ,d\btless1 if y unsph]e ! _s ( ,mr ,hay's !ories1 y w f9d no?+ discordant ) :at ,i h "h said4 ,t is a s\nd view ( ,beauty :i* makes x consi/ 9 t due subord9ation ( ! p>ts to ! :ole1 t due relation ( ! p>ts to ea* o!r1 :i* ,m5delssohn _h 9 8 m9d :5 he said t ! ess5ce ( beauty 0 #8unity 9 v>iety'--v>iety beguil+ ! imag9ation1 ! p]ception ( unity ex]cis+ ! !wes & s9ews ( ! intellect4 ,on su* a view ( beauty1 ,mr ,hay's !ory may1 9 _s1 be said to re/4 ,b "h1 z 9 high] ?+s1 x is ! lett] t kille?1 :ile ! _s give? life4 ,& accord+ly ,i mu/ ent] a prote/ aga9/ any endeav\r to foi/ ^u ! palmy days ( ,hell5ic art sy/ems ( geometrical proportions incompatible1 z ,i believe1 ) ^? high] & broad] pr9ciples by :i* ! progress ( anci5t sculpture 0 ord]$ & gov]n$--sy/ems :i* w be> no?+ ( t #8felicity & *ance by :i*'--& n by rule--#8,"l ,bacon believ$ t a pa9t] may make a bett] face ?an ev] 03' sy/ems :i* take no acc\nt ( t fundam5tal di/9ction betwe5 ! s*ools ( ,a!ns & ( ,argos1 & _! respective disciples & desc5dants1 )\t :i* y w make nons5se ( ! pages ( ,pl9y1 &--:at is worse--s5se ( ! pages ( 8 comm5tators2--sy/ems1 9 %ort1 :i* may h _! value z in/rum5ts = ! education ( ! eye1 & = in/ructions 9 ! arts ( design1 b mu/ be ca/ aside z matt]s ( le>n$ trifl+ & curi\s disputation1 :]e !y pr(ess to be royal roads to art1 & to map ! mighty maze ( a creative m9d4 ,& ev5 z reg>ds ! application ( su* a sy/em ( proportions to ^? works ( sculpture :i* are po/]ior to ! ,pheidian age1 only p>tial c h be5 ! preval5ce :i* x or any o!r "o sy/em c h obta9$4 ,! discrepancies ( diff]5t arti/s 9 ! treatm5t ( :at 0 call$1 te*nically call$1 ,symmetria 7z 9 ! title ( ,euphranor's "w7 71 by ! concurr5t te/imony ( all anci5t writ]s1 f> too sali5t & important to w>rant ! supposition ( any uni=m scale ( proportions1 z advocat$ by ,mr ,hay4 ,ev5 9 ,egypt1 :]e "o might surely h expect$ t su* uni=mity w\ld h be5 obs]v$ ) f> great] rig\r ?an 9 ,greece1 ! discov]ies ( ,dr ,lepsius 7,vorlufige ,na*ri*t1 ,b]l91 #ahdi7 h elicit$ ?ree totally diff]5t 1 "o ( :i* is id5tical ) ! sy/em ( proportions ( ! human figure detail$ 9 ,diodorus4 ,:ile we ?us v5ture to diff] f ,mr ,hay on ! hi/orical data he has mix$ up ) 8 inquiries1 we feel b\nd to pay him a l>ge & glad tribute ( praise = hav+ devis$ a sy/em ( proportions :i* rises sup]ior to ! idiosyncracies ( diff]5t arti/s1 :i* br+s back to "o common type ! s5sations ( eye & e>1 & s makes a giant /ride t[>ds t codification1 if ,i may s speak1 ( ! laws ( ! univ]se :i* x is ! bus9ess ( ! sci5ce to effect4 ,i h no hesitation 9 say+1 t1 = sci5tific precision ( me?od & importance ( results1 ,alb]t ,dur]1 ,da ,v9ci1 & ,hog>?1 n to m5tion less notewor?y writ]s1 mu/ all yield ! palm to ,mr ,hay4 8,i am q aw>e t 9 ! digression ,i h "h all[$ myself1 on sy/ems ( proportions preval5t among anci5t arti/s1 & on ! probable cont5ts ( su* treatises z t ( ,euphranor1 ,de ,symmetria1 ,i h laid myself op5 to ! *>ge ( treat+ an intricate "q 9 a v p]functory way4 ,at pres5t ! exig5cies ( ! subject m imm$iately 9 h& all[ me only to urge 9 reply1 t1 z reg>ds ! po9t at issue--,i mean ! #8solid>it' betwe5 !ories su* z ,mr ,hay's & ! practice ( ,pheidias--! onus prob&i re/s ) my adv]s>ies40 ,i am b\nd1 9 ! fir/ place1 gratefully to ackn[l$ge ! k9d & complim5t>y notice :i*1 not)/&+ our diff]5ce ( op9ion1 ?is au?or has be5 pleas$ to take ( my works2 &1 9 ! second1 to assure him t if any ( !m pr(ess to be 8royal roads to art10 or to 8map ! mighty maze ( a creative m9d10 !y c]ta9ly pr(ess to d m ?an ,i ev] meant !y %\ld2 = ,i nev] ent]ta9$ ! idea t a sy/em ( /hetic culture1 ev5 :5 bas$ ^u a law ( nature1 0 capable ( effect+ any su* object4 ,b ,i d\bt n t ?is too common misappreh5sion ( ! scope & t5d5cy ( my works mu/ arise f a want ( p]spicuity 9 my /yle4 ,i h c]ta9ly1 on "o occasion1#bg gone ! l5g? ( /at+ t z poetic g5ius mu/ yield ob$i5ce to ! rules ( rhy?mical measure1 ev5 9 ! highe/ flights ( h] inspirations2 & musical g5ius mu/1 9 l mann]1 be subject to ! /rictly def9$ laws ( h>mony 9 ! mo/ delicate1 z well z 9 ! mo/ p[]fully gr& ( h] compositions2 s mu/ g5ius1 9 ! =mative arts1 ei!r consci\sly or unconsci\sly h clo!d h] creations ( ideal beauty ) proportions /rictly 9 accordance ) ! laws :i* nature has set up z inflexible /&>ds4 ,if1 !re=e1 ! laws ( proportion1 9 _! relation to ! arts ( design1 con/itute ! h>mony ( geometry1 z def9itely z ^? t are applicable to poetry & music produce ! h>mony ( ac\/ics2 ! =m] ought1 c]ta9ly1 to hold ! same relative position 9 ^? arts :i* are address$ to ! eye1 t is accord$ to ! latt] 9 ^? :i* are address$ to ! e>4 ,until s mu* sci5ce be br\ght to be> ^u ! arts ( design1 ! /ud5t mu/ cont9ue to copy f individual & imp]fect objects 9 nature1 or f ! few exi/+ rema9s ( anci5t ,greek art1 9 total ignorance ( ! laws by :i* _! proportions are produc$1 &1 :at is equally detrim5tal to art1 ! accuracy ( all criticism mu/ cont9ue to re/ ^u ! indef9ite & v>iable basis ( m]e op9ion4 ,x _c be d5i$ t m5 ( great arti/ic g5ius are possess$ ( an intuitive feel+ ( appreciation = :at is beautiful1 by means ( :i* !y imp>t to _! works ! mo/ p]fect proportions1 indep5d5tly ( any k ( ! def9ite laws :i* gov]n t species ( beauty4 ,b !y (t5 d s at ! exp5se ( mu* lab\r1 mak+ _m trials be=e !y c satisfy !mselves 9 imp>t+ to !m ! true proportions :i* _! m9ds c conceive1 & :i*1 along ) ^? o!r qualities ( expression1 action1 or attitude1 :i* belong m exclusively to ! prov9ce ( g5ius4 ,9 su* cases1 an acqua9tance ) ! rules :i* con/itute ! sci5ce ( proportion1 in/ead ( prov+ fett]s to g5ius1 w\ld d\btless af=d h] su* a vantage gr\nd z w\ld promote ! m free ex]cise ( h] p[]s1 & give confid5ce & precision 9 ! embodim5t ( h] inspirations2 qualities :i*1 al?\gh q compatible ) g5ius1 are n always intuitively develop$ along ) t gift4 ,x is also true t ! op]ations ( ! conceptive faculty ( ! m9d are uncontroll$ by def9ite laws1 & t1 !re=e1 !re _c exi/ any rules by ! inculcation ( :i* an ord9>y m9d c be imbu$ ) g5ius suffici5t to produce works ( high art4 ,nev]!less1 su* a m9d may be improv$ 9 its p]ceptive faculty by in/ruction 9 ! sci5ce ( proportion1 s z to be enabl$ to ex]cise z correct & j an appreciation ( ! conceptions ( o!rs1 9 works ( pla/ic art1 z t manife/$ by ! educat$ portion ( mank9d 9 respect to poetry & music4 ,9 %ort1 x appe>s t1 9 ^? arts :i* are address$ to ! e>1 m5 ( g5ius communicate ! orig9al conceptions ( _! m9ds "u ! control ( c]ta9 sci5tific laws1 by means ( :i* ! educat$ easily di/+ui% ! true f ! false1 & by :i* ! works ( ! poet & musical compos] may be plac$ above m]e imitations ( nature1 or ( ! works ( o!rs2 :ile1 9 ^? arts t are address$ to ! eye 9 _! own peculi> language1 su* z sculpture1 ar*itecture1 pa9t+1 & ornam5tal design1 no su* laws are z yet ackn[l$g$4 ,al?\gh ,i am1 & ev] h be51 f> f endeav\r+ 8to foi/ ^u ! palmy days ( ,hell5ic art0 any sy/em incompatible ) ^? high] & m intellectual qualities :i* g5ius alone c imp>t2 yet1 f :at has be5 h&$ d[n to u by writ]s on ! subject1 meagre z x is1 ,i _c help cont9u+ to believe t1 along ) ! physical & metaphysical sci5ces1 /hetic sci5ce 0 taught 9 ! e>ly s*ools ( ,greece4 ,i %all "h take ! lib]ty to repeat ! pro(s ,i advanc$ 9 a =m] "w z ! gr\nd ( ?is belief1 & to :i* ! au?or1 f ^: essay ,i h quot$1 und\bt$ly ref]s4 ,x is well kn[n t1 9 ! "t ( ,py?agoras1 ! treasures ( sci5ce 7 veil$ 9 my/]y to all b ! prop]ly initiat$1 & ! results ( its v>i\s bran*es only giv5 to ! _w 9 ! works ( ^? :o _h acquir$ ?is k4 ,s /rictly 0 ?is secresy ma9ta9$ among/ ! disciples & pupils ( ,py?agoras1 t any "o divulg+ ! sacr$ doctr9es to ! pr(ane1 0 expell$ ! community1 & none ( 8 =m] associates all[$ to hold fur!r int]c\rse ) him2 x is ev5 said1 t "o ( 8 pupils incurr$ ! displeasure ( ! philosoph] = hav+ publi%$ ! solution ( a problem 9 geometry4#bh ,! difficulty1 !re=e1 :i* is express$ by writ]s1 %ortly aft] ! p]iod 9 :i* ,py?agoras liv$1 reg>d+ a precise k ( 8 !ories1 is n to be wond]$ at1 m especially :5 x is consid]$ t he nev] committ$ !m to writ+4 ,x w\ld appe>1 h[ev]1 t he proce$$ ^u ! pr9ciple1 t ! ord] & beauty s app>5t ?r\gh\t ! :ole univ]se1 mu/ compel m5 to believe 91 & ref] !m to1 an intelligible cause4 ,py?agoras & 8 disciples s\ght = prop]ties 9 ! sci5ce ( numb]s1 by ! k ( :i* !y might atta9 to t ( nature2 & !y conceiv$ ^? prop]ties to be indicat$ 9 ! ph5om5a ( sonor\s bodies4 ,obs]v+ t ,nature h]self _h ?us irrevocably fix$ ! num]ical value ( ! int]vals ( musical tones1 !y ju/ly conclud$ t1 z %e is always uni=m 9 h] works1 ! same laws mu/ regulate ! g5]al sy/em ( ! univ]se4#bi ,py?agoras1 !re=e1 consid]$ num]ical proportion z ! great pr9ciple inh]5t 9 all ?+s1 & trac$ ! v>i\s =ms & ph5om5a ( ! _w to numb]s z _! basis & ess5ce4 ,h[ ! pr9ciples ( numb]s 7 appli$ 9 ! arts is n record$1 f>!r ?an :at transpires 9 ! works ( ,plato1 ^: doctr9es 7 f ! s*ool ( ,py?agoras4 ,9 expla9+ ! pr9ciple ( beauty1 z develop$ 9 ! elem5ts ( ! mat]ial _w1 he comm5ces 9 ! foll[+ words3--8,b :5 ! ,artific] began to adorn ! univ]se1 he fir/ ( all figur$ ) =ms & numb]s1 fire & e>?1 wat] & air--:i* possess$1 inde$1 c]ta9 traces ( ! true elem5ts1 b 7 9 e respect s con/itut$ z x becomes any?+ to be f :i* ,deity is abs5t4 ,b we %\ld always p]sev]e 9 ass]t+ t ,div9ity r5d]$ !m1 z mu* z possible1 ! mo/ beautiful & ! be/1 :5 !y 7 9 a /ate ( exi/5ce opposite to su* a condition40 ,plato goes on fur!r to say1 t ^! elem5t>y bodies mu/ h =ms2 & z x is necess>y t e dep? %\ld compreh5d ! nature ( a plane1 & z ( plane figures ! triangle is ! mo/ elem5t>y1 he adopts two triangles z ! orig9als or repres5tatives ( ! isosceles & ! scal5e k9ds4 ,! fir/ triangle ( ,plato is t :i* =ms ! half ( ! squ>e1 & is regulat$ by ! numb]1 #b2 & ! second1 t :i* =ms ! half ( ! equilat]al triangle1 :i* is regulat$ by ! numb]1 #c2 f v>i\s comb9ations ( ^!1 he =m$ ! bodies ( :i* he consid]$ ! elem5ts to be compos$4 ,to ^! elem5t>y figures ,i h already ref]r$4 ,vitruvius1 :o /udi$ ar*itecture ages aft] ! arts ( ,greece _h be5 buri$ 9 ! oblivion :i* succe$$ h] conque/1 gives ! measurem5ts ( v>i\s details ( monum5ts ( ,greek art !n exi/+4 ,b he seems to h _h b a vague tradition>y k ( ! pr9ciple ( h>mony & proportion f :i* ^! measurem5ts result$4 ,he says--8,! sev]al p>ts :i* con/itute a temple ought to be subject to ! laws ( symmetry2 ! pr9ciples ( :i* %\ld be famili> to all :o pr(ess ! sci5ce ( ar*itecture4 ,symmetry results f proportion1 :i*1 9 ! ,greek language1 is t]m$ analogy4 ,proportion is ! comm5suration ( ! v>i\s con/itu5t p>ts ) ! :ole2 9 ! exi/5ce ( :i* symmetry is f\nd to consi/4 ,= no build+ c possess ! attributes ( composition 9 :i* symmetry & proportion are disreg>d$2 nor unless !re exi/ t p]fect con=mation ( p>ts :i* may be obs]v$ 9 a well-=m$ human be+40 ,aft] go+ at "s l5g? into details1 he adds--8,s9ce1 !re=e1 ! human figure appe>s to h be5 =m$ ) su* propriety1 t ! sev]al memb]s are comm5surate ) ! :ole1 ! arti/s ( antiquity 7mean+ ^? ( ,greece at ! p]iod ( h] highe/ ref9em5t7 mu/ be all[$ to h foll[$ ! dictates ( a judgm5t ! mo/ rational1 :51 transf]r+ to works ( art pr9ciples d]iv$ f nature1 e "p 0 s regulat$ z to be> a j proportion to ! :ole4 ,n[1 al?\gh ! pr9ciples 7 univ]sally act$ ^u1 yet !y 7 m p>ticul>ly att5d$ to 9 ! con/ruction ( temples & sacr$ edifices1 ! beauties or defects ( :i* 7 de/9$ to rema9 z a p]petual te/imony ( _! skill or ( _! inability40 ,vitruvius1 h[ev]1 gives no explanation ( ?is anci5t pr9ciple ( proportion1 z d]iv$ f ! human =m2 b pla9ly %ews 8 unc]ta9ty ^u ! subject1 by conclud+ ?is "p ( 8 essay 9 ! foll[+ words3 8,if x be true1 !re=e1 t ! dec5>y notation 0 sugge/$ by ! memb]s ( man1 & t ! laws ( proportion arose f ! relative measures exi/+ betwe5 c]ta9 p>ts ( ea* memb] & ! :ole body1 x w foll[1 t ^? are entitl$ to our comm5dation :o1 9 build+ temples to _! deities1 proportion$ ! edifices1 s t ! sev]al p>ts ( !m might be comm5surate ) ! :ole40 ,x ?us appe>s c]ta9 t ! ,grecians1 at ! p]iod ( _! highe/ excell5ce1 _h arriv$ at a k ( "s def9ite ma!matical law ( proportion1 :i* =m$ a /&>d ( p]fectly symmetrical beauty1 n only 9 ! repres5tation ( ! human figure 9 sculpture & pa9t+1 b 9 ar*itectural design1 & inde$ 9 all works :]e beauty ( =m & h>mony ( proportion con/itut$ excell5ce4 ,t ?is law 0 n d$uc$ f ! proportions ( ! human figure1 z suppos$ by ,vitruvius1 b _h its orig9 9 ma!matical sci5ce1 seems equally c]ta92 = 9 no o!r way c we satisfactorily acc\nt = ! proportions ( ! beau ideal =ms ( ! anci5t ,greek deities1 or ( ^? ( _! ar*itectural /ructures1 su* z ! ,p>!non1 ! temple ( ,!seus1 c41 or = ! beauty t p]vades all ! o!r =mative art ( ! p]iod4 ,?is sy/em ( geometrical h>mony1 f\nd$1 z ,i h %ewn x to be1 ^u num]ical relations1 mu/ consequ5tly h =m$ "p ( ! ,greek philosophy ( ! p]iod1 by means ( :i* ! arts began to progress t[>ds t great excell5ce :i* !y soon aft] atta9$4 ,a little fur!r inve/igation w %ew1 t imm$iately aft] ?is p]iod a !ory connect$ ) art 0 ackn[l$g$ & taught1 & also t !re exi/$ a ,sci5ce ( ,proportion4 ,pamphilus1 ! celebrat$ pa9t]1 :o fl\ri%$ ab\t f\r hundr$ ye>s be=e ! ,*ri/ian era1 f :om ,apelles receiv$ ! rudim5ts ( 8 art1 & ^: s*ool 0 di/+ui%$ = sci5tific cultivation1 arti/ic k1 & ! greate/ accuracy 9 draw+1 w\ld admit no pupil unacqua9t$ ) geometry4#cj ,! t]ms ^u :i* he engag$ ) 8 /ud5ts 71 t ea* %\ld pay him "o tal5t 7#bbe /]l+7 previ\s to receiv+ 8 in/ructions2 = ?is he engag$ 8to give !m1 = t5 ye>s1 lessons f\nd$ on an excell5t !ory40#ca ,x 0 by ! advice ( ,pamphilus t ! magi/rates ( ,sicyon orda9$ t ! /udy ( draw+ %\ld con/itute "p ( ! education ( ! citiz5s--8a law10 says ! ,abb ,b>?lmie1 8:i* rescu$ ! f9e arts f s]vile h&s40 ,x is /at$ ( ,p>rhasius1 ! rival ( ,zeuxis1 :o fl\ri%$ ab\t ! same p]iod z ,pamphilus1 t he accel]at$ ! progress ( art by purity & correctness ( design2 8= he 0 acqua9t$ ) ! sci5ce ( ,proportions4 ,^? he gave 8 gods & h]oes 7 s happy1 t arti/s did n hesitate to adopt !m40 ,p>rhasius1 x is also /at$1 0 s admir$ by 8 contempor>ies1 t !y decre$ him ! "n ( ,legislator4#cb ,! :ole hi/ory ( ! arts 9 ,egypt & ,greece concurs to prove t !y 7 bas$ on geometric precision1 & 7 p]fect$ by a cont9u$ application ( ! same sci5ce2 :ile 9 all o!r c\ntries we f9d !m orig9at+ 9 rude & mis%ap5 imitations ( nature4 ,9 ! e>lie/ /ages ( ,greek art1 ! gods--!n ! only /atues--7 repres5t$ 9 a tranquil & fix$ po/ure1 ) ! features exhibit+ a /iff inflexible e>ne/ness1 _! only claim to excell5ce be+ symmetrical proportion2 & ?is att5tion to geometric precision cont9u$ z art advanc$ t[>ds its culm9at+ po9t1 & 0 !reaft] /ill exhibit$ 9 ! neatly & regul>ly fold$ drap]y1 & 9 ! curi\sly braid$ & symmetrically arrang$ hair4#cc ,^! rese>*es1 imp]fect z !y are1 _c fail to exhibit ! great contra/ t exi/s betwe5 ! sy/em ( elem5t>y education 9 art practis$ 9 anci5t ,greece1 & t adopt$ 9 ?is c\ntry at ! pres5t p]iod4 ,b x w\ld be ( v little s]vice to po9t out ?is contra/1 7 x n accompani$ by "s attempt to develop ! pr9ciples :i* seem to h =m$ ! basis ( ?is excell5ce among/ ! ,greeks4 ,b 9 mak+ su* an attempt1 ,i _c accuse myself ( assum+ any?+ incompatible ) ! free ex]cise ( t spontaneity ( g5ius :i* ! le>n$ essayi/ says is ! p>5t & nurse ( idealism4 ,= x is 9 no way m incompatible ) ! free ex]cise ( arti/ic g5ius1 t ^? :o are s gift$ %\ld h ! advantage ( an elem5t>y education 9 ! sci5ce ( /hetics1 ?an x is incompatible ) ! free ex]cise ( lit]>y or poetic g5ius1 t ^? :o possess x %\ld h ! advantage ( su* an elem5t>y education 9 ! sci5ce ( philology z our lit]>y s*ools & colleges s amply af=d4 ,no4 ,,ii4 ,! lett] f :i* ,i h made a quotation at page #db1 arose out ( ! foll[+ circum/ance3--,9 ord] t my !ory1 z appli$ to ! or?ographic beauty ( ! ,p>!non1 might be br\ght be=e ! highe/ tribunal :i* ?is c\ntry af=d$1 ,i s5t a pap] ^u ! subject1 accompani$ by ample illu/rations1 to ! ,royal ,in/itute ( ,briti% ,ar*itects1 & x 0 read at a meet+ ( t le>n$ body on ! #g? ( ,febru>y #ahec2 at ! conclusion ( :i*1 ,mr ,p5rose k9dly und]took to exam9e my !oretical views1 9 connexion ) ! measurem5ts he _h tak5 ( t beautiful /ructure by ord] ( ! ,dilettanti ,society1 & report ^u ! subject to ! ,royal ,in/itute4 ,?is report 0 publi%$ by ,mr ,p5rose1 vol4 xi41 ,no4 #eci ( ,! ,build]1 & ! lett] f :i* ,i h quot$ appe>$ 9 ,no4 #edb ( ! same j\rnal4 ,x 0 z foll[s3-- 8,,geometrical ,,relations ,,9 ,,ar*itecture4 8,w y all[ me1 ?r\gh ! m$ium ( y\r columns1 to ?ank ,mr ,p5rose = 8 te/imony to ! tru? ( ,mr ,hay's revival ( ,py?agoras8 ,! dim5sions :i* he gives are to me ! sure/ v]ification ( ! !ory t ,i c\ld h desir$4 ,! m9ute discrepancies =m t v elem5t ( practical inc]titude1 bo? z to execution & direct measurem5t1 :i* always prevails 9 mat]ialis+ a ma!matical calculation "u su* conditions4 8,x is "t t ! scatt]$ computations by :i* ar*itecture has be5 analys$--m ?an en\gh--be syn!tis$ into ^? =mul :i*1 z ,mrs ,som]ville tells u1 #8are emblematic ( omnisci5ce4' ,! "y ar*itects ( our day feel trembl+ b5ea? _! feet ! gr\nd :5ce m5 are ab\t to evoke ! great & slumb]+ corpse ( art4 ,sir1 x is food ( ?is k9d a reviv+ poetry dem&s4 ----#8,give u tru?s1 ,= we are we>y ( ! surfaces1 ,& die ( inanition4' 8,i1 = "o1 z ,i li/5 to su* demon/rations1 ^: scope ext5ds ) e rese>* into !m1 feel z if li/5+ to ^? words ( ,py?agoras1 :i* s[$ 9 ! m9d ( ,greece ! poetry ^: manife/ation 9 beauty has en*a9$ ! _w 9 wor%ip ev] s9ce its bir?4 ,& ,i am sure t 9 su* a qu>t]1 & 9 su* ?\ghts1 we mu/ look = ! fir/ %9+ ( t lamp ( art1 :i* ev5 n[ is prep>$ to burn4 8,i "k t ?is all s\nds rhapsodical2 b ,i "k also t until ! ar*itect becomes a poet1 & n a tradesman1 we may look 9 va9 = ar*itecture3 & ,i "k t valuable z isolat$ & detail$ inve/igations are 9 _! prop] be>+s1 yet t su* purposes & be>+s are to be f\nd 9 ! enunciation ( pr9ciples sublime z ! g5]alities ( #8ma!matical beauty4' 8,,autoc?on40 ,no4 ,,iii4 ,( ! "w allud$ to at page #eh ,i 0 fav\r$ ) two op9ions--! "o ref]r+ to ! !ory x prop\nds1 & ! o!r to its anatomical accuracy--bo? ( :i* ,i h be5 k9dly p]mitt$ to publi%4 ,! fir/ is f ,sir ,,william ,,hamilton1 ,b>t41 pr(essor ( logic & metaphysics 9 ! ,univ]sity ( ,ed9burgh1 & is z foll[s3-- 8,y\r v elegant volume is to me extremely int]e/+1 z af=d+ an able contribution to :at is ! anci5t1 &1 ,i conceive1 ! true !ory ( ! ,beautiful4 ,b ?\gh y\r doctr9e co9cides ) ! "o preval5t ?r\gh all antiquity1 x appe>s to me q indep5d5t & orig9al 9 y2 & ,i e/eem x ! m1 t x /&s oppos$ to ! hundr$ "o-sid$ & exclusive views preval5t 9 mod]n times4--#af ,great ,k+ ,/reet1 ,m>* #e1 #ahdi40 ,! second is f ,,john ,,goodsir1 ,esq41 pr(essor ( anatomy 9 ! ,univ]sity ( ,ed9burgh1 & is z foll[s3-- 8,i h exam9$ ! plates 9 y\r "w on ! proportions ( ! human head & c\nt5ance1 & f9d ! head y h giv5 z typical ( human beauty to be anatomically correct 9 its /ructure1 only diff]+ f ord9>y nature 9 its proportions be+ m ma!matically precise1 & consequ5tly m symmetrically beautiful4--,college1 ,ed9burgh1 #ag? ,april #ahdi40 ,no4 ,,iv4 ,i %all "h %ew1 z ,i h done 9 a =m] "w1 h[ ! curvil9e> outl9e ( ! figure is trac$ ^u ! rectil9e> diagrams by portions ( ! ellipse ( 771 771 771 & 774 ,sid5ote3 ,plate ,,xix4 ,! outl9e ( ! head & face1 f po9ts 7#a7 to 7#c7 7fig4 #a1 ,plate ,,xix471 takes ! direction ( ! two fir/ curves ( ! diagram4 ,f po9t 7#c71 ! outl9e ( ! /]no-ma/oid muscle cont9ues to 7#d71 :]e1 jo9+ ! outl9e ( ! trapezius muscle1 at fir/ concave1 x becomes convex aft] pass+ ?r\gh 7#e71 rea*es ! po9t 7#f71 :]e ! convex outl9e ( ! deltoid muscle comm5ces1 &1 pass+ ?r\gh 7#g71 takes ! outl9e ( ! arm z f> z 7#h74 ,! outl9e ( ! muscles on ! side1 ! latissimus dorsi & s]ratus magnus1 comm5ces "u ! arm at ! po9t 7#i71 & jo9s ! outl9e ( ! oblique muscle ( ! abdom5 by a concave curve at 7#aj71 :i*1 ris+ into convexity z x passes ?r\gh ! po9ts 7#aa7 & 7#ab71 ends at 7#ac71 :]e x jo9s ! outl9e ( ! gluteus m$ius muscle4 ,! outl9e ( ?is latt] muscle passes convexly ?r\gh ! po9t 7#ad71 & ends at 7#ae71 :]e ! outl9e ( ! t5sor vag9 femoris & va/us ext]nus muscle ( ! ?igh comm5ces4 ,?is convex outl9e jo9s ! concave outl9e ( ! biceps ( ! ?igh at 7#af71 :i* ends 9 t ( ! slight convexity ( ! condyles ( ! ?igh-bone at 7#ag74 ,f ?is po9t1 ! outl9e ( ! out] surface ( ! leg1 :i* includes ! biceps1 p]oneus longus1 & soleus muscles1 aft] pass+ ?r\gh ! po9t 7#ah71 cont9ues convexly to 7#ai71 :]e ! concave outl9e ( ! t5dons ( ! p]oneus longus cont9ues to 7#bj71 :5ce ! outl9e ( ! out] ankle & foot comm5ces4 ,! outl9e ( ! mamma & fold ( ! arm-pit comm5ces at 7#ba71 & passes ?r\gh ! po9ts 7#bb7 & 7#bc74 ,! circle at 7#bd7 is ! outl9e ( ! areola1 9 ! c5tre ( :i* ! nipple is plac$4 ,! outl9e ( ! pubes comm5ces at 7#be71 & ends at ! po9t 7#bf71 f :i* ! outl9e ( ! inn] surface ( ! ?igh proce$s ov] ! gracilis1 ! s>torius1 & va/us int]nus muscles1 until x meets ! int]nal face ( ! knee-jo9t at 7#bg71 ! outl9e ( :i* ends at 7#bh74 ,! outl9e ( ! inside ( ! leg comm5ces by proce$+ ov] ! ga/rocnemius muscle z f> z 7#bi71 :]e x meets t ( ! soleus muscle1 & cont9ues ov] ! t5dons ( ! heel until x meets ! outl9e ( ! inn] ankle & foot at 7#cj74 ,! outl9e ( ! out] surface ( ! arm1 z view$ 9 front1 proce$s f 7#h7 ov] ! rema9d] ( ! deltoid1 9 :i* !re is "h a slight concavity1 &1 next1 f 7#ca7 ov] ! biceps muscle till 7#cb71 :]e x takes ! l9e ( ! long sup9ator1 & pass+ concavely1 & almo/ imp]ceptibly1 into ! long & %ort radial ext5sor muscles1 rea*es ! wri/ at 7#cc74 ,! outl9e ( ! inn] surface ( ! arm f opposite 7#i7 comm5ces by pass+ ov] ! triceps ext5sor1 :i* ends at 7#cd71 !n ov] ! g5tle convexity ( ! condyles ( ! bone ( ! arm at 7#ce71 &1 la/ly1 ov] ! flexor sublimis :i* ends at ! wri/-jo9t 7#cf74 ,! outl9e ( ! front ( ! figure comm5ces at ! po9t 7#a71 7fig4 #b1 ,plate ,,ii471 &1 pass+ almo/ v]tically ov] ! platzsma-myoidis muscles1 rea*es ! po9t 7#b71 :]e ! neck ends by a concave curve4 ,f 7#b7 ! outl9e rises convexly ov] ! ends ( ! clavicles1 & cont9ues s ov] ! pectoral muscle till x rea*es 7#c71 :]e ! mamma swells out convexly to 7#d71 & returns convexly t[>ds 7#e71 :]e ! curve becomes concave4 ,f 7#e7 ! outl9e foll[s ! undulations ( ! rectus muscle ( ! abdom51 concave at ! po9ts 7#f7 & 7#g71 & hav+ its greate/ convexity at 7#h74 ,?is s]ies ( curves ends ) a slight concavity at ! po9t 7#i71 :]e ! horizontal bran* ( ! pubes is situat$1 ov] :i* ! outl9e is convex & ends at 7#aj74 ,! outl9e ( ! ?igh comm5ces at ! po9t 7#aa7 ) a slight concave curve1 & !n swells out convexly ov] ! ext5sors ( ! leg1 &1 rea*+ 7#ab71 becomes g5tly concave1 &1 pass+ ov] ! patella at 7#ac71 becomes aga9 convex until x rea*es ! ligam5t ( t bone1 :]e x becomes g5tly concave t[>ds ! po9t 7#ad71 :5ce x foll[s ! slightly convex curve ( ! %9-bone1 & !n1 becom+ z slightly concave1 ends ) ! muscles 9 front ( ! leg at 7#ae74 ,! outl9e ( ! back comm5ces at ! po9t 7#af71 &1 foll[+ ) a concave curve ! muscles ( ! neck z f> z 7#ag71 swells into a convex curve ov] ! trapezius muscle t[>ds ! po9t 7#ah72 pass+ ?r\gh :i* po9t1 x cont9ues to swell outw>d until x rea*es 7#ai71 half way betwe5 7#ah7 & 7#bj72 :5ce ! convexity1 becom+ less & less1 falls into ! concave curve ( ! muscles ( ! lo9s at 7#ba71 & pass+ ?r\gh ! po9t 7#bb71 x rises into convexity4 ,x !n passes ?r\gh ! po9t 7#bc71 foll[s ! outl9e ( ! gluteus maximus1 ! convex curve ( :i* rises to ! po9t 7#bd71 & !n returns inw>ds to t ( 7#be71 :]e x ends 9 ! fold ( ! hip4 ,f ?is po9t ! outl9e foll[s ! curve ( ! ham/r+ muscles by a slight concavity z f> z 7#bf71 & !n1 becom+ g5tly convex1 x rea*es 7#bg72 :5ce x becomes aga9 g5tly concave1 ) a slight indication ( ! condyle ( ! ?igh-bone at 7#bh71 &1 rea*+ 7#bi71 foll[s ! convex curve ( ! ga/rocnemius muscle ?r\gh ! po9t 7#cj71 & fall+ into ! convex curve ( ! t5do ,a*illes at 7#ca71 ends 9 ! concavity ov] ! heel at 7#cb74 ,! outl9e ( ! front ( ! arm comm5ces at ! po9t 7#cc71 by a g5tle concavity at ! arm-pit1 & !n swells out 9 a convex curve ov] ! biceps1 rea*+ 7#cd71 :]e x becomes concave1 & pass+ ?r\gh 7#ce71 aga9 becomes convex 9 pass+ ov] ! long sup9ator1 &1 becom+ g5tly concave z x passes ! radial ext5sors1 rises slightly at 7#cf71 & ends at 7#cg71 :]e ! outl9e ( ! wri/ comm5ces4 ,! outl9e ( ! back ( ! arm comm5ces ) a concave curve at 7#ch71 :i* becomes convex z x passes f ! deltoid to ! long ext5sor & ends at ! elb[ 7#ci71 f bel[ :i* ! outl9e foll[s ! convex curve ( ! ext5sor uln>is1 rea*+ ! wri/ at ! po9t 7#dj74 ,x w be se5 t ! v>i\s undulations ( ! outl9e are regulat$ by po9ts :i* are det]m9$ g5]ally by ! int]sections & sometimes by directions & ext5sions ( ! l9es ( ! diagram1 9 ! same mann] 9 :i* ,i %ew$ proportion to be imp>t$1 9 a late "w1 to ! osse\s /ructure4 ,! mode 9 :i* ! curves ( 771 771 771 771 & 77 are ?us s h>moni\sly bl5d$ 9 ! outl9e ( ! female figure1 only rema9s to be expla9$4 ,! curves :i* compose ! outl9e ( ! female =m are !re=e simply ^? ( 771 771 771 771 & 774 ,mann] 9 :i* ^! curves are dispos$ 9 ! lat]al outl9e 7figure #a1 ,plate ,,xix473-- ,po9ts4 ,curves4 ,head f #a to #b 77 ,face 0 #b 0 #c 77 ,neck 0 #c 0 #d 77 ,%\ld] 0 #d 0 #f 77 0 0 #f 0 #h 77 ,trunk 0 #i 0 #ae 77 0 0 #ba 0 #bd 77 ,out] surface ( ?igh & leg 0 #ae 0 #bj 77 ,inn] surface ( ?igh & leg 0 #be 0 #cj 77 ,out] surface ( ! arm 0 #h 0 #cc 77 ,inn] surface ( ! arm 0 #i 0 #cf 77 ,mann] 9 :i* !y are dispos$ 9 ! outl9e 7figure #b1 ,plate ,,xix473-- ,po9ts4 ,curves4 ,front ( neck f #a to #b 77 0 trunk 0 #b 0 #aj 77 ,back ( neck 0 #af 0 #ah 77 0 trunk 0 #ah 0 #bc 77 0 0 0 #bc 0 #be 77 ,front ( ?igh & leg 0 #aa 0 #ac 77 0 0 0 0 #ac 0 #ae 77 ,back ( ?igh & leg 0 #be 0 #cb 77 ,front ( ! arm 0 #cc 0 #cg 77 ,back ( ! arm 0 #ch 0 #dj 77 ,foot 0 #j 0 #j 77 ,sid5ote3 ,plate ,,xx4 ,9 ord] to exemplify m cle>ly ! mann] 9 :i* ^! v>i\s curves appe> 9 ! outl9e ( ! figure1 ,i give 9 ,plate ,,xx4 ! :ole curvil9e> figures1 complete1 to :i* ^! portions belong t =m ! outl9e ( ! sides ( ! head1 neck1 & trunk1 & ( ! out] surface ( ! ?ighs & legs4 ,! v>i\s angles :i* ! axes ( ^! ellipses =m ) ! v]tical1 w be f\nd among/ o!r details 9 ! works ,i h j ref]r$ to4 ,no4 ,v4 ,at page #he ,i h rem>k$ ^u ! v>iety t may be introduc$ into any p>ticul> =m ( vase2 &1 9 ord] to give ! read] an idea ( ! ease ) :i* ?is may be done )\t violat+ ! h>monic law1 ,i %all "h give ?ree examples3-- ,sid5ote3 ,plate ,,xxi4 ,! fir/ ( ^! 7,plate ,,xxi47 diff]s f ! ,portl& vase1 9 ! concave curve ( ! neck fl[+ m gradually into ! convex curve ( ! body4 ,sid5ote3 ,plate ,,xxii4 ,! second 7,plate ,,xxii47 diff]s f ! same vase 9 ! same *ange ( cont\r1 z also 9 be+ ( a small] diamet] at ! top & at ! bottom4 ,sid5ote3 ,plate ,,xxiii4 ,! ?ird 7,plate ,,xxiii47 is ! mo/ simple arrangem5t ( ! elliptic curve by :i* ?is k9d ( =m may be produc$2 & x diff]s f ! ,portl& vase 9 ! relative proportions ( height & diamet]1 & 9 hav+ a full] curve ( cont\r4 ,! foll[+ comp>ison ( ! angles employ$ 9 ^! examples1 ) ! angles employ$ 9 ! orig9al1 w %ew t ! *anges ( cont\r 9 ^! =ms1 arise m f ! mode 9 :i* ! angles are arrang$ ?an 9 a *ange ( ! angles !mselves3-- ,l9e ,l9e ,l9e ,l9e ,plate ,,viii4 ,a ,c 77 ,b ,c 77 o p 7,h7 v u 77 ,plate ,,xxi4 77 77 77 77 ,plate ,,xxii4 77 77 77 77 ,plate ,,xxiii4 77 77 7,h7 7-7 ,l9e ,l9e ,plate ,,viii4 m n 77 i k 77 ellipse 77 rectangle 77 ,plate ,,xxi4 77 77 77 77 ,plate ,,xxii4 77 77 77 77 ,plate ,,xxiii4 77 77 ellipses 77 77 77 ,! h>monic elem5ts ( ea* are !re=e simply ! foll[+ p>ts ( ! "r angle3-- ,tonic4 ,dom9ant4 ,m$iant4 ,subm$iant4 ,plate ,,viii4 77 77 77 77 77 ,tonic4 ,dom9ant4 ,m$iant4 ,sup]tonic4 ,plate ,,xxi4 77 77 77 77 77 ,tonic4 ,dom9ant4 ,m$iant4 ,sup]tonic4 ,plate ,,xxii4 77 77 77 77 77 77 ,tonic4 ,dom9ant4 ,m$iant4 ,plate ,,xxiii4 77 77 77 77 ,no4 ,,vi4 ,s f> z ,i "k1 !re has be5 only "o attempt 9 mod]n times1 besides my own1 to e/abli% a univ]sal sy/em ( proportion1 bas$ on a law ( nature1 & applicable to art4 ,?is attempt consi/s ( a "w ( #deg pages1 ) #aff engrav$ illu/rations1 by ,dr ,zeis+1 a pr(essor 9 ,leipzic1 :]e x 0 publi%$ 9 #ahed4 ,"o ( ! mo/ le>n$ & tal5t$ pr(essors 9 our ,ed9burgh ,univ]sity has review$ t "w z foll[s3-- 8,x has be5 r clev]ly said t ! intellectual di/9ction betwe5 an ,engli%man & a ,scot*man is ?is--#8,give an ,engli%man two facts1 & he looks out = a ?ird2 give a ,scot*man two facts1 & he looks out = a !ory4' ,nei!r ( ^! te/s di/+ui%es ! ,g]man2 he is z likely to seek = a ?ird fact z = a !ory1 & z likely to build a !ory on two facts z to look abroad = fur!r in=mation4 ,b once let him h a !ory 9 8 m9d1 & he w ransack heav5 & e>? until he almo/ buries x "u ! weight ( accumulat$ facts4 ,?is rem>k applies ) m ?an common =ce to a treatise publi%$ la/ ye> by ,dr ,zeis+1 a pr(essor 9 ,leipsic1 #8,on a law ( proportion :i* rules all nature4' ,! +5i\s au?or1 aft] prov+ f ! writ+s ( anci5t & mod]n philosoph]s t !re always exi/$ ! belief 7:5ce d]iv$ x is difficult to say71 t "s law does b9d into "o =mula all ! visible works ( ,god1 proce$s to criticise ! op9ions ( individual writ]s respect+ t connect+ law4 ,x is n our purpose to foll[ him ?r\gh 8 l5g?y exam9ation4 ,suffice x to say t he believes he has f\nd ! lo/ treasure 9 ! ,timu ( ,plato1 c4 #ca4 ,! passage is confess$ly an obscure "o1 & w n be> a lit]al translation4 ,! int]pretation :i* ,dr ,zeis+ puts on x is c]ta9ly a little /ra9$1 b we are dispos$ to admit t he does x ) consid]able reason4 ,agreeably to him1 ! passage runs ?us3--#8,t bond is ! mo/ beautiful :i* b9ds ! ?+s z mu* z possible into "o2 & proportion effects ?is mo/ p]fectly :5 ?ree ?+s are s unit$ t ! great] be>s to ! middle ! same ratio t ! middle be>s to ! less4' 8,we mu/ d ,dr ,zeis+ ! ju/ice to say t he has n made m ?an a legitimate use ( ! mat]ials :i* 7 pres5t$ to him 9 ! writ+s ( ! anci5ts1 9 8 endeav\r to e/abli% ! fact ( ! exi/5ce ( ?is law among/ !m4 ,! canon ( ,polycletes1 ! tradition ( ,v>ro m5tion$ by ,pl9y relative to t canon1 ! writ+s ( ,gal5 & o!rs1 are all br\ght to be> on ! same po9t ) m or less =ce4 ,! sum ( ?is portion ( ! argum5t is fairly ?is1--t ! anci5t sculptors _h "s law ( proportion--"s au?oris$ exampl> to :i* !y ref]r$ z _! "w proce$$4 ,t x 0 ! law "h attribut$ to ,plato is by no means made out2 b1 consid]+ ! incid5tal mann] 9 :i* t law is ref]r$ to1 & ! obscurity ( ! passages z !y exi/1 x is1 p]haps1 too mu* to expect m ?an ?is broad feature ( co9cid5ce--! fact t "s law 0 kn[n & appeal$ to4 ,dr ,zeis+ n[ proce$s to exam9e mod]n !ories1 & x is fair to /ate t he appe>s g5]ally to take a v j view ( !m4 8,let u n[ turn to ,dr ,zeis+'s own !ory4 ,x is ?is--t 9 e beautiful =m l9es are divid$ 9 extreme & mean ratio2 or1 t any l9e consid]$ z a :ole1 be>s to its l>g] "p ! same proportion t ! l>g] be>s to ! small]--?us1 a l9e ( #e in*es w be divid$ into p>ts :i* are v ne>ly #b & #c in*es respectively 7#ai & #ca in*es74 ,?is is a well-kn[n division ( a l9e1 & has be5 call$ ! ,,gold5 rule1 b :5 or :y1 x is n easy to asc]ta94 ,) ?is rule 9 8 h&1 ,dr ,zeis+ proce$s to exam9e all nature & art2 nay1 he ev5 v5tures beyond ! ?re%old ( nature to scan ,deity4 ,we w n foll[ him s f>4 ,let u turn ov] ! pages ( 8 c>efully illu/rat$ "w1 & see h[ he applies 8 l9e4 ,we meet fir/ ) ! ,apollo ,belvid]e--! gold5 l9e divides him happily4 ,we _c say ! same ( ! division ( a h&some face :i* occurs a little fur!r on4 ,our preconceiv$ notions h made ! face t]m9ate ) ! *91 & n ) ! c5tre ( ! ?roat4 ,x is evid5t t1 ) su* a rule z ?is1 a little latitude z to ! extreme po9t ( ! object to be measur$1 relieves its inv5tor f a _w ( p]plexities4 ,?is rem>k is equally applicable to ! arm :i* foll[s1 to :i* ! rule appe>s to apply admirably1 yet we h tri$ x on sundry plates ( arms1 bo? fle%y & bony1 )\t a %ad[ ( success4 ,:e!r ! rule 0 made = ! arm or ! arm = ! rule1 we d n pret5d to decide4 ,b let u pass ha/ily on to page #bhd1 :]e ! ,v5us de ,m$icis & ,raphael's ,eve are pres5t$ to u4 ,!y be> ! application ( ! l9e "r well4 ,x might1 p]haps1 be object$ t x is rem>kable t ! same rule applies s exactly to ! exi/+ position ( ! figures1 su* z ! ,apollo & ! ,v5us1 ! "o ( :i* is upright1 & ! o!r cr\*+4 ,b let t pass4 ,we f9d ,dr ,zeis+ next endeav\r+ to squ>e 8 !ory ) ! di/ances ( ! planets1 ) w(ully scanty success4 ,desc5d+ f 8 l(ty position1 he spans ! e>? f corn] to corn]1 at :i* occupation we w leave him = a mom5t1 :il/ we (f] a sugge/ion :i* is equally applicable to poets1 pa9t]s1 noveli/s1 & !oris]s4 ,nev] err 9 excess--defect is ! safe side--x is seldom a fault1 (t5 a real m]it4 ,leave some?+ = ! /ud5t ( y\r works to d--don't *ew ! cud = him4 ,be assur$ he w n omit to pay y = e little ?+ :i* y h enabl$ him to discov]4 ,poor ,pr(essor ,zeis+6 he is f> too ,g]man to leave any field ( discov]y op5 = 8 read]s4 ,b let u return to him2 we left him on 8 back1 lo/ = a "t 9 a hopeless attempt to d\ble ,cape ,horn4 ,we w be k9d to him1 z ! *ild is to 8 man 9 ! ,noah's ark1 & set him on 8 legs among/ 8 toys aga94 ,he is n[ 9 ! vegetable k+dom1 amid/ oak leaves & sections ( ! /ems ( div]s plants4 ,he is 9 8 elem5t once m1 & x 7 ung5]\s n to admit ! m]it ( 8 endeav\rs1 & ! success :i* n[ & !n att5ds x4 ,we w pass ov] 8 horses & _! rid]s1 toge!r ) t portly p]sonage1 ! ,durham ox1 = we h caught a glimpse ( a =m famili> to our eyes1 ! ev]-to-be-admir$ ,p>!non4 ,?is is ! true te/ ( a !ory4 ,unlike ! ,durham ox j pass$ be=e u1 ! ,p>!non w /& /ill to be measur$4 ,x has s /ood = tw5ty c5turies1 & e "o t has scann$ its proportions has pron\nc$ !m exquisite4 ,beauty is n an adaptation to ! acquir$ ta/e ( a s+le nation1 or ! conv5tionality ( a s+le g5]ation4 ,x emanates f a deep-root$ pr9ciple 9 nature1 & appeals to ! v]dict ( our :ole humanity4 ,we don't f9d fault ) ! ,durham ox--8 proportions are probably good1 ?\gh !y be ! result ( bre$+ & cross-bre$+2 /ill we are n sure :e!r1 9 ! m>* ( agriculture1 our gr&*ildr5 may n ?9k him a v wret*$ bea/4 ,b !re is no mi/ake ab\t ! ,p>!non2 z a type ( proportion x /&s1 has /ood1 & %all /&4 ,well1 !n1 let u see h[ ,dr ,zeis+ succe$s ) 8 rule "h4 ,alas6 n a s+le po9t comes "r4 ,! ,p>!non is condemn$1 or its condemnation condemns ! !ory4 ,*oose y\r "p4 ,we *oose ! latt] alt]native2 & n[1 our *oice be+ made1 we ne$ proce$ no fur!r4 ,b a "q or two h pres5t$ !mselves z we w5t along1 :i* dem& an answ]4 ,x may be ask$--,h[ d y acc\nt = ! e/eem 9 :i* ?is law ( ! section 9 extreme & mean ratio 0 held8 ,we reply--,t x 0 e/eem$ j 9 ! same way t a tree is e/eem$ = its fruit4 ,to divide a "r angle into two or ?ree1 f\r or six1 equal p>ts 0 easy en\gh4 ,b to divide x into five or t5 su* p>ts 0 a real difficulty4 ,& h[ 0 ! difficulty got ov]8 ,x 0 effect$ by means ( ?is gold5 rule4 ,?is is its great1 its rul+ application2 & if we adopt ! notion t ! anci5ts 7 possess$ ) ! idea ( ! exi/5ce ( angul> symmetry1 we %all h no difficulty 9 acc\nt+ = _! appreciation ( ?is problem4 ,nay1 we may ev5 g fur!r1 & admit1 ) ,dr ,zeis+1 ! int]pretation ( ! passage ( ,plato1--only ) ?is limitation1 t ,plato1 z a geomet]1 0 c>ri$ away by ! geometry ( /hetics f ! ?+ itself4 ,x may be ask$ aga9--,is x n probable t "s proportionality does exi/ among/ ! p>ts ( natural objects8 ,we reply--,t1 priori1 we expect "s su* sy/em to exi/1 b t x is inconsi/5t ) ! s*eme ( lea/ ef=t1 :i* p]vades & *>act]ises all natural succession 9 space or 9 "t1 t t sy/em %\ld be a complicat$ "o4 ,:atev] x is1 its ess5ce mu/ be simplicity4 ,& no sy/em ( simple l9e> proportion is f\nd 9 nature2 q ! contr>y4 ,we are1 !re=e1 driv5 to ano!r hypo!sis1 viz4--t ! simplicity is "o ( angles1 n ( l9es2 t ! eye e/imates by se>* r\nd a po9t1 n by asc5d+ & desc5d+1 go+ to ! "r & to ! left1--a !ory :i* we conceive all nature conspires to prove4 ,beauty 0 n creat$ = ! eye ( man1 b ! eye ( man & 8 m5tal eye 7 creat$ = ! appreciation ( beauty4 ,exam9e ! =ms ( animals & plants s m9ute t no?+ %ort ( ! mo/ rec5t improvem5ts 9 ! microscope c succe$ 9 detect+ _! symmetry2 or exam9e ! =ms ( ^? little silici\s creations :i* grew ?\s&s ( ye>s be=e ,man 0 plac$ on ! e>?1 &1 ) =ms ( m>vell\s & v>i$ beauty1 !y all po9t to its s\rce 9 angul> symmetry4 ,?is is ! key/one ( =mal beauty1 alike 9 ! m9ute/ animalcule1 & 9 ! noble/ ( ,god's works1 8 own image--,man40 ,,! ,,end4 ,,ballantyne ,,& ,,company1 ,,pr9t]s1 ,,ed9burgh4 ,,footnotes #a ,sir ,david ,brew/]4 #b ,no4 ,,clviii41 ,octob] #ahdc4 #c ,diog5es ,lartius's 8,lives ( ! ,philosoph]s10 lit]ally translat$4 ,bohn3 ,london4 #d ,ibid4 #e ,rose's 8,biographical ,diction>y40 #f ,pr(essor ,laycock1 n[ ( ! ,univ]sity ( ,ed9burgh4 #g 8,! ,geometric ,beauty ( ! ,human ,figure ,def9$10 c4 #h ,longman & ,co41 ,london4 #i ,see ,app5dix4 #aj 8,! ,or?ographic ,beauty ( ! ,p>!non10 c41 & 8,! ,h>monic ,law ( ,nature appli$ to ,ar*itectural ,design40 #aa ,= fur!r details1 see 8,h>monic ,law ( ,nature10 c4 #ab ,by a v simple ma*9e1 :i* ,i h lately inv5t$1 an ellipse ( any giv5 proportions1 ev5 to ^? ( 771 :i* is ! curve ( ! entases ( ! columns ( ! ,p>!non 7see ,plate ,,vii471 & ( any l5g?1 f half an in* to fifty feet or upw>ds1 may be easily & correctly describ$2 ! l5g? & angle ( ! requir$ ellipse be+ all t ne$ be giv54 #ac 8,! ,or?ographic ,beauty ( ! ,p>!non10 c4 #ad 8,! ,or?ographic ,beauty ( ! ,p>!non10 c4 #ae ,ibid4 #af 8,! ,h>monic ,law ( ,nature appli$ to ,ar*itectural ,design40 #ag 8,physio-philosophy40 ,by ,dr ,ok54 ,translat$ by ,talk2 & publi%$ by ! ,ray ,society4 ,london1 #ahdh4 #ah 8,! ,sci5ce ( ^? ,proportions by :i* ! ,human ,head & ,c\nt5ance1 z repres5t$ 9 ,works ( anci5t ,greek ,art1 are di/+ui%$ f ^? ( ord9>y ,nature40 #ai 8,! ,geometric ,beauty ( ! ,human ,figure ,def9$10 c41 & 8,! ,natural ,pr9ciples ( ,beauty ,develop$ 9 ! ,human ,figure40 #bj 8,! ,geometric ,beauty ( ! ,human ,figure ,def9$10 c4 #ba 8,essay on ,ornam5tal ,design10 c41 & 8,! ,geometric ,beauty ( ! ,human ,figure10 c4 #bb 8,a ,nom5clature ( ,col\rs1 applicable to ! ,arts & ,natural ,sci5ces10 c41 c4 #bc ,see pp4 #bd & #be4 #bd 8,! ,pr9ciples ( ,beauty 9 ,col\r+ ,sy/ematis$10 ,f\rte5 ,diagrams1 ea* conta9+ ,six ,col\rs & ,hues4 8,a ,nom5clature ( ,col\rs10 c41 ,=ty ,diagrams1 ea* conta9+ ,twelve ,examples ( ,col\rs1 ,hues1 ,t9ts1 & ,%ades4 8,! ,laws ( ,h>moni\s ,col\r+10 c41 ,"o ,diagram1 conta9+ ,eighte5 ,col\rs & ,hues4 #be 8,et*+s ,repres5t+ ! ,be/ ,examples ( ,grecian & ,roman ,ar*itectural ,ornam5t1 drawn f ! ,orig9als10 c4 ,by ,*>les ,hea?cote ,ta?am1 ,ar*itect4 ,london3 ,prie/ly & ,weale4 #ahbf4 #bf 8,! ,or?ographic ,beauty ( ! ,p>!non10 c4 #bg 8,sci5ce ( ^? ,proportions10 c4 #bh ,abb ,b>?lmie's 8,travels ( ,ana*>sis 9 ,greece10 vol iv41 pp4 #aic1 #aie4 #bi ,abb ,b>?lmie 7vol4 ii41 pp4 #afh1 #afi71 :o cites z 8 au?orities1 ,cic]4 ,de ,nat4 ,deor41 lib4 i41 cap4 ii41 t4 #b1 p4 #dje2 ,ju/9 ,m>t41 ,ovat4 ad ,g5t41 p4 #aj2 ,ari/ot4 ,metaph41 lib4 i41 cap4 v41 t4 #b1 p4 #hde4 #cj ,mll]'s 8,anci5t ,art & its ,rema9s40 #ca 8,ana*>sis' ,travels 9 ,greece40 ,by ! ,abb ,b>?lmie1 vol4 ii41 p4 #cbe4 #cb 8,ana*>sis' ,travels 9 ,greece40 ,by ! ,abb ,b>?lmie1 vol4 vi41 p4 #bbe4 ,! au?orities ! ,abb quotes are--,qu9til41 lib4 xii41 cap4 x41 p4 #gdd2 ,pl941 lib4 xxxv41 cap4 ix41 p4 #fia4 #cc ,mll]'s 8,ar*ology ( ,art10 c4 ,works by ! ,same ,au?or4 ,i4 ,9 royal #hvo1 ) ,copp]plate ,illu/rations1 price #bs4 #f;d41 ,,! ,,h>monic ,,law ,,( ,,nature ,,appli$ ,,to ,,ar*itectural ,,design4 ,f ! ,a!num4 ,! beauty ( ! !ory is its univ]sality1 & its simplicity4 ,9 nature1 ! ,creator accompli%$ 8 purposes by ! simple/ means--! h>mony ( nature is inde/ructible & self-re/or+4 ,mr ,hay's book on ! 8,p>!non10 on ! 8,natural ,pr9ciples ( ,beauty z develop$ 9 ! ,human ,figure10 8 8,pr9ciples ( ,symmetrical ,beauty10 8 8,pr9ciples ( ,col\r+1 & ,nom5clature ( ,col\rs10 8 8,sci5ce ( ,proportion10 & 8,essay on ,ornam5tal ,design10 we h already notic$ ) praise z ! results ( philosophical & orig9al ?\ght4 ,f ! ,daily ,news4 ,?is essay is a new application to ,l9coln ca!dral 9 ,go?ic ar*itecture1 & to ! ,temple ( ,!seus 9 ,greek ar*itecture1 ( ! pr9ciples ( symmetrical beauty already s pr(usely illu/rat$ & demon/rat$ by ,mr ,hay4 ,! !ory :i* ,mr ,hay has prop\nd$ 9 s _m volumes is n only a spl5did contribution t[>ds a sci5ce ( /hetic proportions1 b1 = ! fir/ "t 9 ! hi/ory ( art1 proves ! possibility1 & lays ! f\ndations ( su* a sci5ce4 ,to ^? :o are n acqua9t$ ) ! facts1 ^! expressions w s\nd hyp]bolical1 b !y are mo/ true4 ,,ii4 ,9 royal #hvo1 ) ,copp]plate ,illu/rations1 price #es41 ,,! ,,natural ,,pr9ciples ,,( ,,beauty1 ,,z ,,develop$ ,,9 ,,! ,,human ,,figure4 ,f ! ,spectator4 ,we _c refuse to ent]ta9 ,mr ,hay's sy/em z ( s+ul> intr9sic excell5ce4 ,! simplicity ( 8 law & its g5]ality impress !mselves m deeply on ! conviction ) ea* "t ( en=cem5t4 ,8 !ory proce$s f ! idea1 t 9 nature e ?+ is effect$ by means m simple ?an any o!r t c\ld h be5 conceiv$1--an idea c]ta9ly consi/5t ) :atev] we c trace out or imag9e ( ! all-wise fram+ ( ! univ]se4 ,f ! ,sun4 ,by f\nd+ 7if we may s phrase x7 ?is noble !ory1 ,mr ,hay has cov]$ 8 "n ) di/9ction1 & has laid ! basis1 we conceive1 ( no ephem]al reputation4 ,by illu/rat+ x anew1 ?r\gh ! m$ium ( ?is graceful treatise1 he has conf]r$ a real boon ^u ! community1 = he has af=d$ ! public ano!r opportunity ( foll[+ ! gold5 rule ( ! poet--by look+ ?r\gh ! holy & awful my/]y ( creation to ! holi] & yet m awful my/]y ( ,omnipot5ce4 ,f ! ,cambridge ,j\rnal ( ,classical & ,sacr$ ,philology4 ,! inquiries :i* ( late ye>s h be5 in/itut$ by ,mr ,d4 ,r4 ,hay ( ,ed9burgh1 on ! proportions ( ! human figure1 & on ! natural pr9ciples ( beauty1 z illu/rat$ by works ( ,greek art1 con/itute an epo* 9 ! /udy ( /hetics & ! philosophy ( =m4 ,,iii4 ,9 royal #hvo1 ) ,copp]plate ,illu/rations1 price #es41 ,,! ,,or?ographic ,,beauty ,,( ,,! ,,p>!non ,,ref]r$ ,,to ,a ,,law ,,( ,,nature4 ,to :i* are prefix$1 a few ,obs]vations on ! ,importance ( /hetic ,sci5ce z an ,elem5t 9 ,ar*itectural ,education4 ,f ! ,scotti% ,lit]>y ,gazette4 ,we ?9k ?is "w w satisfy e imp>tial m9d t ,mr ,hay has develop$ ! true !ory ( ! ,p>!non--t he has1 9 fact1 to use a k9dr$ phraseology1 bo? p>s$ & scann$ ?is exquisitely beautiful piece ( ar*itectural composition1 & t1 9 do+ s1 he has provid$ ! true key by :i* ! treasures ( ,greek art may be fur!r unlock$1 & r5d]$ ! means ( correct+1 improv+1 & elevat+ mod]n practice4 ,f ! ,ed9burgh ,gu>dian4 ,aga9 & aga9 ! attempt has be5 made to detect h>monic ratios 9 ! measurem5t ( ,a!nian ar*itecture1 b ev] )\t rew>d4 ,mr ,hay has1 h[ev]1 made ! discov]y1 & to an ext5t ( :i* no "o _h previ\sly dreamt4 ,,iv4 ,9 #hvo1 #ajj ,plates1 price #fs41 ,,fir/ ,,pr9ciples ,,( ,,symmetrical ,,beauty4 ,f ! ,spectator4 ,?is is a gramm> ( pure =m1 9 :i* ! elem5ts ( symmetrical1 z di/+ui%$ f picturesque beauty1 are demon/rat$1 by r$uc+ ! outl9es or planes ( curvil9e> & rectil9e> =ms to _! orig9 9 ! pr9ciples ( geometrical proportion4 ,9 ?us analys+ symmetry ( outl9e 9 natural & artificial objects1 ,mr ,hay det]m9es ! fix$ pr9ciples ( beauty 9 positive %ape1 & %ews h[ beautiful =ms may be reproduc$ & inf9itely v>i$ ) ma!matical precision4 ,hi!rto ! orig9at+ & copy+ ( beautiful =ms h be5 alike empirical2 ! production ( a new design = a vase or a jug has be5 a matt] ( *ance betwe5 ! eye & ! h&2 & ! copy+ ( a ,greek m\ld+ or ornam5t1 a m]ely me*anical process4 ,by a s]ies ( problems1 ,mr ,hay places bo? ! inv5tion & imitation ( beautiful =ms on a sure basis ( sci5ce1 giv+ to ! fancy ( orig9al m9ds a clue to ! evolv+ ( new & elegant %apes1 9 :i* ! inf9ite res\rces ( nature are made subs]vi5t to ! uses ( art4 ,! volume is illu/rat$ by "o hundr$ diagrams beautifully execut$1 t s]ve to expla9 ! text1 & sugge/ new ideas ( beauty ( cont\r 9 common objects4 ,to design]s ( pott]y1 h>dw>e1 & ar*itectural ornam5ts1 ?is "w is p>ticul>ly valuable2 b arti/s ( e k9d1 & workm5 ( intellig5ce1 w f9d x ( great utility4 ,f ! ,a!num4 ,! volume be=e u is ! sev5? ( ,mr ,hay's works4 ,x is ! mo/ practical & sy/ematic1 & likely to be "o ( ! mo/ useful4 ,x is1 9 %ort1 a gramm> ( =m1 or a spell+-book ( beauty4 ,?is is beg9n+ at ! "r end ( ! matt]2 & ! necessity = ?is k9d ( k w inevitably1 ?\gh gradually1 be felt4 ,! "w w1 !re=e1 be ultimately appreciat$ & adopt$ z an introduction to ! /udy ( beautiful =ms4 ,! ?ird "p ( ! "w treats ( ! ,greek oval or composite ellipse1 z ,mr ,hay calls x4 ,x is an ellipse ( ?ree foci1 & gives practical =ms = vases & ar*itectural m\ld+s1 :i* are curi\s to ! ar*itect1 & w be v useful bo? to ! pott]1 ! m\ld]1 & ! patt]n-draw]4 ,a f\r? "p conta9s applications ( ?is to practice4 ,( ! details work$ out ) s mu* judgm5t & +5uity by ,mr ,hay1 we %\ld 9 va9 attempt to communicate j notions )\t ! engrav+s ( :i* 8 book is full4 ,we mu/1 !re=e1 ref] to ! "w itself4 ,! =ms !re giv5 are full ( beauty1 & s f> t5d to prove ! sy/em4 ,v4 ,9 #hvo1 #ad ,col\r$ ,diagrams1 ,second ,edition1 price #aes41 ,,! ,,pr9ciples ,,( ,,beauty ,,9 ,,col\r+ ,,sy/ematis$4 ,f ! ,spectator4 ,9 ?is new analysis ( ! h>monies ( col\r1 ,mr ,hay has p]=m$ ! useful s]vice ( trac+ to ! op]ation ( c]ta9 fix$ pr9ciples ! s\rces ( beauty 9 p>ticul> comb9ations ( hues & t9ts2 s t arti/s may1 by ! aid ( ?is book1 produce1 ) ma!matical c]ta9ty1 ! ri*e/ effects1 hi!rto atta9able by g5ius alone4 ,mr ,hay has r$uc$ ?is bran* ( art to a p]fect sy/em1 & prov$ t an (f5ce aga9/ good ta/e 9 respect to comb9ations ( col\r is1 9 effect1 a violation ( natural laws4 ,,vi4 ,9 #hvo1 #bbh ,examples ( ,col\rs1 ,hues1 ,t9ts1 & ,%ades1 price #fcs41 ,a ,,nom5clature ,,( ,,col\rs1 ,,applicable ,,to ,,! ,,arts ,,& ,,natural ,,sci5ces4 ,f ! ,daily ,news4 ,9 ?is "w ,mr ,hay has br\ght a l>g] am\nt ( practical k to be> on ! subject ( col\r ?an any o!r writ] ) :om we are acqua9t$1 & 9 proportion to ?is practical k is1 z might be expect$1 ! excell5ce ( 8 treatise4 ,!re is mu* 9 ?is volume :i* we w\ld mo/ e>ne/ly recomm5d to ! notice ( arti/s1 h\se decorators1 &1 inde$1 to all ^: bus9ess or pr(ession requires a k ( ! managem5t ( col\r4 ,! "w is replete ) h9ts :i* !y might turn to pr(itable acc\nt1 & :i* !y w f9d n[h]e else4 ,f ! ,a!num4 ,we h =m]ly /at$ ! high op9ion we ent]ta9 ( ,mr ,hay's previ\s ex]tions = ! improvem5t ( decorative art 9 ?is c\ntry4 ,we h already aw>d$ him ! m]it ( inv5tion & creation ( ! new & ! beautiful 9 =m4 ,9 8 =m] treatises he furni%$ a !ory ( def9ite proportions = ! creation ( ! beautiful 9 =m4 ,9 ! pres5t "w he proposes to supply a scale ( def9ite proportions = *romatic beauty4 ,= ?is purpose he sets out v prop]ly ) a precise nom5clature ( col\r4 ,9 ?is he has con/ruct$ a vocabul>y = ! arti/--an alphabet = ! artizan4 ,he has gone fur!r--he con/ructs words = ?ree syllables4 ,f ?is "t1 x w be possible to write a lett] 9 ,ed9burgh ab\t a col\r$ composition1 :i* %all be read (f 9 ,london1 ,p>is1 ,/ ,pet]sburg1 or ,pek91 & %all s express its nature t x c be reproduc$ 9 p]fect id5tity4 ,?is ,mr ,hay has done1 or at lea/ s ne>ly1 z to des]ve our ?anks on behalf ( art1 & arti/s ( all grades1 ev5 to ! decorative artizan--n "o ( :om1 be he h\se-pa9t]1 *9a patt]n-draw]1 or calico pr9t]1 %\ld be )\t ! simple manual ( 8words = col\rs40 ,,vii4 ,9 po/ #hvo1 ) a ,col\r$ ,diagram1 ,six? ,edition1 price #gs4 #f;d41 ,,! ,,laws ,,( ,,h>moni\s ,,col\r+ ,,adapt$ ,,to ,,int]ior ,,decorations4 ,f ! ,atlas4 ,e l9e ( ?is useful book %ews t ! au?or has contriv$ to intellectualise 8 subject 9 a v int]e/+ mann]4 ,! pr9ciples ( h>mony 9 col\r z appli$ to decorative purposes1 are expla9$ & en=c$ 9 a lucid & practical /yle1 & ! relations ( ! v>i\s t9ts & %ades to ea* o!r1 s z to produce a h>moni\s result1 are descant$ ^u mo/ satisfactorily & orig9ally4 ,f ! ,ed9burgh ,review4 ,9 s f> z we "k1 ,mr ,hay is ! fir/ & only mod]n arti/ :o has ent]$ ^u ! /udy ( ^! subjects )\t ! trammels ( prejudice & au?ority4 ,sett+ aside ! ord9ances ( fa%ion1 z well z ! dicta ( speculation1 he has s\ght ! f\ndation ( 8 pr(ession 9 ! prop]ties ( light1 & 9 ! laws ( visual s5sation1 by :i* ^! prop]ties are recognis$ & modifi$4 ,! tru?s to :i* he has appeal$ are fundam5tal & irrefragable4 ,f ! ,a!num4 ,we h reg>d$1 & d /ill reg>d1 ! production ( ,mr ,hay's works z a rem>kable psy*ological ph5om5on--"o :i* is in/ructive bo? = ! philosoph] & ! critic to /udy ) c>e & int]e/1 n unm+l$ ) respect4 ,we see h[ 8 m9d has be5 gradually guid$ by ,nature h]self out ( "o track1 & into ano!r1 & ev] & anon lead+ him to "s ve9 ( ! beautiful & true1 hi!rto unwork$4 ,,viii4 ,9 #dto1 #be ,plates1 price #cfs41 ,,on ,,! ,,sci5ce ,,( ,,^? ,,proportions ,,by ,,:i* ,,! ,,human ,,head ,,& ,,c\nt5ance1 ,,z ,,repres5t$ ,,9 ,,anci5t ,,greek ,,art1 ,,are ,,di/+ui%$ ,,f ,,^? ,,( ,,ord9>y ,,nature4 7,,pr9t$ ,,by ,,p]mission47 ,f a ,lett] to ! ,au?or by ,sir ,william ,hamilton1 ,b>t41 ,pr(essor ( ,logic & ,metaphysics 9 ! ,ed9burgh ,univ]sity4 ,y\r v elegant volume1 8,sci5ce ( ^? ,proportions10 c41 is to me extremely int]e/+1 z af=d+ an able contribution to :at is ! anci5t1 &1 ,i conceive1 ! true !ory ( ! beautiful4 ,b ?\gh y\r doctr9e co9cides ) ! "o preval5t ?r\gh all antiquity1 x appe>s to me q indep5d5t & orig9al 9 y2 & ,i e/eem x ! m t x /&s oppos$ to ! hundr$ "o-sid$ & exclusive views preval5t 9 mod]n times4 ,f ,*amb]s's ,ed9burgh ,j\rnal4 ,we n[ come to ano!r1 & mu* m rem>kable corroboration1 :i* calls ^u u to introduce to our read]s "o ( ! mo/ valuable & orig9al contributions t h ev] be5 made to ! ,philosophy ( ,art1 viz41 ,mr ,hay's "w 8,on ! ,sci5ce ( ^? ,proportions10 c4 ,mr ,hay's plan is simply to =m a scale compos$ ( ! well-kn[n vibrations ( ! mono*ord1 :i* are ! alphabet ( music1 & !n to draw ^u ! quadrant ( a circle angles answ]+ to ^! vibrations4 ,) ! s]ies ( triangles ?us obta9$ he comb9es a circle & an ellipse1 ! proportions ( :i* are d]iv$ f ! triangles !mselves2 & ?us he obta9s an infallible rule = ! composition ( ! head ( ideal beauty4 ,,ix4 ,9 #dto1 #af ,plates1 price #cjs41 ,,! ,,geometric ,,beauty ,,( ,,! ,,human ,,figure ,,def9$4 ,to :i* is prefix$1 a ,,sy/em ( ,,/hetic ,,proportion applicable to ,,ar*itecture & ! o!r ,,=mative ,,arts4 ,f ! ,cambridge ,j\rnal ( ,classical & ,sacr$ ,philology4 ,we feel b\nd to pay ,mr ,hay a l>ge & glad tribute ( praise = hav+ devis$ a sy/em ( proportions :i* rises sup]ior to ! idiosyncrasies ( diff]5t arti/s1 :i* br+s back to "o common type ! s5sations ( ,eye & ,e>1 & s makes a giant /ride t[>ds t codification ( ! laws ( ! univ]se :i* x is ! bus9ess ( sci5ce to effect4 ,we h no hesitation 9 say+ t1 = sci5tific precision ( me?od & importance ( results1 ,alb]t ,dur]1 ,da ,v9ci1 & ,hog>?--n to m5tion less notewor?y writ]s--mu/ all yield ! palm to ,mr ,hay4 ,x4 ,9 oblong folio1 #eg ,plates & num]\s ,woodcuts1 price #dbs41 ,,an ,,essay ,,on ,,ornam5tal ,,design1 ,,9 ,,:i* ,,its ,,true ,,pr9ciples ,,are ,,develop$ ,,& ,,elucidat$1 c4 ,f ! ,a!num4 ,9 conclusion1 ,mr ,hay's book goes =? ) our be/ wi%es4 ,x mu/ be good4 ,x mu/ be prolific ( ?\ght--/imulant ( inv5tion4 ,x is to be ackn[l$g$ z a b5efit ( an unusual "* conf]r$ on ! arts ( ornam5tal design4 ,f ! ,spectator4 ,mr ,hay has /udi$ ! subject deeply & sci5tifically4 ,9 ?is treatise on ornam5tal design1 ! /ud5t w f9d a clue to ! discov]y ( ! s\rce ( an endless v>iety ( beautiful =ms & comb9ations ( l9es1 9 ! application ( c]ta9 fix$ laws ( h>moni\s proportion to ! purposes ( art4 ,mr ,hay also exemplifies ! application ( 8 !ory ( l9e> h>mony to ! production ( beautiful =ms g5]ally1 te/+ its s\ndness by apply+ x to ! human figure1 & ! pure/ creations ( ,greek art4 ,f ,fras]'s ,magaz9e4 ,ea* "p ( ?is "w is enri*$ by diagrams ( great beauty1 direct emanations ( pr9ciple1 &1 consequ5tly1 pres5t+ entirely new comb9ations ( =m4 ,_h our space p]mitt$1 we %\ld h made "s extracts f ?is 8,essay on ,ornam5tal ,design20 & we w\ld h done s1 because ( ! discrim9at+ ta/e by :i* x is p]vad$1 & ! =cible obs]vations :i* x conta9s2 b we _c v5ture on ! indulg5ce4 ,,xi4 ,9 #dto1 #ag ,plates & #ch ,woodcuts1 price #bes41 ,,proportion1 ,,or ,,! ,,geometric ,,pr9ciple ,,( ,,beauty ,,analys$4 ,,xii4 ,9 #dto1 #ah ,plates & num]\s ,woodcuts1 price #aes41 ,,! ,,natural ,,pr9ciples ,,& ,,analogy ,,( ,,! ,,h>mony ,,( ,,=m4 ,f ! ,ed9burgh ,review4 ,not)/&+ "s trivial po9ts ( diff]5ce betwe5 ,mr ,hay's views & our own1 we h d]iv$ ! greate/ pleasure f ! p]usal ( ^! works4 ,!y are all compos$ ) accuracy & ev5 elegance4 ,8 op9ions & views are di/9ctly br\ght be=e ! read]1 & /at$ ) t mode/y :i* *>act]ises g5ius1 & t firmness :i* indicates tru?4 ,f ,blackwood's ,magaz9e4 ,we h no d\bt t :5 ,mr ,hay's ,art-discov]y is duly develop$ & taught1 z x %\ld be1 9 our s*ools1 x w d m to improve ! g5]al ta/e ?an any?+ :i* has yet be5 devis$4