,,! ,,beautiful ,,necessity ,sev5 ,essays on ,!osophy & ,ar*itecture by ,,claude ,,bragdon1 ,f4,a4,i4,a4 ,,mcmxxii ,let u build alt>s to ! ,beautiful ,necessity --,,em]son ,by ! ,same ,au?or3 ,episodes ,f ,an ,unwritt5 ,hi/ory ,! ,gold5 ,p]son ,9 ,! ,he>t ,ar*itecture ,& ,democracy ,a ,prim] ,( ,high] ,space ,f\r ,dim5sional ,vi/as ,projective ,ornam5t ,oracle ,,cont5ts ,i ,,! ,,art ,,( ,,ar*itecture ,,ii ,,unity ,,& ,,pol>ity ,,iii ,,*angeless ,,*ange ,,iv ,,! ,,bodily ,,temple ,v ,,lat5t ,,geometry ,,vi ,,! ,,ari?metic ,,( ,,beauty ,,vii ,,froz5 ,,music ,,conclusion ,,preface ,,to ,,! ,,second ,,edition ,! ,beautiful ,necessity 0 fir/ publi%$ 9 #aiaj4 ,save = a slim volume ( privately pr9t$ v]se x 0 my fir/ book4 ,i work$ h>d on x4 ,fifte5 ye>s elaps$ betwe5 its beg9n+ & completion2 x 0 twice publi%$ s]ially--writt51 rewritt5 & tre-writt5--be=e x rea*$ its ultimate inc>nation 9 book =m4 ,confront$ n[ ) ! opportunity to revise ! text aga91 ,i f9d myself 9 ! position ( a surgeon :o feels t ! op]ation he is call$ ^u to p]=m may p]haps h>m m ?an x c help4 ,prud5ce !re=e prevails ov] my passion = dissection3 w>n$ by em95t examples1 ,i fe> t any injection ( my m mature & less cocksure consci\sness into ?is book might impair its unity--t ,i nev] c\ld recapture ! fir/ f9e c>eless rapture4 ,! text /&s !re=e z orig9ally publi%$ save = a few v]bal *anges1 & :atev] res]vations ,i h ab\t x %all be /at$ 9 ?is preface4 ,^! are n _m nor important3 ,! ,beautiful ,necessity conta9s no?+ t ,i ne$ repudiate or c>e to contradict4 ,its !sis1 briefly /at$1 is t art 9 all its manife/ations is an expression ( ! cosmic life1 & t its symbols con/itute a language by means ( :i* ?is life is publi%$ & repres5t$4 ,art is at all times subject to ! ,beautiful ,necessity ( proclaim+ ! _w ord]4 ,9 attempt+ to develop ?is !sis x 0 n necess>y 7nor z ,i n[ ?9k1 desirable7 to l9k x up 9 s def9ite a mann] ) !osophy4 ,! individual consci\sness is color$ by ! p>ticul> m$ium ?r\gh :i* x receives tru?1 & = me t m$ium 0 !osophy4 ,?\gh ! book might ga9 a m unprejudic$ he>+1 & f a l>g] audi5ce1 by ! removal ( ! !osophic color-scre51 x %all rema91 = its removal n[ might seem to imply a loss ( fai? 9 ! fundam5tal t5ets ( !osophy1 & su* an implication w\ld n be true4 ,! ideas 9 reg>d to "t & space are ^? commonly curr5t 9 ! _w until ! adv5t ( ! ,!ory ( ,relativity4 ,to a g5]ation br\ght up on ,e9/e9 & ,ousp5sky !y are b\nd to appe> l[] dim5sional4 ,m]ely to /ate ?is fact is to deal ) x to ! ext5t x ne$s to be dealt )4 ,! integrity ( my argum5t is n impair$ by ^! new views4 ,! "o important influ5ce t has op]at$ to modify my op9ions conc]n+ ! ma!matical basis ( ! arts ( space has be5 ! discov]ies ( ,mr4 ,jay ,hambidge ) reg>d to ! practice ( ! ,greeks 9 ^! matt]s1 z exemplifi$ 9 _! temples & _! c]amics1 & nam$ by him ,dynamic ,symmetry4 ,9 trac+ ev]y?+ back to ! log>i?mic spiral 7:i* embodies ! pr9ciple ( extreme & mean ratios7 ,i consid] t ,mr4 ,hambidge has made "o ( ^? g5]alizations :i* reorganizes ! old k & organizes ! new4 ,x w\ld be only natural if 9 8 imm]sion 9 8 idea he ov]works x1 b ,mr4 ,hambidge is a man ( su* intellectual integrity & ?or\ghness ( me?od t he may be tru/$ n to w>p ! facts to fit 8 !ories4 ,! tru? ( ! matt] is t ! entire field ( rese>* into ! ma!matics ( ,beauty is ( su* ri*ness t :]ev] a man plants 8 metaphysical spade he is sure to come ^u pay dirt4 ,! ,beautiful ,necessity repres5ts ! result ( my own prospect+2 ,dynamic ,symmetry repres5ts ! result ( 84 ,if at any po9t our f9d+s appe> to conflict1 x is less likely t "o or ! o!r ( u is mi/ak5 ?an t ea* is "r f 8 own po9t ( view4 ,be t z x may1 ,i %\ld be ! la/ man 9 ! _w to diff] f ,mr4 ,hambidge1 = if he convict$ me ( e conceivable error 8 "w w\ld /ill rema9 ! greate/ ju/ification & confirmation ( my fundam5tal cont5tion--t art is an expression ( ! _w ord] & is !re=e ord]ly1 organic2 subject to ma!matical law1 & susceptible ( ma!matical analysis4 ,,claude ,,bragdon ,ro*e/]1 ,n4,y4 ,april1 #aibb ,i ,,! ,,art ,,( ,,ar*itecture ,"o ( ! advantages ( a ?or\gh assimilation ( :at may be call$ ! !osophic idea is t x c be appli$ ) advantage to e dep>tm5t ( k & ( human activity3 l ! key to a cryptogram x r5d]s cle> & simple t :i* be=e seem$ intricate & obscure4 ,let u apply ?is key to ! subject ( art1 & to ! art ( ar*itecture 9 p>ticul>1 & see if by s do+ we may n le>n m ( art ?an we knew be=e1 & m ( !osophy too4 ,! !osophic idea is t ev]y?+ is an expression ( ! ,self--or :atev] o!r "n "o may *oose to give to t imman5t unkn[n reality :i* =ev] hides beh9d all ph5om5al life--b because1 imm]s$ z we are 9 mat]iality1 our *ief av5ue ( k is s5se p]ception1 a m exact expression ( ! !osophic idea w\ld be3 ,ev]y?+ is ! expression ( ! ,self 9 t]ms ( s5se4 ,art1 accord+ly1 is ! expression ( ! ,self 9 t]ms ( s5se4 ,n[ ?\gh ! ,self is "o1 s5se is n "o1 b manifold3 & !re=e !re are arts1 ea* address$ to "s p>ticul> faculty or gr\p ( faculties1 & ea* express+ "s p>ticul> quality or gr\p ( qualities ( ! ,self4 ,! :ite light ( ,tru? is ?us brok5 up into a ra9b[-t9t$ spectrum ( ,beauty1 9 :i* ! v>i\s arts are colors1 ea* di/9ct1 yet m]g+ "o into ano!r--poetry into music2 pa9t+ into decoration2 decoration becom+ sculpture2 sculpture--ar*itecture1 & s on4 ,9 su* a spectrum ( ! arts ea* "o occupies a def9ite place1 & all toge!r =m a s]ies ( :i* music & ar*itecture are ! two extremes4 ,t su* is _! relative position may be demon/rat$ 9 v>i\s ways4 ,! !osophic explanation involv+ ! famili> idea ( ! pairs ( opposites w\ld be some?+ z foll[s4 ,accord+ to ! ,h9du-,aryan !ory1 ,brahma1 t ! _w might be born1 fell asund] into man & wife--became 9 o!r words "n & =m,a ,! two univ]sal aspects ( "n & =m are :at philosoph]s call ! two modes ( consci\sness1 "o ( "t1 & ! o!r ( space4 ,^! are ! two gates ?r\gh :i* ideas ent] ph5om5al life2 ! two boxes1 z x 71 t conta9 all ! toys ) :i* we play4 ,ev]y?+1 7 we only ke5 en\gh to p]ceive x1 be>s ! m>k ( "o or ! o!r ( !m1 & may be classifi$ accord+ly4 ,9 su* a classification music is se5 to be alli$ to "t1 & ar*itecture to space1 because music is successive 9 its mode ( manife/ation1 & 9 "t alone ev]y?+ w\ld occur successively1 "o ?+ foll[+ ano!r2 :ile ar*itecture1 on ! o!r h&1 impresses itself ^u ! behold] all at once1 & 9 space alone all ?+s w\ld exi/ simultane\sly4 ,music1 :i* is 9 "t alone1 )\t any relation to space2 & ar*itecture1 :i* is 9 space alone1 )\t any relation to "t1 are ?us se5 to /& at opposite ends ( ! art spectrum1 & to be1 9 a s5se1 ! only pure arts1 because 9 all ! o!rs ! elem5ts ( bo? "t & space ent] 9 v>y+ proportion1 ei!r actually or by implication4 ,poetry & ! drama are alli$ to music inasmu* z ! ideas & images ( :i* !y are made up are pres5t$ successively1 yet ^! images are = ! mo/ "p =ms ( space4 ,sculpture on ! o!r h& is cle>ly alli$ to ar*itecture1 & s to space1 b ! elem5t ( action1 susp5d$ ?\gh x be1 affiliates x ) ! opposite or "t pole4 ,pa9t+ occupies a middle position1 s9ce 9 x space in/ead ( be+ actual has become ideal--?ree dim5sions be+ express$ ?r\gh ! m$ium%ip ( two--& "t ent]s into x m l>gely ?an into sculpture by reason ( ! great] ease ) :i* complicat$ action c be indicat$3 a picture be+ ne>ly always "t arre/$ 9 midc\rse z x 7--a mom5t transfix$4 ,9 ord] to =m a j conception ( ! relation betwe5 music & ar*itecture x is necess>y t ! two %\ld be conceiv$ ( n z /&+ at opposite ends ( a s]ies repres5t$ by a /raight l9e1 b r 9 juxtaposition1 z 9 ! anci5t ,egyptian symbol ( a s]p5t hold+ its tail 9 its m\?1 ! head 9 ?is case correspond+ to music1 & ! tail to ar*itecture2 9 o!r words1 ?\gh 9 "o s5se !y are ! mo/-widely sep>at$ ( ! arts1 9 ano!r !y are ! mo/ closely relat$4 ,music be+ purely 9 "t & ar*itecture be+ purely 9 space1 ea* is1 9 a mann] & to a degree n possible ) any ( ! o!r arts1 conv]tible into ! o!r1 by reason ( ! correspond5ce subsi/+ betwe5 int]vals ( "t & int]vals ( space4 ,a p]ception ( ?is may h inspir$ ! fam\s say+ t ar*itecture is froz5 music1 a poetical /atem5t ( a philosophical tru?1 s9ce t :i* 9 music is express$ by means ( h>moni\s int]vals ( "t & pit*1 successively1 aft] ! mann] ( "t1 may be translat$ into correspond+ int]vals ( ar*itectural void & solid1 height & wid?4 ,9 ano!r s5se music & ar*itecture are alli$4 ,!y alone ( all ! arts are purely creative1 s9ce 9 !m is pres5t$1 n a lik5ess ( "s kn[n idea1 b a ?+-9-itself br\ght to a di/9ct & complete expression ( its nature4 ,nei!r a musical composition nor a "w ( ar*itecture dep5ds = its effectiv5ess ^u resemblances to natural s\nds 9 ! "o case1 or to natural =ms 9 ! o!r4 ,( none ( ! o!r arts is ?is to su* a degree true3 !y are n s mu* creative z re-creative1 = 9 !m all ! arti/ takes 8 subject ready made f nature & pres5ts x anew accord+ to ! dictates ( 8 g5ius4 ,! *>act]i/ic diff]5ces betwe5 music & ar*itecture are ! same z ^? :i* subsi/ betwe5 "t & space4 ,n[ "t & space are su* ab/ract ideas t !y c be dealt ) be/ ?r\gh _! correspond+ correlatives 9 ! natural _w1 = x is a fundam5tal !osophic t5et t nature ev]y:]e ab\nds 9 su* correspond5ces2 t nature1 9 its myriad =ms1 is inde$ ! concrete pres5tm5t ( ab/ract unities4 ,! en]gy :i* ev]y:]e animates =m is a type ( "t )9 space2 ! m9d work+ 9 & ?r\gh ! body is ano!r expression ( ! same ?+4 ,correspond+ly1 music is dynamic1 subjective1 m5tal1 ( "o dim5sion2 :ile ar*itecture is /atic1 objective1 physical1 ( ?ree dim5sions2 su/a9+ ! same relation to music & ! o!r arts z does ! human body to ! v>i\s organs :i* compose1 & consci\snesses :i* animate x 7x be+ ! res]vatory ( ^! organs & ! vehicle ( ^! consci\snesses72 & a "w ( ar*itecture 9 l mann] may & sometimes does include all ( ! o!r arts )9 itself4 ,sculpture acc5tuates & enri*es1 pa9t+ adorns1 works ( lit]ature are /or$ )9 x1 poetry & ! drama awake its e*oes1 :ile music ?rills to its utt]mo/ recesses1 l ! v _s ( life t+l+ ?r\gh ! body's fibres4 ,su* be+ ! relation betwe5 !m1 ! diff]5ce 9 ! nature ( ! ideas bodi$ =? 9 music & 9 ar*itecture becomes app>5t4 ,music is int]ior1 ab/ract1 subjective1 speak+ directly to ! s\l 9 a simple & univ]sal language ^: mean+ is made p]sonal & p>ticul> 9 ! brea/ ( ea* li/5]3 ,music alone ( all ! arts1 says ,balzac1 has p[] to make u live )9 ourselves4 ,a "w ( ar*itecture is ! exact opposite ( ?is3 exi/+ pr9cipally & prim>ily = ! uses ( ! body1 x is l ! body a concrete organism1 atta9+ to e/hetic expression only 9 ! reconciliation & fulfilm5t ( _m conflict+ practical requirem5ts4 ,music is pure beauty1 ! voice ( ! unfett]$ & p]petually vani%+ s\l ( ?+s2 ar*itecture is t s\l imprison$ 9 a =m1 become subject to ! law ( causality1 beat5 ^u by ! elem5ts1 at w> ) gravity1 ! slave ( man4 ,"o is ! ,ariel ( ! arts2 ! o!r1 ,caliban4 ,com+ n[ to ! consid]ation ( ar*itecture 9 its hi/orical r ?an its philosophical aspect1 x w be %[n h[ c]ta9 !osophical concepts are applicable "h4 ,( ^! none is m famili> & none m fundam5tal ?an ! idea ( re9c>nation4 ,by re9c>nation m ?an m]e physical re-bir? is meant1 = physical re-bir? is b a s+le manife/ation ( t univ]sal law ( alt]nation ( /ate1 ( animation ( vehicles1 & progression ?r\gh relat$ planes1 9 accordance ) :i* all ?+s move1 & z x 7 make music--ea* cycle complete1 yet "p ( a l>g] cycle1 ! inc>nate monad pass+ ?r\gh correlat$ *anges1 c>ry+ along & br++ into manife/ation 9 ea* successive arc ( ! spiral ! exp]i5ce accumulat$ 9 all prec$+ /ates1 & at ! same "t unfold+ t p[] ( ! ,self peculi> to ! plane 9 :i* x is mom5t>ily manife/+4 ,?is law f9ds exemplification 9 ! hi/ory ( ar*itecture 9 ! ord]ly fl[ ( ! build+ impulse f "o nation & "o c\ntry to a diff]5t nation & a diff]5t c\ntry3 its new vehicle ( manife/ation2 also 9 ! cont9uity & increas+ complexity ( ! developm5t ( t impulse 9 manife/ation2 ea* inc>nation summ>iz+ all ^? :i* h gone be=e1 & add+ "s new factor peculi> to itself alone2 ea* be+ a gr[?1 a life1 ) p]iods correspond+ to *ildhood1 y\?1 maturity & decad5ce2 ea* also typify+ 9 its entirety "s s+le "o ( ^! life-p]iods1 & reveal+ "s special aspect or p[] ( ! ,self4 ,= ! sake ( cle>ness & brevity ! consid]ation ( only "o ( sev]al ar*itectural evolutions w be attempt$3 t :i*1 aris+ 9 ! nor? ( ,africa1 spread to s\!rn ,europe1 !nce to ! nor?we/ ( ,europe & to ,engl&--! ar*itecture1 9 %ort1 ( ! s-call$ civiliz$ _w4 ,?is ar*itecture1 ant]ior to ! ,*ri/ian era1 may be broadly divid$ into ?ree great p]iods1 dur+ :i* x 0 successively practic$ by ?ree peoples3 ! ,egyptians1 ! ,greeks & ! ,romans4 ,!n int]v5$ ! ,d>k ,ages1 & a new art arose1 ! ,go?ic1 :i* 0 a fl[]+ out 9 /one ( ! _s ( ,*ri/ianity4 ,?is 0 9 turn succe$$ by ! ,r5aissance1 ! impulse ( :i* rema9s to-day unexhau/$4 ,9 ea* ( ^! ar*itectures ! peculi> g5ius ( a p & ( a p]iod atta9$ to a beautiful1 complete & coh]5t utt]ance1 & not)/&+ ! consid]able int]vals ( "t :i* sometimes sep>at$ !m !y succe$$ "o ano!r logically & inevitably1 & ea* 0 relat$ to ! "o :i* prec$$ & :i* foll[$ x 9 a p>ticul> & intimate mann]4 ,! p[] & wisdom ( anci5t ,egypt 0 ve/$ 9 its prie/hood1 :i* 0 compos$ ( individuals exceptionally qualifi$ by bir? & tra9+ = _! high (fice1 tri$ by ! sev]e/ ordeals & b\nd by ! mo/ solemn oa?s4 ,! prie/s 7 honor$ & privileg$ above all o!r m51 & sp5t _! lives dwell+ ap>t f ! multitude 9 va/ & magnific5t temples1 d$icat+ !mselves to ! /udy & practice ( religion1 philosophy1 sci5ce & art--subjects !n intimately relat$1 n widely sep>at$ z !y are n[4 ,^! m5 7 ! ar*itects ( anci5t ,egypt3 !irs ! m9ds :i* direct$ ! h&s t built ^? "t-defy+ monum5ts4 ,! rites t ! prie/s practic$ c5t]$ ab\t :at are kn[n z ! ,less] & ! ,great] ,my/]ies4 ,^! consi/$ ( repres5tations by means ( symbol & allegory1 "u conditions & amid surr\nd+s ! mo/ awe-inspir+1 ( ^? great tru?s conc]n+ man's nature1 orig9 & de/9y ( :i* ! prie/s--9 reality a bro!rhood ( initiates & _! pupils--7 ! cu/odians4 ,^! c]emonies 7 made ! occasion = ! initiation ( neophytes into ! ord]1 & ! advancem5t ( ! already initiat$ into its successive degrees4 ,= ! practice ( su* rites1 & o!rs design$ to impress n ! elect b ! multitude1 ! great temples ( ,egypt 7 con/ruct$4 ,ev]y?+ ab\t !m 0 calculat$ to induce a deep s]i\sness ( m9d1 & to inspire feel+s ( awe1 dread & ev5 t]ror1 s z to te/ ! c&idate's =titude ( s\l to ! utmo/4 ,! av5ue ( approa* to an ,egyptian temple 0 flank$ on bo? sides1 sometimes = a mile or m1 ) great /one sph9xes--t emblem ( man's dual nature1 ! god em]g+ f ! bea/4 ,! entrance 0 ?r\gh a s+le high doorway betwe5 two t[]+ pylons1 pres5t+ a va/ surface sculptur$ & pa9t$ ov] ) _m /range & enigmatic figures1 & flank$ by aspir+ obelisks & seat$ colossi ) faces au/]e & calm4 ,! l>ge c\rt ?us ent]$ 0 surr\nd$ by high walls & colonnades1 b 0 op5 to ! sky4 ,opposite ! fir/ doorway 0 ano!r1 admitt+ to a some:at small] enclosure1 a =e/ ( enorm\s c>v$ & pa9t$ columns support+ a ro( ?r\gh ! ap]tures ( :i* sun%9e gleam$ or dim light filt]$ d[n4 ,beyond ?is 9 turn 7 o!r c\rts & ap>tm5ts culm9at+ 9 "s inmo/ sacr$ sanctu>y4 ,n alone 9 _! temples1 b 9 _! tombs & pyramids & all ! sculptur$ monum5ts ( ! ,egyptians1 !re is ! same insi/5ce ^u ! sublimity1 my/]y & awefulness ( life1 :i* !y seem to h felt s pr(\ndly4 ,b m ?an ?is1 ! consci\s ?\ght ( ! ma/]s :o conceiv$ !m1 ! build+s ( ,egypt give utt]ance also to ! toil & suff]+ ( ! ?\s&s ( slaves & captives :i* hew$ ! /ones out ( ! he>t ( ! rock1 dragg$ !m long di/ances & plac$ !m "o ^u ano!r1 s t ^! build+s oppress :ile !y inspire1 = !re is 9 !m no fre$om1 no spontaneity1 no individuality1 b ev]y:]e ! felt pres5ce ( an iron conv5tionality1 ( a /]n immutable law4 ,9 ,egyptian ar*itecture is symboliz$ ! condition ( ! human s\l awak5$ f its long sleep 9 nature1 & become consci\s at once ( its div9e s\rce & ( ! lead5 burd5 ( its fle%y envelope4 ,egypt is humanity new-born1 b\nd /ill ) an umbilical cord to nature1 & /rong n s mu* ) its own /r5g? z ) ! /r5g? ( its "m4 ,?is idea is aptly symboliz$ 9 ^? gigantic colossi flank+ ! entrance to "s rock-cut temple1 :i* ?\gh entire are yet "p ( ! liv+ cliff out ( :i* !y 7 fa%ion$4 ,9 ! ar*itecture ( ,greece ! note ( dread & my/]y yields to "o ( pure joy\sness & fre$om4 ,! t]rors ( *ildhood h be5 outgr[n1 & man revels 9 ! indulg5ce ( 8 unjad$ appetites & 9 ! ex]cise ( 8 awak5$ reason+ faculties4 ,9 ,greek art is pres]v$ t evanesc5t beauty ( y\? :i*1 com+ b once & cont9u+ b = a %ort int]val 9 e human life1 is yet t = :i* all antec$5t /ates seem a prep>ation1 & ( :i* all subsequ5t ones are 9 "s sort an effect4 ,greece typifies adolesc5ce1 ! love age1 & s ?r\gh\t ! c5turies humanity has turn$ to ! contemplation ( h]1 j z a man all 8 life long secretly *]i%es ! memory ( 8 fir/ love4 ,an impassion$ s5se ( beauty & an enlight5$ reason *>act]ize ! productions ( ,greek ar*itecture dur+ its be/ p]iod4 ,! p]fection !n atta9$ 0 possible only 9 a nation :]e( ! citiz5s 7 !mselves critics & amateurs ( art1 "o :]e9 ! arti/ 0 honor$ & 8 "w appreciat$ 9 all its beauty & subtlety4 ,! ,greek ar*itect 0 less b\nd by tradition & prec$5t ?an 0 ! ,egyptian1 & he work$ unhamp]$ by any re/rictions save su* z1 l ! laws ( h>mony 9 music1 help$ r ?an h9d]$ 8 g5ius to express itself--re/rictions f\nd$ on s\nd reason1 ! value ( :i* _h be5 prov$ by exp]i5ce4 ,! ,doric ord] 0 employ$ = all l>ge temples1 s9ce x possess$ 9 fulle/ measure ! qualities ( simplicity & dignity1 ! attributes appropriate to greatness4 ,q prop]ly also its =mulas 7 m fix$ ?an ^? ( any o!r /yle4 ,! ,ionic ord]1 ! fem99e ( :i* ! ,doric may be consid]$ ! correspond+ mascul9e1 0 employ$ = small] temples2 l a woman x 0 m supple & adaptable ?an ! ,doric1 its proportions 7 m sl5d] & graceful1 its l9es m fl[+1 & its ornam5t m delicate & pr(use4 ,a fre] & m elaborate /yle ?an ei!r ( ^!1 inf9itely v>i\s1 seem+ to obey no law save t ( beauty1 0 us$ sometimes = small monum5ts & temples1 su* z ! ,t[] ( ! ,w9ds1 & ! monum5t ( ,lysicrates at ,a!ns4 ,illu/ration #a ,because ! ,greek ar*itect 0 at lib]ty to improve ^u ! "w ( 8 pr$ecessors if he c\ld1 no temple 0 j l any o!r1 & !y =m an asc5d+ scale ( excell5ce1 culm9at+ 9 ! ,acropolis gr\p4 ,e detail 0 consid]$ n only ) relation to its position & function1 b 9 reg>d to its intr9sic beauty z well1 s t ! m]e/ fragm5t1 deta*$ f ! build+ ( :i* x =m$ a "p1 is f\nd wor?y ( be+ treasur$ 9 our museums = its own sake4 ,j z e detail ( a ,greek temple 0 adju/$ to its position & express$ its (fice1 s ! build+ itself 0 made to fit its site & to %[ =? its purpose1 =m+ ) ! surr\nd+ build+s a unit ( a l>g] :ole4 ,! ,a!nian ,acropolis is an illu/ration ( ?is3 x is an irregul> =tifi$ hill1 be>+ div]se monum5ts 9 v>i\s /yles1 at unequal levels & at diff]5t angles ) "o ano!r1 yet ! :ole arrangem5t seems z organic & inevitable z ! disposition ( ! features ( a face4 ,! ,acropolis is an example ( ! ideal ar*itectural republic :]e9 ea* individual contributes to ! welf>e ( all1 & at ! same "t enjoys ! utmo/ p]sonal lib]ty 7,illu/ration #a74 ,v diff]5t is ! _s bodi$ =? 9 ! ar*itecture ( ,imp]ial ,rome4 ,! iron h& ( its sov]eignty encas$ )9 ! silk5 glove ( its luxury f9ds its prototype 9 build+s :i* 7 /up5d\s crude brute masses ( brick & concrete1 hidd5 )9 a cov]+ ( ri* m>bles & mosaics1 wr\ght 9 beautiful b (t5 mean+less =ms by clev] deg5]ate ,greeks4 ,! g5ius ( ,rome f9ds its mo/ *>act]i/ic expression1 n 9 temples to ! high gods1 b r 9 ^? va/ & complicat$ /ructures--basilicas1 amphi!atres1 ba?s--built = ! amusem5t & purely temporal ne$s ( ! p4 ,if ,egypt typifies ! *ildhood ( ! race & ,greece its beautiful y\?1 ,republican ,rome repres5ts its /rong manhood--a soldi] fill$ ) ! lu/ ( w> & ! love ( glory--& ,imp]ial ,rome its deg5]acy3 t soldi] become conqu]or1 deck$ out 9 plund]$ f9]y & sunk 9 s5suality1 tol]ant ( all :o m9i/] to 8 pleasures b t]rible to all :o int]f]e ) !m4 ,! fall ( ,rome m>k$ ! end ( ! anci5t ,pagan _w4 ,above its ru9 ,*ri/ian civilization 9 ! c\rse ( "t arose4 ,go?ic ar*itecture is an expression ( ! ,*ri/ian _s2 9 x is manife/ ! reaction f lic5ti\sness to asceticism4 ,man's spiritual nature1 awak5+ 9 a body worn & weak5$ by debau*]ies1 longs ard5tly & tries va9ly to escape4 ,( "s su* mood a ,go?ic ca!dral is ! expression3 its vault+1 m>vel\sly support$ ^u sl5d] %afts by reason ( a nicely adju/$ equilibrium ( =ces2 its re/less1 upw>d-rea*+ p9nacles & spires2 its ornam5t1 intricate & enigmatic--all ^! sugge/ ! ov]-/ra9$ organism ( an ascetic2 :ile its va/ %ad[y int]ior lit by m>vel\sly trac]i$ & jewel$ w9d[s1 :i* hold ! eyes 9 a hypnotic ?rall1 is l 8 s\l3 fill$ ) _w sadness1 dead to ! bright brief joys ( s5se1 see+ only heav5ly visions1 kn[+ none b my/ic raptures4 ,?us x is t ! hi/ory ( ar*itecture illu/rates & en=ces ! !osophical tea*+ t ev]y?+ ( man's creat+ is made 9 8 own image4 ,ar*itecture mirrors ! life ( ! individual & ( ! race1 :i* is ! life ( ! individual writt5 l>ge 9 "t & space4 ,! t]rors ( *ildhood2 ! ke5 int]e/s & appetites ( y\?2 ! /rong /]n joy ( conflict :i* comes ) manhood2 ! lu/1 ! gre$1 ! cruelty ( a mat]ializ$ old age--all ^! s]ve b z a prep>ation = ! life ( ! _s1 9 :i* ! man becomes aga9 z a little *ild1 go+ ov] ! :ole r\nd1 b on a high] arc ( ! spiral4 ,! f9al1 or f\r? /ate be+ only 9 "s sort a repetition ( ! fir/1 x w\ld be reasonable to look = a c]ta9 correspond5ce betwe5 ,egyptian & ,go?ic ar*itecture1 & su* a correspond5ce !re is1 ?\gh x is m easily div9$ ?an demon/rat$4 ,9 bo? !re is ! same deeply religi\s _s2 bo? convey1 9 "s obscure yet pot5t mann]1 a s5se ( ! s\l be+ ne> ! surface ( life4 ,!re is ! same love ( my/]y & ( symbolism2 & 9 bo? may be obs]v$ ! t5d5cy to create /range composite figures to typify transc5d5tal ideas1 ! sph9x seem+ a blood-bro!r to ! g>goyle4 ,! conditions "u :i* ea* ar*itecture fl\ri%$ 7 n dissimil>1 = ea* 0 =mulat$ & controll$ by small well-organiz$ bodies ( s9c]ely religi\s & highly enlight5$ m5--! prie/hood 9 ! "o case1 ! masonic guilds 9 ! o!r--work+ toge!r t[>d ! consummation ( great und]tak+s amid a populace = ! mo/ "p oblivi\s ( ! pr(\nd & subtle mean+s ( :i* _! "w 0 full4 ,9 ,m$ival ,europe1 z 9 anci5t ,egypt1 fragm5ts ( ! ,anci5t ,wisdom--transmitt$ 9 ! symbols & secrets ( ! ca!dral build]s--det]m9$ mu* ( ,go?ic ar*itecture4 ,! ar*itecture ( ! ,r5aissance p]iod1 :i* succe$$ ! ,go?ic1 corresponds aga91 9 ! _s :i* animates x1 to ,greek ar*itecture1 :i* succe$$ ! ,egyptian1 = ! ,r5aissance z ! "n implies 0 no?+ o!r ?an an attempt to revive ,classical antiquity4 ,s*ol>s writ+ 9 :at !y conceiv$ to be a ,classical /yle1 sculptors model+ ,pagan deities1 & ar*itects build+ accord+ to _! und]/&+ ( ,vitruvian me?ods succe$$ 9 produc+ works l1 yet diff]5t f ! orig9als !y foll[$--diff]5t because1 animat$ by a _s unkn[n to ! anci5ts1 !y embodi$ a new ideal4 ,9 all ! productions ( ! e>ly ,r5aissance1 t fir/ transc5d5t spr+tide ( ! mod]n _w1 !re is ! evanesc5t grace & beauty ( y\? :i* 0 se5 to h p]vad$ ,greek art1 b x is a grace & beauty ( a diff]5t sort4 ,! ,greek arti/ s\ght to atta9 to a c]ta9 ab/ract p]fection ( type2 to build a temple :i* %\ld comb9e all ! excell5cies ( e simil> temple1 to c>ve a figure1 imp]sonal 9 ! highe/ s5se1 :i* %\ld embody e beauty4 ,! arti/ ( ! ,r5aissance on ! o!r h& delight$ n s mu* 9 ! type z 9 ! v>iation f x4 ,preoccupi$ ) ! unique my/]y ( ! individual s\l--a s5se ( :i* 0 ,*ri/ianity's gift to ,*ri/5dom--he endeavor$ to portray t :]e9 a p>ticul> p]son is unique & s+ul>4 ,acutely consci\s also ( 8 own individuality1 in/ead ( effac+ x he made 8 "w ! vehicle & expression ( t individuality4 ,! hi/ory ( ,r5aissance ar*itecture1 z ,symonds has po9t$ out1 is ! hi/ory ( a few em95t individuals1 ea* "o m\ld+ & modify+ ! /yle 9 a mann] peculi> to himself alone4 ,9 ! h&s ( ,brunelles*i x 0 /]n & p[]ful2 ,bramante made x *a/e1 elegant & graceful2 ,palladio made x =mal1 cold1 symmetrical2 :ile ) ,sansov9o & ,sammi*ele x became sumptu\s & bomba/ic4 ,z ! ,r5aissance rip5$ to decay its ar*itecture assum$ m & m ! *>act]i/ics :i* di/+ui%$ t ( ,rome dur+ ! decad5ce4 ,9 bo? !re is ! same lack ( simplicity & s9c]ity1 ! same pr(usion ( debas$ & mean+less ornam5t1 & !re is an increas+ disposition to conceal & falsify ! con/ruction by surface decoration4 ,! f9al "p ( ?is second or mod]n ar*itectural cycle lies /ill 9 ! future4 ,x is n unreasonable to believe t ! movem5t t[>d my/icism1 ( :i* mod]n !osophy is a phase & ! spiritualization ( sci5ce an episode1 w fl[] out into an ar*itecture :i* w be 9 "s sort a re9c>nation ( & a return to ! ,go?ic _s1 employ+ new mat]ials1 new me?ods1 & develop+ new =ms to %[ =? ! _s ( ! mod]n _w1 )\t violat+ anci5t v]ities4 ,9 /udy+ ^! crucial p]iods 9 ! hi/ory ( ,european ar*itecture x is possible to trace a gradual gr[? or unfold+ z ( a plant4 ,x is a fact fairly well e/abli%$ t ! ,greeks d]iv$ _! ar*itecture & ornam5t f ,egypt2 ! ,romans 9 turn borr[$ f ! ,greeks2 :ile a ,go?ic ca!dral is a l9eal desc5dant f a ,roman basilica4 ,illu/ration #b ,illu/ration #c ,! ,egyptians 9 _! con/ructions did little m ?an to place enorm\s /ones on end1 & pile "o huge block ^u ano!r4 ,!y us$ _m columns plac$ close toge!r3 ! spaces :i* !y spann$ 7 inconsid]able4 ,! upright or support+ memb] may be said to h be5 9 ,egyptian ar*itecture ! pr$om9ant "o4 ,a v]tical l9e !re=e may be tak5 z ! simple/ & mo/ ab/ract symbol ( ,egyptian ar*itecture 7,illu/ration #b74 ,x rema9$ = ! ,greeks fully to develop ! l9tel4 ,9 _! ar*itecture ! v]tical memb]1 or column1 exi/$ solely = ! sake ( ! horizontal memb]1 or l9tel2 x r>ely /ood alone z 9 ! case ( an ,egyptian obelisk4 ,! columns ( ! ,greek temples 7 r$uc$ to ^? proportions mo/ consi/5t ) /r5g? & beauty1 & ! int]columnations 7 relatively great] ?an 9 ,egyptian examples4 ,x may truly be said t ,greek ar*itecture exhibits ! p]fect equality & equipoise ( v]tical & horizontal elem5ts & ^! only1 no o!r factor ent]+ 94 ,its graphic symbol w\ld !re=e be compos$ ( a v]tical & a horizontal l9e 7,illu/ration #c74 ,! ,romans1 :ile reta9+ ! column & l9tel ( ! ,greeks1 depriv$ !m ( _! /ructural significance & subord9at$ !m to ! semicircul> ar* & ! semi-cyl9drical & hemisph]ical vault1 ! truly *>act]i/ic & det]m9+ =ms ( ,roman ar*itecture4 ,our symbol gr[s !re=e by ! addition ( ! arc ( a circle 7,illu/ration #d74 ,9 ,go?ic ar*itecture column1 l9tel1 ar* & vault are all reta9$ 9 *ang$ =m1 b t :i* m ?an any?+ else diff]5tiates ,go?ic ar*itecture f any /yle :i* prec$$ x is ! introduction ( ! pr9ciple ( an equilibrium ( =ces1 ( a /ate ( balance r ?an a /ate ( re/1 arriv$ at by ! opposition ( "o ?ru/ ) ano!r contr>y to x4 ,?is fact c be indicat$ graphically by two oppos+ incl9$ l9es1 & ^! unit$ to ! prec$+ symbol yield an accurate ab/ract ( ! elem5ts ( ,go?ic ar*itecture 7,illu/ration #e74 ,illu/ration #d ,illu/ration #e ,all ?is is b an unusual application ( a famili> !osophic tea*+1 namely1 t x is ! me?od ( nature on e plane & 9 e dep>tm5t n to omit any?+ t has gone be=e1 b to /ore x up & c>ry x along & br+ x into manife/ation lat]4 ,nature ev]y:]e proce$s l ! j+le ( ,! ,h\se t ,jack ,built3 %e repeats ea* "t all %e has le>n$1 & adds ano!r l9e = subsequ5t repetition4 ,footnote ,a3 ,! qua9t ,ori5tal imag]y "h employ$ %\ld n bl9d ! read] to ! precise sci5tific accuracy ( ! idea ( :i* ?is imag]y is ! vehicle4 ,s*op5hau] says3 ,pol>ity1 or ! sund]+ ( a =ce into two quantitively diff]5t & oppos$ activities /riv+ aft] re-union1444 is a fundam5tal type ( almo/ all ! ph5om5a ( nature1 f ! magnet & ! cry/al to man himself4 ,,ii ,,unity ,,& ,,pol>ity ,!osophy1 bo? z a philosophy1 or sy/em ( ?\ght1 :i* discov]s correlations betwe5 ?+s app>5tly unrelat$1 & z a life1 or sy/em ( tra9+ :]eby x is possible to ga9 ! p[] to p]ceive & use ^! correlations = wor?y ends1 is ( great value to ! creative arti/1 ^: success dep5ds on ! ext5t to :i* he works organically1 con=m+ to ! cosmic patt]n1 proce$+ rationally & rhy?mically to "s pr$et]m9$ end4 ,x is ( value no less to ! layman1 ! critic1 ! art amateur--to anyone 9 fact :o w\ld come to an accurate & intimate und]/&+ & appreciation ( e v>iety ( e/hetic endeavor4 ,= ! b5efit ( su* ,i %all try to trace "s ( ^? correlations :i* !osophy affirms1 & indicate _! be>+ ^u art1 & ^u ! art ( ar*itecture 9 p>ticul>4 ,"o ( ! ?+s :i* !osophy tea*es is t ^? transc5d5t glimpses ( a div9e ord] & h>mony ?r\gh\t ! univ]se v\*saf$ ! poet & ! my/ic 9 _! mom5ts ( vision are n ! p>adoxes--! p>onomasia z x 7--( an intoxicat$ /ate ( consci\sness1 b glimpses ( reality4 ,we are all ( u p>ticipators 9 a _w ( concrete music1 geometry & numb]--a _w ( s\nds1 odors1 =ms1 motions1 colors1 s ma!matically relat$ & coord9at$ t our pigmy bodies1 equally ) ! f>!/ />1 vibrate to ! music ( ! sph]es4 ,!re is a ,beautiful ,necessity :i* rules ! _w1 :i* is a law ( nature & equally a law ( art1 = art is idealiz$ creation3 nature c>ri$ to a high] p[] by reason ( its passage ?r\gh a human consci\sness4 ,?\ght & emotion t5d to cry/allize into =ms ( beauty z inevitably z does ! fro/ on a w9d[ pane4 ,art !re=e 9 "o ( its aspects is ! weav+ ( a patt]n1 ! communication ( an ord] & a me?od to ! mat]ial or m$ium employ$4 ,al?\gh no ma/]piece 0 ev] creat$ by ! consci\s foll[+ to set rules1 = ! true arti/ works unconsci\sly1 in/9ctively1 z ! bird s+s or z ! bee builds its honey-cell1 yet an analysis ( any ma/]piece reveals ! fact t its au?or 7l ! bird & ! bee7 has foll[$ ! rules )\t kn[+ !m4 ,helmholtz says1 ,no d\bt is n[ ent]ta9$ t beauty is subject to laws & rules dep5d5t on ! nature ( human intellig5ce4 ,! difficulty consi/s 9 ! fact t ^! laws & rules1 on ^: fulfilm5t beauty dep5ds1 are n consci\sly pres5t 9 ! m9d ( ! arti/ :o creates ! "w1 or ( ! obs]v] :o contemplates x4 ,nev]!less !y are discov]able1 & c be =mulat$1 aft] a fa%ion4 ,we h only to read aright ! lessons ev]y:]e portray$ 9 ! va/ picture-books ( nature & ( art4 ,! fir/ tru? !re9 publi%$ is ! law ( ,unity--on5ess2 = !re is "o ,self1 "o ,life1 :i*1 myriad 9 manife/ation1 is yet 9 ess5ce ev] "o4 ,atom & univ]se1 man & ! _w--ea* is a unit1 an organic & coh]5t :ole4 ,! application ( ?is law to art is s obvi\s z to be almo/ unnecess>y ( elucidation1 = to say t a "w ( art mu/ possess unity1 mu/ seem to proce$ f a s+le impulse & be ! embodim5t ( "o dom9ant idea1 is to /ate a truism4 ,9 a "w ( ar*itecture ! cord9ation ( its v>i\s p>ts ) "o ano!r is almo/ ! measure ( its success4 ,we rememb] any ma/]piece--! ca!dral ( ,p>is no less ?an ! pyramids ( ,egypt--by ! s+l5ess ( its appeal2 complex x may be1 b x is a coord9at$ complexity2 v>iety x may possess1 b x is a v>iety 9 an all-embrac+ unity4 ,! second law1 n contradict+ b supplem5t+ ! fir/ is ! law ( ,pol>ity1 i4e41 duality4 ,all ?+s h sex1 are ei!r mascul9e or fem99e4 ,?is too is ! reflection on a l[] plane ( "o ( ^? transc5d5tal tru?s taught by ! ,anci5t ,wisdom1 namely t ! ,logos1 9 8 volunt>ily circumscrib+ 8 inf9ite life 9 ord] t he may manife/1 encloses himself )9 8 limit+ veil1 maya1 & t 8 life appe>s z _s 7male71 & 8 maya z matt] 7female71 ! two be+ nev] disjo9$ dur+ manife/ation4 ,! two t]ms ( ?is pol>ity are endlessly repeat$ ?r\gh\t nature3 9 sun & moon1 day & night1 fire & wat]1 man & woman--& s on4 ,a close int]-relation is always se5 to subsi/ betwe5 correspond+ memb]s ( su* pairs ( opposites3 sun1 day1 fire1 man express & embody ! primal & active aspect ( ! manife/+ deity2 moon1 night1 wat]1 woman1 its second>y & passive aspect4 ,moreov]1 ea* implies or br+s to m9d ! o!rs ( its class3 man1 l ! sun1 is "l ( day2 he is l fire1 a deva/at+ =ce2 woman is subject to ! lun> rhy?m2 l wat]1 %e is s(t1 s9u\s1 fecund4 ,! "p :i* ?is pol>ity plays 9 ! arts is important1 & ! con/ant & *>act]i/ic di/9ction betwe5 ! two t]ms is a ?+ f> beyond m]e contra/4 ,9 music !y are ! major & m9or modes3 ! typical1 or repres5tative *ords ( ! dom9ant sev5?1 & ( ! tonic 7! two *ords into :i* ,s*op5hau] says all music c be resolv$73 a p>tial dissonance1 & a consonance3 a *ord ( susp5se1 & a *ord ( satisfaction4 ,9 spee* ! two are v[el1 & consonant s\nds3 ! type ( ! fir/ be+ a1 a s\nd ( susp5se1 made ) ! m\? op52 & ( ! second m1 a s\nd ( satisfaction1 made by clos+ ! m\?2 _! comb9ation =ms ! sacr$ syllable ,om 7,aum74 ,9 pa9t+ !y are w>m colors1 & cold3 ! pole ( ! fir/ be+ 9 r$1 ! color ( fire1 :i* excites2 & ( ! second 9 blue1 ! color ( wat]1 :i* calms2 9 ! ,arts ( design !y are l9es /raight 7l fire71 & fl[+ 7l wat]72 masses light 7l ! day71 & d>k 7l night74 ,9 ar*itecture !y are ! column1 or v]tical memb]1 :i* resi/s ! =ce ( gravity2 & ! l9tel1 or horizontal memb]1 :i* succumbs to x2 !y are v]tical l9es1 :i* are aspir+1 ef=tful2 & horizontal l9es1 :i* are re/ful to ! eye & m9d4 ,x is desirable to h an in/ant & ke5 realization ( ?is sex quality1 & to make ?is easi] "s sort ( classification & analysis mu/ be attempt$4 ,^? ?+s :i* are alli$ to & p>take ( ! nature ( "t are mascul9e1 & ^? :i* are alli$ to & p>take ( ! nature ( space are fem99e3 z motion1 & matt]2 m9d1 & body2 etc4 ,! ,engli% words mascul9e & fem99e are too intimately associat$ ) ! idea ( physical sex prop]ly to designate ! t]ms ( ?is pol>ity4 ,9 ,japanese philosophy & art 7d]iv$ f ! ,*9ese7 ! two are call$ ,9 & ,yo 7,91 fem99e2 ,yo1 mascul9e72 & ^! little words1 be+ free f ! limitations ( _! ,engli% correlatives1 w be f\nd conv5i5t1 ,yo to designate t :i* is simple1 direct1 prim>y1 active1 positive2 & ,91 t :i* is complex1 indirect1 d]ivative1 passive1 negative4 ,?+s h>d1 /raight1 fix$1 v]tical1 are ,yo2 ?+s s(t1 curv$1 horizontal1 fluctuat+1 are ,9--& s on4 ,illu/ration #f3 ,,wild ,,*]ry2 ,,maple ,,leaf ,illu/ration #g3 ,,callas ,,9 ,,yo ,9 pass+ x may be said t ! sup]iority ( ! l9e1 mass1 & color composition ( ,japanese pr9ts & kakemonos to t exhibit$ 9 ! va/ly m pret5ti\s easel pictures ( mod]n ,occid5tal arti/s--a sup]iority n[ g5]ally ackn[l$g$ by connoisseurs--is l>gely due to ! consci\s foll[+1 on ! "p ( ! ,japanese1 ( ?is pr9ciple ( sex-complem5t>ies4 ,n[h]e are ,9 & ,yo m simply & adequately imag$ ?an 9 ! vegetable k+dom4 ,! trunk ( a tree is ,yo1 its foliage1 ,92 & 9 ea* /em & leaf ! two are repeat$4 ,a calla1 consi/+ ( a s+le /raight & rigid spadix embrac$ by a s(t & t5d]ly curv$ spa!1 af=ds an almo/ p]fect expression ( ! *>act]i/ic diff]5ces betwe5 ,yo & ,9 & _! reciprocal relation to ea* o!r4 ,! two are n (t5 comb9$ 9 su* simplicity & p]fection 9 a s+le =m4 ,! /raight1 v]tical re$s :i* s (t5 gr[ 9 /ill1 %all[ wat]1 f9d _! complem5t 9 ! curv$ lily-pads :i* lie horizontally on its surface4 ,trees su* z p9e & hemlock1 :i* are excurr5t--^? 9 :i* ! bran*es />t successively 7i4e41 aft] ! mann] ( "t7 f a /raight & v]tical c5tral /em--are ,yo2 trees su* z ! elm & will[1 :i* are deliquesc5t--^? 9 :i* ! trunk dissolves z x 7 simultane\sly 7aft] ! mann] ( space7 into its bran*es--are ,94 ,all tree =ms lie 9 or betwe5 ^! two extremes1 & leaves are susceptible ( a simil> classification4 ,x w be se5 to be a classification accord+ to "t & space1 = ! *>act]i/ic ( "t is succession1 & ( space1 simultane\sness3 ! fir/ is express$ symbolically by elem5ts arrang$ ) relation to axial l9es2 ! second1 by elem5ts arrang$ ) relation to focal po9ts 7,illu/rations #f1g74 ,! /ud5t %\ld tra9 himself to recognize ,9 & ,yo 9 all _! ,protean pres5tm5ts ?r\gh\t nature--9 ! cl\d ^u ! m\nta91 ! wave aga9/ ! cliff1 9 ! trac]y ( trees aga9/ ! sky--t he may ! m readily recognize !m 9 8 *os5 art1 :atev] t art may be4 ,if x happ5s to be pa9t+1 he w endeavor to disc]n ?is law ( duality 9 ! composition ( e ma/]piece1 recogniz+ an in/9ctive ob$i5ce to x 9 t favorite device ( ! great ,r5aissance ma/]s ( mak+ an ar*itectural sett+ = _! gr\ps ( figures1 & he w delight to trace ! law 9 all its ramifications ( contra/ betwe5 complem5t>ies 9 l9e1 color1 & mass 7,illu/ration #h74 ,illu/ration #h3 ,,! ,,law ,,( ,,pol>ity ,,cleopatra ,,melt+ ,,! ,,pe>l4 ,,by ,,tiepolo ,) ref]5ce to ar*itecture1 x is true1 g5]ally speak+1 t ar*itectural =ms h be5 develop$ ?r\gh necessity1 ! function seek+ & f9d+ its appropriate =m4 ,= example1 ! buttress ( a ,go?ic ca!dral 0 develop$ by ! necessity ( resi/+ ! ?ru/ ( ! int]ior vault+ )\t encroa*+ ^u ! nave2 ! ma9 l9es ( a buttress con=m to ! direction ( ! ?ru/1 & ! p9nacle ) :i* x t]m9ates is a logical %ape = ! masonry necess>y to hold ! top 9 position 7,illu/ration #i74 ,rese>* along ^! l9es is int]e/+ & fruitful ( result1 b !re rema9s a c]ta9 numb] ( ar*itectural =ms ^: orig9 _c be expla9$ 9 any su* mann]4 ,! secret ( _! undy+ *>m lies 9 ! fact t 9 !m ,9 & ,yo /& symboliz$ & contra/$4 ,!y no long] obey a law ( utility1 b an ab/ract law ( beauty1 = 9 becom+ sexually expressive z x 71 ! con/ruction itself is sometimes weak5$ or falsifi$4 ,! famili> classic console or modillion is an example3 al?\gh 9 g5]al cont\r x is well adapt$ to its function z a support+ bracket1 emb$d$ 91 & project+ f a wall1 yet ! scroll-l ornam5t ) :i* its sides are embelli%$ gives x ! appe>ance ( n ent]+ ! wall at all1 b ( be+ /uck aga9/ x 9 "s miracul\s mann]4 ,?is defect 9 functional expressiv5ess is m ?an comp5sat$ = by ! p]fection ) :i* fem99e & mascul9e *>act]i/ics are express$ & contra/$ 9 ! exquisite d\ble spiral1 oppos$ to ! /raight l9es ( ! m\ld+ :i* x subt5ds 7,illu/ration #aj74 ,aga91 by flut+ ! %aft ( a column its area ( cross-section is dim9i%$ b ! appe>ance ( /r5g? is enhanc$ because its mascul9e "*--z a support+ memb] resi/+ ! =ce ( gravity--is emphasiz$4 ,illu/ration #i3 ,,cross ,,section ,,( ,,buttress4 ,! importance ( ! s-call$ ord]s lies 9 ! fact t !y are ar*itecture epitomiz$ z x 74 ,a build+ consi/s ( a wall uphold+ a ro(3 support & weight4 ,! type ( ! fir/ is ! column1 :i* may be conceiv$ ( z a cond5s$ section ( wall2 & ( ! second1 ! l9tel1 :i* may be conceiv$ ( z a cond5s$ section ( ro(4 ,! column1 be+ v]tical1 is ,yo2 ! l9tel1 be+ horizontal1 is ,94 ,to m>k an entablature ) horizontal l9es 9 ! =m ( m\ld+s1 & ! columns ) v]tical l9es 9 ! =m ( flutes1 z is done 9 all ! classic ord]s1 is a ga9 9 functional & sex expressiv5ess1 & consequ5tly 9 art 7,illu/ration #aa74 ,illu/ration #aj3 ,,cor9?ian ,,modillion2 ,,classic ,,console2 ,,ionic ,,cap ,! column is aga9 divid$ into ! %aft1 :i* is ,yo2 & ! capital1 :i* is ,94 ,! capital is itself tw(old1 consi/+ ( a curv$ memb] & an angul> memb]4 ,^! two appe> 9 _! utmo/ simplicity 9 ! e*9us 7,97 & ! abacus 7,yo7 ( a ,greek ,doric cap4 ,! =m] 0 adorn$ ) pa9t$ leaf =ms1 *>act]i/ically fem99e1 & ! latt] ) ! angul> fret & me&] 7,illu/ration #ab74 ,! ,ionic capital1 belong+ to a m fem99e /yle1 exhibits ! abacus subord9at$ to t beautiful cu%ion-%ap$ memb] ) its two spirally m>k$ volutes4 ,?is1 ?\gh a less rational & expressive =m = its p>ticul> (fice ?an is ! e*9us ( ! ,doric cap1 is a f> m p]fect symbol ( ! fem99e elem5t 9 nature4 ,!re is an ess5tial id5tity betwe5 ! ,ionic cap & ! classic console be=e ref]r$ to--al?\gh sup]ficially ! two d n resemble ea* o!r--= a /raight l9e & a d\ble spiral are elem5ts common to bo? 7,illu/ration #aj74 ,! ,cor9?ian capital consi/s ( an ord]$ mass ( delicately sculptur$ leaf & scroll =ms su/a9+ an abacus :i* ?\gh relatively mascul9e is yet m curv$ & fem99e ?an t ( any o!r /yle4 ,9 ! caulicole ( a ,cor9?ian cap ,9 & ,yo are aga9 contra/$4 ,9 ! unique & exquisite capital f ! ,t[] ( ! ,w9ds at ,a!ns1 ! two are well sugge/$ 9 ! simple1 erect1 & po9t$ leaf =ms ( ! upp] "p1 contra/$ ) ! complex1 deliquesc5t1 r\nd$ ones f :i* !y spr+4 ,! ess5tial id5tity ( pr9ciple subsi/+ betwe5 ?is cap & ! ,r5aissance balu/] by ,san ,gallo is easily se5 7,illu/ration #ac74 ,illu/ration #aa ,illu/ration #ab ,?is law ( sex-expressiv5ess is ( su* univ]sality t x c be made ! basis ( an analysis ( ! ar*itectural ornam5t ( any /yle or p]iod4 ,x is m ?an m]e opposition & contra/4 ,! egg & tongue motif1 :i* has p]si/$ ?r\gh\t s _m c5turies & surviv$ s _m /yles1 exhibits an alt]nation ( =ms resembl+ phallic emblems4 ,yo & ,9 are well sugge/$ 9 ! *annel$ triglyphs & ! sculptur$ metopes ( a ,doric frieze1 9 ! /raight & v]tical mullions & ! fl[+ trac]y ( ,go?ic w9d[s1 9 ! b&$ torus1 ! bead & reel1 & o!r famili> ornam5t$ m\ld+s 7,illu/rations #ad1 #ae1 #af74 ,!re are indications t at "s "t dur+ ! developm5t ( ,go?ic ar*itecture 9 ,france1 ?is sex-di/9ction became a recogniz$ pr9ciple1 m\ld+ & modify+ ! design ( a ca!dral 9 mu* ! same way t sex modifies bodily /ructure4 ,! masonic guilds ( ! ,middle ,ages 7 cu/odians ( ! esot]ic--:i* is ! !osophic--side ( ! ,*ri/ian fai?1 & e /ud5t ( esot]icism kn[s h[ fundam5tal & h[ f>-rea*+ is ?is idea ( sex4 ,illu/ration #ac3 ,,capital ,,f ,,! ,,t[] ,,( ,,! ,,w9ds1 ,,a!ns2 ,,cor9?ian ,,cap ,,f ,,hadrian ,,build+s1 ,,a!ns2 ,,rosette ,,f ,,temple ,,( ,,m>s1 ,,rome2 ,,cauliculus ,,( ,,cor9?ian ,,cap2 ,,bulu/] ,,by ,,san ,,gallo ,illu/ration #ad3 ,,egg ,,& ,,tongue2 ,,bead ,,& ,,reel2 ,,b&$ ,,torus ,! entire ca!dral symboliz$ ! crucifi$ body ( ,*ri/2 its two t[]s1 man & woman--t ,adam & t ,eve = ^: r$emption accord+ to curr5t tea*+ ,*ri/ suff]$ & 0 crucifi$4 ,! nor? or "r-h& t[] 7! man's side7 0 call$ ! sacr$ male pill>1 ,ja*92 & ! s\?1 or left-h& t[] 7! woman's side71 ! sacr$ female pill>1 ,boaz1 f ! two columns flank+ ! gate to ,solomon's ,temple--itself an allegory to ! bodily temple4 ,9 only a few ( ! ,fr5* ca!drals is ?is di/9ction cle>ly & consi/5tly ma9ta9$1 & ( ^! ,t\rs =ms p]haps ! mo/ rem>kable example1 = 9 its flamboyant faade1 ov] & above ! diff]5ce 9 actual bread? & app>5t /urd9ess ( ! two t[]s 7! s\? be+ ! m sl5d] & delicate71 !re is a cle>ly m>k$ di/9ction 9 ! "* ( ! ornam5tation1 t ( ! nor? t[] be+ m sali5t1 angul>1 radial--m mascul9e 9 po9t ( fact 7,illu/ration #ag74 ,9 ,notre ,dame1 ! ca!dral ( ,p>is1 z 9 ! ca!dral ( ,t\rs1 ! nor? t[] is p]ceptibly broad] ?an ! s\?4 ,! only o!r important diff]5ce appe>s to be 9 ! angul> label-m\ld above ! nor? entrance3 :atev] may h be5 its orig9al function or significance1 x s]ves to def9e ! t[] sexually1 s to speak1 z effectively z does ! be>d on a man's face4 ,9 ,ami5s ! nor? t[] is tall] ?an ! s\?1 & m massive 9 its upp] /ages4 ,! only traceable indication ( sex 9 ! ornam5tation occurs 9 ! sp&rels at ! sides ( ! entrance ar*es3 ^? ( ! nor? t[] conta9+ s+le circles1 & ^? ( ! s\? t[] conta9+ two 9 "o4 ,?is diff]5ce1 small z x may seem1 is significant1 = 9 ,europe dur+ ! ,middle ,ages1 j z anci5tly 9 ,egypt & aga9 9 ,greece--9 fact :]ev] & :5ev] ! ,secret ,doctr9e 0 kn[n--sex 0 attribut$ to numb]s1 odd numb]s be+ conceiv$ ( z mascul9e1 & ev51 z fem99e4 ,two1 ! fir/ fem99e numb]1 ?us became a symbol ( fem99ity1 accept$ z su* s univ]sally at ! "t ! ca!drals 7 built1 t two /rokes ( a bell ann\nc$ ! dea? ( a woman1 ?ree1 ! dea? ( a man4 ,illu/ration #ae3 ,,frieze ,,( ,,! ,,f>nese ,,palace2 ,,roman ,,console4 ,,vatican ,,museum2 ,,frieze ,,9 ,,! ,,empire ,,/yle ,,by ,,p]ci] ,,& ,,fonta9e4 ,,frieze ,,f ,,! ,,temple ,,( ,,ve/a ,,at ,,tivoli4 7,,roman72 ,,roman ,,doric ,,frieze--,,vignole ,illu/ration #af ,illu/ration #ag ,! vital1 organic quality s conspicu\s 9 ! be/ ,go?ic ar*itecture has be5 attribut$ to ! fact t necessity det]m9$ its *>act]i/ic =ms4 ,pr(essor ,goodye> has demon/rat$ t x may be due also 9 "p to c]ta9 subtle v]tical leans & horizontal b5ds2 & to nicely calculat$ v>iations f /rict uni=mity1 :i* f9d _! analogue 9 nature1 :]e /ructure is seldom rigidly geometrical4 ,! au?or haz>ds ! !ory t /ill ano!r reason :y a ,go?ic ca!dral seems s liv+ a ?+ is because x ab\nds 9 contra/s betwe5 :at1 = lack ( m descriptive adjectives1 he is =c$ to call mascul9e & fem99e =ms4 ,illu/ration #ah ,illu/ration #ai ,rusk9 says1 9 ,/ones ( ,v5ice1 ,all good ,go?ic is no?+ m ?an ! developm5t1 9 v>i\s ways1 & on e conceivable scale1 ( ! gr\p =m$ by ! po9t$ ar* = ! be>+ l9e bel[1 & ! gable = ! protect+ l9e above1 & f ! huge1 gray1 %aly slope ( ! ca!dral ro(1 ) its ela/ic po9t$ vaults b5ea?1 to ! cr[n-l po9ts t enri* ! smalle/ ni*e ( its doorway1 "o law & "o expression w be f\nd 9 all4 ,! modes ( support & ( decoration are inf9itely v>i\s1 b ! real "* ( ! build+1 9 all good ,go?ic1 dep5ds on ! s+le l9es ( ! gable ov] ! po9t$ ar* endlessly re>rang$ & repeat$4 ,^! two1 an angul> & a curv$ =m1 l ! ev]y:]e recurr+ column & l9tel ( classic ar*itecture1 are b pres5tm5ts ( ,yo & ,9 7,illu/ration #ah74 ,e ,go?ic trac]i$ w9d[1 ) /raight & v]tical mullions 9 ! rectangle1 los+ !mselves 9 ! intricate foliations ( ! ar*1 celebrates ! m>riage ( ?is ev] div]se pair4 ,! circle & ! triangle are ! ,9 & ,yo ( ,go?ic trac]y1 its ,eve & ,adam1 z x 71 = f _! union spr+s t prog5y ( trefoil1 quatrefoil1 c9quefoil1 ( %apes fl[+ l wat]1 & %apes d>t+ l flame1 :i* makes su* visible music to ! entranc$ e>4 ,illu/ration #bj3 ,,san ,,gimignano ,s4 ,,jacopo4 ,by seek+ to discov] ,9 & ,yo 9 _! myriad manife/ations1 by le>n+ to discrim9ate betwe5 !m1 & by attempt+ to express _! *>act]i/ic qualities 9 new =ms ( beauty--f ! disposition ( a faade to ! %ap+ ( a m\ld+--! ar*itectural design] w *>ge 8 "w ) t esot]ic significance1 t excess ( beauty1 by :i* ar*itecture rises to ! dignity ( a f9e art 7,illu/rations #ai1 #bj74 ,9 s do+1 h[ev]1 he %\ld nev] =get1 & ! layman also %\ld ev] rememb]1 t ! supreme ar*itectural excell5ce is fitness1 appropriat5ess1 ! p]fect adaptation ( means to ends1 & ! adequate expression ( bo? means & ends4 ,^! two aims1 ! "o ab/ract & univ]sal1 ! o!r concrete & individual1 c always be comb9$1 j z 9 e human c\nt5ance are comb9$ a type1 :i* is univ]sal1 & a "*1 :i* is individual4 ,,iii ,,*angeless ,,*ange ,,tr9ity1 ,,consonance1 ,,div]sity ,,9 ,,monotony1 ,,balance1 ,,rhy?mic ,,*ange1 ,,radiation ,! prec$+ essay 0 devot$ = ! mo/ "p to t inevitable duality :i* f9ds concrete expression 9 c\ntless pairs ( opposites1 su* z day & night1 fire & wat]1 man & woman2 9 ! art ( music by two *ords1 "o ( susp5se & ! o!r ( fulfilm5t2 9 spee* by v[el & consonant s\nds1 epitomiz$ 9 a & 9 m2 9 pa9t+ by w>m colors & cold1 epitomiz$ 9 r$ & blue2 9 ar*itecture by ! v]tical column & ! horizontal l9tel1 by void & solid--& s on4 ,,tr9ity ,?is concept %\ld n[ be modifi$ by ano!r1 namely1 t 9 e duality a ?ird is lat5t2 t two implies ?ree1 = ea* sex s to speak is 9 process ( becom+ ! o!r1 & ?is alt]nation eng5d]s & is accompli%$ by means ( a ?ird t]m or neut]1 :i* is l nei!r ( ! orig9al two b p>takes ( ! nature ( !m bo?1 j z a *ild may resemble bo? its p>5ts4 ,twilight comes betwe5 day & night2 e>? is ! *ild ( fire & wat]2 9 music1 besides ! *ord ( long+ & /riv+1 & ! *ord ( re/ & satisfaction 7! dom9ant sev5? & ! tonic71 !re is a ?ird or resolv+ *ord 9 :i* ! two are reconcil$4 ,9 ! sacr$ syllable ,om 7,aum71 :i* epitomizes all spee*1 ! u s\nd effects a transition betwe5 ! a s\nd & ! m2 among ! s-call$ prim>y colors yell[ comes betwe5 r$ & blue2 & 9 ar*itecture ! ar*1 :i* is bo? weight & support1 :i* is nei!r v]tical nor horizontal1 may be consid]$ ! neut] ( ! gr\p ( :i* ! column & ! l9tel are respectively mascul9e & fem99e4 ,^! are ! ?ree1 says ,mr4 ,l\is ,sullivan1 ! only ?ree lett]s f :i* has be5 exp&$ ! ar*itectural art1 z a great & sup]b language :]e) man has express$1 ?r\gh ! g5]ations1 ! *ang+ drift ( 8 ?\ghts4 ,illu/ration #ba3 ,,! ,,law ,,( ,,tr9ity4 ,a ,,roman ,,ionic ,,arcade1 ,,by ,,vignole4--,,! ,,column1 ,,! ,,entablature1 ,,& ,,! ,,ar* ,,correspond ,,to ,,l9es ,,v]tical1 ,,horizontal ,,& ,,curv$4 ,x w\ld be sup]]ogatory to dwell at any l5g? on ?is tr9ity ( manife/ation z ! concrete expression ( t unmanife/ & my/ical tr9ity1 t ?ree-9-"o :i* "u v>i\s names occurs 9 e _w-religion1 :]e1 defy+ def9ition1 x 0 wont to f9d expression symbolically 9 "s comb9ation ( v]tical1 horizontal & curv$ l9es4 ,! an/at$ cross ( ! ,egyptians is su* a symbol1 ! ,buddhi/ :eel1 & ! fylfot or swa/ika inscrib$ )9 a circle1 also ^? num]\s ,*ri/ian symbols comb9+ ! circle & ! cross4 ,su* ideographs h spell$ pr(\nd mean+ to ! ?9k]s ( pa/ ages4 ,we ( to-day are n giv5 to discov]+ any?+ wond]ful 9 ?ree /rokes ( a p51 b e arti/ 9 ! weav+ ( 8 patt]n mu/ ne$s employ ^! my/ic symbols 9 "o =m or ano!r1 & if he employs !m ) a full s5se ( _! hidd5 mean+ 8 "w w be apt to ga9 9 orig9ality & beauty--= orig9ality is a new & p]sonal p]ception ( beauty1 & beauty is ! "n we give to tru? we _c und]/&4 ,9 ar*itecture1 ?is tr9ity ( v]tical1 horizontal & curv$ l9es f9ds admirable illu/ration 9 ! application ( columns & entablature to an ar* & impo/ con/ruction1 s common 9 ,roman & ,r5aissance "w4 ,?is is a r$undancy1 & f9ds no ju/ification 9 reason1 because ! weight is su/a9$ by ! ar*1 & ! ord] is an app5dage m]ely2 yet ! comb9ation1 illogical z x is1 satisfies ! s5se ( beauty because ! ar* effects a transition betwe5 ! columns & ! entablature1 & completes ! tr9ity ( v]tical1 horizontal & curv$ l9es 7,illu/ration #ba74 ,9 ! entrances to _m ( ! ,go?ic ca!drals & *ur*es ! same elem5ts are bett] because m logically dispos$4 ,"h ! horizontal l9tel & its v]tical supports are n decorative m]ely1 b really p]=m _! prop] functions1 :ile ! ar*1 too1 has a raison d'tre 9 t x s]ves to relieve ! l9tel ( ! sup]9cumb5t weight ( masonry4 ,! same arrangem5t sometimes occurs 9 classic ar*itecture also1 z :5 an op5+ spann$ by a s+le ar* is subdivid$ by means ( an ord] 7,illu/ration #bb74 ,?ree is pre-em95tly ! numb] ( ar*itecture1 because x is ! numb] ( space1 :i* = u is ?ree-dim5sional1 & ( all ! arts ar*itecture is mo/ conc]n$ ) ! expression ( spatial relations4 ,! division ( a composition into ?ree relat$ p>ts is s univ]sal t x w\ld seem to be ! result ( an in/9ctive action ( ! human m9d4 ,! tw9 pylons ( an ,egyptian temple ) its entrance betwe51 = a ?ird division1 has its correspond5ce 9 ! two t[]s ( a ,go?ic ca!dral & ! int]v5+ scre5 wall ( ! nave4 ,9 ! palaces ( ! ,r5aissance a ?reefold division--v]tically by means ( quo9s or pila/]s1 & horizontally by means ( cornices or /r+ c\rses--0 common1 z 0 also ! division into a pr9cipal & two subord9ate masses 7,illu/ration #bc74 ,illu/ration #bb3 ,,! ,,law ,,( ,,tr9ity4 ,,! ,,tr9ity ,,( ,,horizontal ,,v]tical ,,& ,,curv$ ,,l9es4 ,! ar*itectural ord]s are divid$ ?reefold into p$e/al or /ylobate1 column & entablature2 & ea* ( ^! is aga9 divid$ ?reefold3 ! fir/ into pl9?1 die & cornice2 ! second into base1 %aft & capital2 ! ?ird into ar*itrave1 frieze & cornice4 ,9 _m cases ^! aga9 l5d !mselves to a ?reefold subdivision4 ,a m detail$ analysis ( ! capitals already %[n to be tw(old reveals a ?ird memb]3 9 ! ,greek ,doric ?is consi/s ( ! annulets imm$iately bel[ ! abacus2 9 ! o!r ord]s1 ! neck+ :i* divides ! %aft f ! cap4 ,,consonance ,z is ! small1 s is ! great is a p]petually recurr+ phrase 9 ! lit]ature ( !osophy1 & naturally s1 = x is a succ9ct /atem5t ( a fundam5tal & f>-rea*+ tru?4 ,! sci5ti/ recognizes x n[ & !n & "h & !re1 b ! occulti/ tru/s x always & utt]ly4 ,to him ! microcosm & ! macrocosm are "o & ! same 9 ess5ce1 & ! =?-go+ impulse :i* calls a univ]se into be+ & ! indraw+ impulse :i* ext+ui%es x aga91 ea* la/+ millions ( ye>s1 are e*o$ & repeat$ 9 ! infl[ & outfl[ ( ! brea? ?r\gh ! no/rils1 9 nutrition & excretion1 9 daily activity & nightly re/1 9 t long] day :i* we "n a lifetime1 & t long] re/ 9 ,deva*an--& s on until "t itself is transc5d$4 ,illu/ration #bc ,9 ! same way1 9 nature1 a ?+ is e*o$ & repeat$ ?r\gh\t its p>ts4 ,ea* leaf on a tree is itself a tree 9 m9iature1 ea* blossom a modifi$ leaf2 e v]tebrate animal is a complicat$ sy/em ( sp9es2 ! ripple is ! wave ( a l>g] wave1 & t l>g] wave is a "p ( ! ebb+ & fl[+ tide4 ,9 music ?is law is illu/rat$ 9 ! return ( ! tonic to itself 9 ! octave1 & its p>tial return 9 ! dom9ant2 also 9 a m ext5d$ s5se 9 ! repetition ( a major !me 9 ! m9or1 or 9 ! treble & aga9 9 ! bass1 ) modifications p]haps ( "t & key4 ,9 ! art ( pa9t+ ! law is exemplifi$ 9 ! repetition ) v>iation ( c]ta9 colors & comb9ations ( l9es 9 diff]5t p>ts ( ! same picture1 s dispos$ z to lead ! eye to "s focal po9t4 ,e pa9t] kn[s t any important color 9 8 picture mu/ be e*o$1 z x 71 9 diff]5t places1 = h>mony ( ! :ole4 ,illu/ration #bd ,9 ! drama ! repetition ( a spee* or ( an entire sc5e1 b "u circum/ances :i* give x a diff]5t mean+1 is (t5 mo/ effective1 z :5 ,gratiano1 9 ! trial sc5e ( ,! ,m]*ant ( ,v5ice taunts ,%ylock ) 8 own words1 ,a ,daniel come to judgm5t6 or1 z :5 9 "o ( ! lat] sc5es ( ,z ,y ,l ,x an e>li] sc5e is repeat$1 b ) ,rosal9d speak+ 9 h] prop] p]son & no long] z ! boy ,ganym$e4 ,^! recurr5ces1 ^! inn] consonances1 ^! repetitions ) v>iations are common 9 ar*itecture also4 ,! *annel$ triglyphs ( a ,greek ,doric frieze e*o ! flut$ columns bel[ 7,illu/ration #bd74 ,! balu/rade :i* cr[ns a colonnade is a repetition1 9 "s sort1 ( ! colonnade itself4 ,! modillions ( a ,cor9?ian cornice are b elaborat$ & embelli%$ d5tils4 ,ea* p9nacle ( a ,go?ic ca!dral is a little t[] ) its spire4 ,z ,rusk9 has po9t$ out1 ! great vault ( ! ca!dral nave1 toge!r ) ! po9t$ ro( above x1 is repeat$ 9 ! entrance ar* ) its gable1 & ! same two elem5ts appe> 9 e /atue-en%r9+ ni*e ( ! doorway4 ,9 classic ar*itecture1 z has be5 %[n1 in/ead ( ! ar* & gable1 ! column & entablature ev]y:]e recur "u diff]5t =ms4 ,! m9or domes :i* flank ! great dome ( ! ca!dral ( ,flor5ce enhance & re9=ce ! latt]1 & prep>e ! eye = a climax :i* w\ld o!rwise be too abrupt4 ,! c5tral pavilion ( ! ,*teau ,ma9t5on1 ) its two turrets1 e*oes ! entire faade ) its two t[]s4 ,l ! ov]ture to an op]a1 x introduces !mes :i* f9d a m ext5d$ developm5t else:]e 7,illu/ration #bf74 ,illu/ration #be ,illu/ration #bf ,illu/ration #bg ,?is law ( ,consonance is op]ative 9 ar*itecture m obscurely 9 ! =m ( recurr+ num]ical ratios1 id5tical geometrical det]m9+ figures1 p>allel diagonals & ! l1 :i* w be discuss$ 9 a subsequ5t essay4 ,x has also to d ) /yle & scale1 ! adh]5ce to sub/antially "o me?od ( con/ruction & mann] ( ornam5t1 j z 9 music ! key1 or *os5 s]ies ( notes1 may n be dep>t$ f except ?r\gh prop] modulations1 or 9 a specific mann]4 ,?us x is se5 t 9 a "w ( art1 z 9 a piece ( tape/ry1 ! same ?read runs ?r\gh ! web1 b goes to make up diff]5t figures4 ,! idea is deeply !osophic3 "o life1 _m manife/ations2 h5ce1 inevitably1 e*oes1 resemblances--,consonance4 ,,div]sity ,,9 ,,monotony ,ano!r pr9ciple ( natural beauty1 closely alli$ to ! =ego+1 its complem5t z x 71 is t ( ,div]sity 9 ,monotony--n id5tity1 b diff]5ce4 ,x %[s itself = ! mo/ "p z a p]ceptible & piquant v>iation betwe5 individual units belong+ to ! same class1 type1 or species4 ,no two trees put =? _! bran*es 9 j ! same mann]1 & no two leaves f ! same tree exactly correspond2 no two p]sons look alike1 ?\gh !y h simili> memb]s & features2 ev5 ! m>k+s on ! sk9 ( ! ?umb are diff]5t 9 e human h&4 ,br[n+ says1 ,z l z a h& to ano!r h&6 ,:oev] said t fooli% ?+1 ,c\ld n h /udi$ to und]/&-- ,n[ e pr9ciple ( natural beauty is b ! pres5tm5t ( "s occult law1 "s !osophical tru?2 & ?is law ( ,div]sity 9 ,monotony is ! pres5tm5t ( ! tru? t id5tity does n exclude diff]5ce4 ,! law is b9d+1 yet ! w is free3 all m5 are bro!rs unit$ by ! ties ( bro!rhood1 yet ea* is unique1 a free ag5t1 & nev] s free z :5 mo/ b\nd by ! ,good ,law4 ,?is tru? nature beautifully proclaims1 & art also4 ,9 ar*itecture x is admirably exemplifi$ 9 ! metopes ( ! ,p>!non frieze3 se5 at a di/ance ^! mu/ h pres5t$ a sc>cely di/+ui%able texture ( sunlit m>ble & cool %ad[1 yet 9 reality ea* is a sep>ate "w ( art4 ,s ) ! capitals ( ! columns ( ! wond]ful sea-arcade ( ! ,v5etian ,ducal palace3 alike 9 g5]al cont\r !y diff] widely 9 detail1 & unfold a ,bible /ory4 ,9 ,go?ic ca!drals1 9 ,romanesque mona/]y cloi/]s1 a teem+ v>iety ( inv5tion is hidd5 b5ea? app>5t uni=mity4 ,! g>goyles ( ,notre ,dame make simili> silh\ettes aga9/ ! sky1 b se5 ne> at h& :at a m5ag]ie ( mon/]s6 ,! same _s ( controll$ individuality1 ( lib]ty subs]vi5t to ! law ( all1 is exemplifi$ 9 ! bases ( ! columns ( ! temple ( ,apollo ne> ,miletus--ea* "o a sep>ate ma/]piece ( v>i\s ornam5tation adorn+ an e/abli%$ ar*itectural =m 7,illu/ration #bh74 ,illu/ration #bh ,illu/ration #bi ,! build]s ( ! e>ly ,italian *ur*es1 in/9ctively obey+ ?is law ( ,div]sity 9 ,monotony1 v>i$ ! size ( ! ar*es 9 ! same arcade 7,illu/ration #bi71 & t ?is 0 an effect ( art & n ( accid5t or c>elessness ,rusk9 long ago discov]$1 & ! ,brooklyn ,in/itute surveys h amply confirm$ 8 view4 ,al?\gh by ^! means ! build]s ( t day produc$ effects ( deceptive p]spective1 ( subtle concord & contra/1 _! %e] hatr$ ( monotony & mean+less repetition may h l$ !m to div]sify _! arcades 9 ! mann] describ$1 = a rigidly equal & regul> division lacks int]e/ & vitality4 ,,balance ,if "o 7 to e/abli% an axial plane v]tically ?r\gh ! c5t] ( a tree1 9 mo/ cases x w\ld be f\nd t ! masses ( foliage1 h[ev] irregul>ly %ap$ on ei!r side ( su* an axis1 j ab\t balanc$ ea* o!r4 ,simil>ly1 9 all our bodily movem5ts1 = e *ange ( equilibrium !re occurs an opposition & adju/m5t ( memb]s ( su* a nature t an axial plane ?r\gh ! c5t] ( gravity w\ld divide ! body into two sub/antially equal masses1 z 9 ! case ( ! tree4 ,?is physical plane law ( ,balance %[s itself = ! mo/ "p on ! human plane z ! law ( ,comp5sation1 :]eby1 to ! vision ( ! occulti/1 all acc\nts are squ>$1 s to speak4 ,x is 9 effect ! law ( ,ju/ice1 aptly symboliz$ by ! scales4 ,! law ( ,balance f9ds abundant illu/ration 9 art3 9 music by ! opposition1 ! answ]+1 ( "o phrase by ano!r ( ! same elem5ts & ! same l5g?1 b involv+ a diff]5t sequ5ce ( int]vals2 9 pa9t+ by ! disposition ( masses 9 su* a way t !y ab\t equalize "o ano!r1 s t !re is no s5se ( /ra9 9 ! composition4 ,9 ar*itecture ! common & obvi\s recognition ( ! law ( ,balance is 9 ! symmetrical disposition ( ! elem5ts1 :e!r ( plan or ( elevation1 on ei!r side ( axial l9es4 ,a f> m subtle & vital illu/ration ( ! law occurs :5 ! oppos$ elem5ts d n exactly mat*1 b diff] f ea* o!r1 z 9 ! case ( ! two t[]s ( ,ami5s1 = example4 ,?is sort ( balance may be said to be *>act]i/ic ( ,go?ic1 z symmetry is *>act]i/ic ( ,classic1 ar*itecture4 ,,rhy?mic ,,*ange ,!re is 9 nature a univ]sal t5d5cy t[>d ref9em5t & compactness ( =m 9 space1 or contr>iwise1 t[>d increm5t & diffusion2 & ?is manife/s itself 9 "t z accel]ation or ret>dation4 ,x is gov]n$1 9 ei!r case1 by an exact ma!matical law1 l ! law ( fall+ bodies4 ,x %[s itself 9 ! wid5+ circles :i* appe> :5 "o drops a /one into /ill wat]1 9 ! convolutions ( %ells1 9 ! bran*+ ( trees & ! ve9+ ( leaves2 ! dim9ution 9 ! size ( ! pipes ( an organ illu/rates x1 & ! spac+ ( ! frets ( a guit>4 ,m & m sci5ce is com+ to recognize1 :at !osophy affirms1 t ! spiral vortex1 :i* s beautifully illu/rates ?is law1 bo? 9 its "t & its space aspects is ! univ]sal ar*etype1 ! patt]n ( all t is1 has be51 or w be1 s9ce x is ! =m assum$ by ! ultimate physical atom1 & ! ultimate physical atom is ! physical cosmos 9 m9iature4 ,?is ,rhy?mic ,dim9ution is ev]y:]e3 x is 9 ! eye itself1 = any s]ies ( ma!matically equal units1 su* = example z ! columns & int]columnations ( a colonnade1 become :5 se5 9 p]spective rhy?mically unequal1 dim9i%+ accord+ to ! univ]sal law4 ,! entasis ( a ,classic column is det]m9$ by ?is law1 ! spirals ( ! ,ionic volute1 ! annulets ( ! ,p>!non cap1 obey x 7,illu/ration #cj74 ,9 recognition ( ! same pr9ciple ( ,rhy?mic ,dim9ution a build+ is (t5 made to gr[1 or appe> to gr[ light]1 m intricate1 f9]1 f ! gr\nd upw>d1 an end atta9$ by v>i\s devices1 "o ( ! mo/ common be+ ! employm5t ( ! m att5uat$ & highly ornam5t$ ord]s above ! simpl] & /urdi]1 z 9 ! ,roman ,colosseum1 or 9 ! ,palazzo ,uguccioni1 9 ,flor5ce--to m5tion only two examples out ( a great numb]4 ,9 ! ,ricc>di ,palace an effect ( increas+ ref9em5t is obta9$ by dim9i%+ ! boldness ( ! ru/ication ( ! a%l> 9 successive /ories2 9 ! ,f>nese1 by ! gradual r$uction ( ! size ( ! angle quo9s 7,illu/ration #cj74 ,9 an ,egyptian pylon x is a*iev$ mo/ simply by batt]+ ! wall2 9 a ,go?ic ca!dral mo/ elaborately by a k9d ( segregation1 or break+ up1 analog\s to t :i* a tree und]goes--! /rong1 relatively unbrok5 base correspond+ to ! trunk1 ! dim9i%+ buttresses to ! tap]+ limbs1 & ! multitude ( delicate p9nacles & crockets1 to ! out]mo/ bran*es & twigs1 se5 aga9/ ! sky4 ,,radiation ,! f9al pr9ciple ( natural beauty to :i* ! au?or w\ld call att5tion is ! law ( ,radiation1 :i* is 9 a mann] a return to ! fir/1 ! law ( ,unity4 ,! v>i\s p>ts ( any organism radiate f1 or o!rwise ref] back to common c5t]s1 or foci1 & ^! to c5t]s ( _! own4 ,! law is repres5t$ 9 its simplicity 9 ! />-fi%1 9 its complexity 9 ! body ( man2 a tree spr+s f a se$1 ! sol> sy/em c5t]s 9 ! sun4 ,! idea "h express$ by ! t]m radiation is a famili> "o to all /ud5ts ( !osophy4 ,! ,logos radiates 8 life & light ?r\gh\t 8 univ]se1 br++ into activity a ho/ ( entities :i* become !mselves radial c5t]s2 ^! g5]ate /ill o!rs1 & s on endlessly4 ,?is pr9ciple1 l e o!r1 pati5tly publi%es itself to u1 unhe$+1 ev]y:]e 9 nature1 & 9 all great art z well2 x is a law ( optics1 = example1 t all /raight l9es hav+ a common direction if suffici5tly prolong$ appe> to meet 9 a po9t1 i4e41 radiate f x 7,illu/ration #ca74 ,leon>do da ,v9ci employ$ ?is pr9ciple ( p]spective 9 8 ,la/ ,supp] to draw ! spectator's eye to ! picture's c5tral figure1 ! po9t ( sight t[>d :i* ! l9es ( ! walls & ceil+ conv]ge c5t]+ 9 ! head ( ,*ri/4 ,puvis de ,*avannes1 9 8 ,bo/on ,libr>y decoration1 leads ! eye by a sy/em ( triangulation to ! small figure ( ! ,g5ius ( ,enlight5m5t above ! c5tral door 7,illu/ration #cb72 & ,rusk91 9 8 ,elem5ts ( ,draw+1 has %[n h[ artfully ,turn] arrang$ "s ( 8 compositions to attract att5tion to a focal po9t4 ,?is law ( ,radiation ent]s l>gely into ar*itecture4 ,! ,colosseum1 bas$ ^u ! ellipse1 a figure g5]at$ f two po9ts or foci1 & ! ,pan!on1 bas$ ^u ! circle1 a figure g5]at$ f a c5tral po9t1 are famili> examples4 ,! di/9ctive *>act]i/ic ( ,go?ic con/ruction1 ! conc5tration or focalization ( ! weight ( ! vaults & ar*es at c]ta9 po9ts1 is ano!r illu/ration ( ! same pr9ciple appli$ to ar*itecture1 beautifully exemplifi$ 9 ! semicircul> apse ( a ca!dral1 :]e ! l9es ( ! plan conv]ge to a common c5t]1 & ! ribs ( ! vault+ meet ^u ! capitals ( ! pi]s & columns1 seem+ to radiate !nce to /ill o!r c5t]s 9 ! l(ti] vaults :i* f9ally meet 9 a c5t] common to all4 ,illu/ration #cj ,illu/ration #ca ,illu/ration #cb ,! trac]y ( ! great roses1 high up 9 ! faades ( ! ca!drals ( ,p>is & ( ,ami5s1 illu/rate ,radiation1 9 ! "o case mascul9e3 /raight1 angul>1 direct2 9 ! fem99e3 curv$1 fl[+1 s9u\s4 ,! same ,beautiful ,necessity det]m9$ ! *>act]i/ics ( mu* ( ! ornam5t ( widely sep>at$ /yles & p]iods3 ! ,egyptian lotus1 ! ,greek honeysuckle1 ! ,roman acan?us1 ,go?ic leaf "w--to snat* at r&om f\r blossoms f ! %eaf ( "t4 ,! radial pr9ciple /ill inh]5t 9 ! debas$ ornam5t ( ! late ,r5aissance gives t ornam5t a unity1 a coh]5ce1 & a k9d ( beauty all its own 7,illu/ration #ce74 ,illu/ration #cc ,illu/ration #cd ,su* are a few ( ! m obvi\s laws ( natural beauty & _! application to ! art ( ar*itecture4 ,! li/ is by no means exhau/$1 b x is n ! multiplicity & div]sity ( ^! laws :i* is important to keep 9 m9d1 s mu* z _! relat$ness & cord9ation1 = !y are b diff]5t aspects ( ! ,"o ,law1 t :]eby ! ,logos manife/s 9 "t & space4 ,a brief recapitulation w s]ve to make ?is correlation pla91 & at ! same "t fix :at has be5 writt5 m firmly 9 ! read]'s m9d4 ,illu/ration #ce ,illu/ration #cf ,fir/ comes ! law ( ,unity2 !n1 s9ce e unit is 9 its ess5ce tw(old1 !re is ! law ( ,pol>ity2 b ?is duality is n /atic b dynamic1 ! two p>ts act+ & react+ ^u "o ano!r to produce a ?ird--h5ce ! law ( ,tr9ity4 ,giv5 ?is ?ird t]m1 & ! innum]able comb9ations made possible by its relations to & reactions ^u ! orig9al pair1 ! law ( ,multiplicity 9 ,unity naturally foll[s1 z does ! law ( ,consonance1 or repetition1 s9ce ! primal process ( diff]5tiation t5ds to repeat itself1 & ! orig9al comb9ations to reappe>--b to reappe> 9 *ang$ =m1 h5ce ! law ( ,div]sity 9 ,monotony4 ,! law ( ,balance is se5 to be b a modification ( ! law ( ,pol>ity1 & s9ce all ?+s are wax+ & wan+1 !re is ! law :]eby !y wax & wane1 t ( ,rhy?mic ,*ange4 ,radiation r$iscov]s & reaffirms1 ev5 9 ! utmo/ complexity1 t ess5tial & fundam5tal unity f :i* complexity 0 wr\ght4 ,ev]y?+1 beautiful or ugly1 obeys & illu/rates "o or ano!r ( ^! laws1 s univ]sal are !y1 s insep>ably att5dant ^u e k9d ( manife/ation 9 "t & space4 ,x is ! numb] ( !m :i* f9ds illu/ration )9 small compass1 & ! aptness & complet5ess ( su* illu/ration1 :i* makes = beauty1 because beauty is ! f9e fl[] ( a sort ( sublime +5uity4 ,a "w ( art is no?+ if n artful3 l an acro/ic1 ! m diff]5t ways x c be read--up1 d[n1 across1 f "r to left & f left to "r--! bett] x is1 o!r ?+s be+ equal4 ,?is /atem5t1 ( c\rse1 may be con/ru$ 9 su* a way z to appe> absurd2 :at is meant is simply t ! m a "w ( art is freight$ & fraught ) mean+ beyond mean+1 ! m secure its immortality1 ! m p[]ful its appeal4 ,= enjoym5t1 x is n necess>y t all ^! mean+s %\ld be fa?om$1 x is only necess>y t !y %\ld be felt4 ,consid] = a mom5t ! mann] 9 :i* ,leon>do da ,v9ci's ,la/ ,supp]1 an ackn[l$g$ ma/]piece1 con=ms to ev]yone ( ! laws ( beauty enum]at$ above 7,illu/ration #cb74 ,x illu/rates ! law ( ,unity 9 t x mov+ly portrays a s+le significant episode 9 ! life ( ,*ri/4 ,! eye is l$ to dwell ^u ! c5tral p]sonage ( ?is drama by _m artful exp$i5ts3 ! visible "p ( ! figure ( ,*ri/ con=ms to ! l9es ( an equilat]al triangle plac$ exactly 9 ! c5t] ( ! picture2 ! figure is sep>at$ by a consid]able space f ! gr\ps ( ! disciples on ei!r h&1 & /&s reliev$ aga9/ ! l>ge/ p>allelogram ( light1 & ! vani%+ po9t ( ! p]spective is 9 ! head ( ,*ri/1 at ! apex1 !re=e1 ( ! triangle4 ,! law ( ,pol>ity f9ds fulfilm5t 9 ! complex & fl[+ l9es ( ! drap$ figures contra/$ ) ! simple p>allelogram ( ! clo?-cov]$ table1 & ! sev]e ar*itecture ( ! room4 ,! law ( ,tr9ity is exemplifi$ 9 ! ?ree w9d[s1 & 9 ! subdivision ( ! twelve figures ( ! disciples into f\r gr\ps ( ?ree figures ea*4 ,! law ( ,consonance appe>s 9 ! repetition ( ! horizontal l9es ( ! table 9 ! ceil+ above2 & 9 ! c5tral triangle be=e ref]r$ to1 cont9u$ & e*o$1 z x 71 9 ! triangul> supports ( ! table visible und]nea? ! clo?4 ,! law ( ,div]sity 9 ,monotony is illu/rat$ 9 ! v>y+ disposition ( ! heads ( ! figures 9 ! f\r gr\ps ( ?ree2 ! law ( ,balance 9 ! ess5tial symmetry ( ! entire composition2 ! law ( ,rhy?mic ,*ange 9 ! dim9i%+ ( ! wall & ceil+ spaces2 & ! law ( ,radiation 9 ! conv]g5ce ( all ! p]spective l9es to a s+le significant po9t4 ,to illu/rate fur!r ! univ]sality ( ^! laws1 consid] n[ _! application to a s+le "w ( ar*itecture3 ! ,taj ,mahal1 "o ( ! mo/ beautiful build+s ( ! _w 7,illu/ration #cf74 ,x is a unit1 b tw(old1 = x consi/s ( a curv$ "p & an angul> "p1 r\ghly figur$ z an inv]t$ cup ^u a cube2 ea* ( ^! 7se5 9 p>allel p]spective1 at ! end ( ! pr9cipal vi/a7 is ?reefold1 = !re are two sides & a c5tral p>allelogram1 & two less] domes flank ! great dome4 ,! composition is ri* 9 consonances1 = ! side ar*es e*o ! c5tral "o1 ! subord9ate domes ! great dome1 & ! lant]ns ( ! out/&+ m9>ets repeat ! pr9cipal motif4 ,div]sity 9 ,monotony appe>s abundantly 9 ! ornam5t1 :i* is intricate & inf9itely v>i\s2 ! law ( ,balance is ev]y:]e op]ative 9 ! symmetry ( ! entire design4 ,rhy?mic ,*ange appe>s 9 ! tap]+ ( ! m9>ets1 ! outl9es ( ! domes & _! mass relations to "o ano!r2 & f9ally1 ! :ole effect is ( radiation f a c5tral po9t1 ( elem5ts dispos$ on radial l9es4 ,x w\ld be fatu\s to cont5d t ! prime object ( a "w ( ar*itecture is to obey & illu/rate ^! laws4 ,! prime object ( a "w ( ar*itecture is to fulfill c]ta9 def9ite conditions 9 a practical1 economical1 & admirable way1 & 9 fulfill+ to express z f> z possible ^! conditions1 mak+ ! =m express ! function4 ,! ar*itect :o is also an arti/ h[ev] w d ?is & some?+ beyond3 work+ = ! mo/ "p unconsci\sly1 h>moni\sly1 joy\sly1 8 build+ w obey & illu/rate natural laws--^! laws ( beauty--& to ! ext5t x does s x w be a "w ( art2 = art is ! me?od ( nature c>ri$ into ^? high] regions ( ?\ght & feel+ :i* man alone inhabits3 regions :i* x is "o ( ! purposes ( !osophy to explore4 ,,iv ,,! ,,bodily ,,temple ,c>lyle says3 ,!re is b "o temple 9 ! _w1 & t is ! body ( man4 ,if ! body is1 z he decl>es1 a temple1 x is n less true t a temple or any "w ( ar*itectural art is a l>g] body :i* man has creat$ = 8 uses1 j z ! individual self is h\s$ )9 its /ronghold ( fle% & bones4 ,ar*itectural beauty l human beauty dep5ds ^u ! prop] subord9ation ( p>ts to ! :ole1 ! h>moni\s int]relation betwe5 ^! p>ts1 ! expressiv5ess ( ea* ( its function or functions1 & :5 ^! are _m & div]se1 _! reconcilem5t "o ) ano!r4 ,?is be+ s1 a /udy ( ! human figure ) a view to analyz+ ! s\rces ( its beauty _c fail to be pr(itable4 ,pursu$ intellig5tly1 su* a /udy w /imulate ! m9d to a p]ception ( ^? simple yet subtle laws accord+ to :i* nature ev]y:]e works1 & x w educate ! eye 9 ! f9e/ kn[n s*ool ( proportion1 tra9+ x to di/+ui% m9ute diff]5ces1 9 ! same way t ! he>+ ( good music cultivates ! e>4 ,^? pr9ciples ( natural beauty :i* =m$ ! subject ( ! two prec$+ essays are all exemplifi$ 9 ! ideally p]fect human figure4 ,?\gh ess5tially a unit1 !re is a well m>k$ division into "r & left--,h&s to h&s1 & feet to feet1 9 "o body grooms & brides4 ,!re are two arms1 two legs1 two e>s1 two eyes1 & two lids to ea* eye2 ! nose has two no/rils1 ! m\? has two lips4 ,moreov]1 ! t]ms ( su* pairs are mascul9e & fem99e ) respect to ea* o!r1 "o be+ active & ! o!r passive4 ,ow+ to ! great size & "o-sid$ position ( ! liv]1 ! "r half ( ! body is heavi] ?an ! left2 ! "r arm is usually long] & m muscul> ?an ! left2 ! "r eye is slightly high] ?an its fell[4 ,9 speak+ & eat+ ! l[] jaw & "u lip are active & mobile ) relation to ! upp]2 9 w9k+ x is ! upp] eyelid :i* is ! m active4 ,t inevitable duality :i* is exhibit$ 9 ! =m ( ! body *>act]izes its motions also4 ,9 ! act ( walk+ = example1 a =w>d movem5t is atta9$ by means ( a =w>d & a backw>d movem5t ( ! ?ighs on ! axis ( ! hips2 ?is leg movem5t becomes tw(old aga9 bel[ ! knee1 & ! feet move up & d[n indep5d5tly on ! axis ( ! ankle4 ,a simil> progression is foll[$ 9 rais+ ! arm & h&3 motion is communicat$ fir/ to ! l>g] p>ts1 ?r\gh !m to ! small] & !nce to ! extremities1 becom+ m rapid & complex z x progresses1 s t all free & natural movem5ts ( ! limbs describe invisible l9es ( beauty 9 ! air4 ,coexi/5t ) ?is p]vasive duality !re is a ?reefold division ( ! figure into trunk1 head & limbs3 a sup]ior tr9ity ( head & arms1 & an inf]ior tr9ity ( trunk & legs4 ,! limbs are divid$ ?reefold into upp]-arm1 =e>m & h&2 ?igh1 leg & foot4 ,! h& fl[]s out into f+]s & ! foot into toes1 ea* ) a ?reefold articulation2 & 9 ?is way is effect$ t transition f unity to multiplicity1 f simplicity to complexity1 :i* appe>s to be s univ]sal ?r\gh\t nature1 & ( :i* a tree is ! p]fect symbol4 ,illu/ration #cg3 ,,! ,,law ,,( ,,rhy?mic ,,dim9ution ,,illu/rat$ ,,9 ,,! ,,tap]+ ,,body1 ,,limbs1 ,,f+]s ,,toes4 ,illu/ration #ch ,illu/ration #ci ,! body is ri* 9 veil$ repetitions1 e*oes1 consonances4 ,! head & arms are 9 a s5se a ref9em5t ^u ! trunk & legs1 !re be+ a cle>ly traceable correspond5ce betwe5 _! v>i\s p>ts4 ,! h& is ! body 9 little--,y\r s(t h& is a woman ( itself--! palm1 ! trunk2 ! f\r f+]s1 ! f\r limbs2 & ! ?umb1 ! head2-ea* f+] is a little arm1 ea* f+] tip a little palm4 ,! lips are ! lids ( ! m\?1 ! lids are ! lips ( ! eyes--& s on4 ,! law ( ,rhy?mic ,dim9ution is illu/rat$ 9 ! tap]+ ( ! entire body & ( ! limbs1 9 ! graduat$ sizes & l5g?s ( ! palm & ! toes1 & 9 ! successively decreas+ l5g? ( ! palm & ! jo9ts ( ! f+]s1 s t 9 clos+ ! h& ! f+]s describe natural spirals 7,illu/rations #cg1 #ch74 ,f9ally1 ! limbs radiate z x 7 f ! trunk1 ! f+]s f a po9t 9 ! wri/1 ! toes f a po9t 9 ! ankle4 ,! ribs radiate f ! sp9al column l ! ve9s ( a leaf f its midrib 7,illu/ration #ci74 ,illu/ration #dj ,! relation ( ^! laws ( beauty to ! art ( ar*itecture has be5 %[n already4 ,!y are reit]at$ "h only to %[ t man is inde$ ! microcosm--a little _w fa%ion$ f ! same elem5ts & 9 accordance ) ! same ,beautiful ,necessity z is ! great] _w 9 :i* he dwells4 ,:5 he builds a h\se or temple he builds x n lit]ally 9 8 own image1 b accord+ to ! laws ( 8 own be+1 & !re are correspond5ces n altoge!r fanciful betwe5 ! animate body ( fle% & ! inanimate body ( /one4 ,d we n all ( u1 consci\sly or unconsci\sly1 recognize ! fact ( "* & physiognomy 9 build+s8 ,are !y n1 to our imag9ation1 mascul9e or fem99e1 w9n+ or =bidd+--human1 9 po9t ( fact--to a great] degree ?an any?+ else ( man's creat+8 ,!y are ?is c]ta9ly to a true lov] & /ud5t ( ar*itecture4 ,se5 f a di/ance ! great ,fr5* ca!drals appe> l cr\*+ mon/]s1 half bea/1 half human3 ! two t[]s /& l a man & a woman1 my/]i\s & gigantic1 look+ out ov] city & pla94 ,! campaniles ( ,italy rise above ! *ur*es & h\ses l ! s5t9els ( a sleep+ camp--nor is _! /rangely human aspect :olly imag9>y3 ^! giants ( m\nta9 & campagna h eyes & braz5 tongues2 ris+ f\r squ>e1 /ory above /ory1 ) a belfry or look\t1 l a head1 atop1 _! lik5ess to a man is n infrequ5tly enhanc$ by a c]ta9 id5tity ( proportion--( ratio1 t is1 ( height to wid?3 ,giotto's beautiful t[] is an example4 ,! c>yatid is a support+ memb] 9 ! =m ( a woman2 9 ! ,ionic column we disc]n h] /iff5$1 l ,lot's wife1 into a pill>1 ) no?+ to %[ h] fem99e b ! spirals ( h] beautiful hair4 ,! columns :i* uphold ! p$im5t ( ! ,p>!non are unmi/akably mascul9e3 ! ratio ( _! bread? to _! height is ! ratio ( ! bread? to ! height ( a man 7,illu/ration #dj74 ,illu/ration #da3 ,,! ,,body ,,! ,,ar*etype ,,( ,,sacr$ ,,edifices4 ,illu/ration #db3 ,,! ,,vesica ,,piscis ,,& ,,! ,,plan ,,( ,,*>tres4 ,at c]ta9 p]iods ( ! _w's hi/ory1 p]iods ( my/ical enlight5m5t1 m5 h be5 wont to use ! human figure1 ! s\l's temple1 z a sort ( ar*etype = sacr$ edifices 7,illu/ration #da74 ,! colossi1 ) calm inscrutable faces1 :i* flank ! entrance to ,egyptian temples2 ! great bronze ,buddha ( ,japan1 ) its dream+ eyes2 ! little kn[n colossal figures ( ,india & ,*9a--all ^! belong sc>cely less to ! doma9 ( ar*itecture ?an ( sculpture4 ,! relation above ref]r$ to h[ev] is a matt] m subtle & occult ?an m]e obvi\s imitation on a l>ge scale1 be+ bas$ ^u "s correspond5ce ( p>ts1 or simil>ity ( proportions1 or bo?4 ,! correspond5ce betwe5 ! inn]mo/ sanctu>y or %r9e ( a temple & ! he>t ( a man1 & betwe5 ! gates ( t temple & ! organs ( s5se is suffici5tly obvi\s1 & a relation once e/abli%$1 ! idea is susceptible ( almo/ inf9ite developm5t4 ,t ! anci5ts proportion$ _! temples f ! human figure is no new idea1 nor is x at all surpris+4 ,! sculpture ( ! ,egyptians & ! ,greeks reveals ! fact t !y /udi$ ! body ab/ractly1 9 its ext]ior pres5tm5t4 ,x is cle> t ! rules ( its proportions mu/ h be5 e/abli%$ = sculpture1 & x is n unreasonable to suppose t !y became canonical 9 ar*itecture also4 ,vitruvius & ,alb]ti bo? lay /ress on ! fact t all sacr$ build+s %\ld be f\nd$ on ! proportions ( ! human body4 ,illu/ration #dc3 ,a ,,go?ic ,,ca!dral ,,! ,,symbol ,,( ,,! ,,body ,,( ,,jesus ,,*ri/ ,illu/ration #dd3 ,,! ,,symbolism ,,( ,a ,,go?ic ,,ca!dral ,,f ,,! ,,rosicrucians3 ,,h>grave ,,j5n+s ,9 ,france1 dur+ ! ,middle ,ages1 a ,go?ic ca!dral became1 at ! h&s ( ! secret masonic guilds1 a glorifi$ symbol ( ! body ( ,*ri/4 ,to practical-m9d$ /ud5ts ( ar*itectural hi/ory1 famili> ) ! sl[ & halt+ evolution ( a ,go?ic ca!dral f a ,roman basilica1 su* an idea may seem to be only ! maund]+s ( a my/ical imag9ation1 a !ory evolv$ f ! inn] consci\sness1 entitl$ to no m consid]ation ?an ! famili> fallacy t vault$ nave ( a ,go?ic *ur* 0 an attempt to imitate ! gre5 aisles ( a =e/4 ,x %\ld be rememb]$ h[ev] t ! habit ( ! ?\ght ( t "t 0 my/ical1 z t ( our own age is utilit>ian & sci5tific2 & ! *os5 language ( my/icism is always an elaborate & involv$ symbolism4 ,:at c\ld be m natural ?an t a build+ devot$ to ! wor%ip ( a crucifi$ ,savior %\ld be made a symbol1 n ( ! cross only1 b ( ! body crucifi$8 ,illu/ration #de3 ,,! ,,geometrical ,,basis ,,( ,,! ,,human ,,figure ,illu/ration #df ,! vesica piscis 7a figure =m$ by ! develop+ arcs ( two equilat]al triangles hav+ a common side7 :i* 9 s _m cases seems to h det]m9$ ! ma9 proportion ( a ca!dral plan--! int]ior l5g? & wid? across ! transepts--appe>s z an aureole ar\nd ! figure ( ,*ri/ 9 e>ly repres5tations1 a fact :i* c]ta9ly po9ts to a relation betwe5 ! two 7,illu/rations #db1 #dc74 ,a curi\s little book1 ,! ,rosicrucians1 by ,h>grave ,j5n+s1 conta9s an int]e/+ diagram :i* well illu/rates ?is conception ( ! symbolism ( a ca!dral4 ,a copy ( x is "h giv54 ,! apse is se5 to correspond to ! head ( ,*ri/1 ! nor? transept to 8 "r h&1 ! s\? transept to ! left h&1 ! nave to ! body1 & ! nor? & s\? t[]s to ! "r & left feet respectively 7,illu/ration #dd74 ,illu/ration #dg ,! ca!dral build]s excell$ all o!rs 9 ! artfulness ) :i* !y e/abli%$ & ma9ta9$ a relation betwe5 _! ar*itecture & ! /ature ( a man4 ,?is is p]haps "o reason :y ! ,fr5* & ,engli% ca!drals1 ev5 ^? ( mod]ate dim5sions are m truly impressive ?an ev5 ! l>ge/ ( ! great ,r5aissance /ructures1 su* z ,/4 ,pet]'s 9 ,rome4 ,a gigantic ord] furni%es no true measure = ! eye3 its va/ness is reveal$ only by ! accid5t ( "s human pres5ce :i* =ms a basis ( comp>ison4 ,t ar*itecture is n necess>ily ! mo/ awe-inspir+ :i* gives ! impression ( hav+ be5 built by giants = ! abode ( pigmies2 l ! o!r arts1 ar*itecture is highe/ :5 x is mo/ human4 ,! m$ival build]s1 true to ?is dictum1 employ$ /ones ( a size proportionate to ! /r5g? ( a man work+ )\t unusual me*anical aids2 ! great pi]s & columns1 built up ( _m su* /ones1 7 commonly subdivid$ into clu/]s1 & ! circumf]5ce ( ea* %aft ( su* a clu/] approximat$ ! gir? ( a man2 by ?is device ! m\ld+ ( ! base & ! foliation ( ! caps 7 easily kept 9 scale4 ,:]ev] a balu/rade occurr$ x 0 proportion$ n ) relation to ! height ( ! wall or ! column bel[1 z 9 classic ar*itecture1 b ) relation to a man's /ature4 ,illu/ration #dh3 ,,figure ,,divid$ ,,accord+ ,,to ,,! ,,egyptian ,,canon ,x may be /at$ z a g5]al rule t e "w ( ar*itecture1 ( :atev] /yle1 %\ld h some:]e ab\t x some?+ fix$ & endur+ to relate x to ! human figure1 if x be only a flight ( /eps 9 :i* ea* "o is ! measure ( a /ride4 ,9 ! ,f>nese1 ! ,ricc>di1 ! ,/rozzi1 & _m ano!r ,italian palace1 ! /one seat ab\t ! base gives scale to ! build+ because ! behold] kn[s in/9ctively t ! height ( su* a seat mu/ h "s relation to ! l5g? ( a man's leg4 ,9 ! ,pitti palace ! balu/rade :i* cr[ns ea* /ory answ]s a simil> purpose3 x /&s 9 no intimate relation to ! gigantic ar*es bel[1 b is ( a height conv5i5t = l\ng+ elb[s4 ,! door to ,giotto's campanile reveals ! true size ( ! t[] z no?+ else c\ld1 because x is s evid5tly relat$ to ! human figure & n to ! great w9d[s high] up 9 ! %aft4 ,illu/ration #di3 ,,! ,,m$i,,val ,,me?od ,,( ,,draw+ ,,! ,,figure ,! geometrical plane figures :i* play ! mo/ important "p 9 ar*itectural proportion are ! squ>e1 ! circle & ! triangle2 & ! human figure is intimately relat$ to ^! elem5t>y =ms4 ,if a man /& ) heels toge!r1 & arms out/ret*$ horizontally 9 opposite directions1 he w be inscrib$1 z x 71 )9 a squ>e2 & 8 arms w m>k1 ) fair accuracy1 ! base ( an inv]t$ equilat]al triangle1 ! apex ( :i* w t\* ! gr\nd at 8 feet4 ,if ! arms be ext5d$ upw>d at an angle1 & ! legs correspond+ly sep>at$1 ! extremities w t\* ! circumf]5ces ( a circle hav+ its c5t] 9 ! navel 7,illu/rations #de1 #df74 ,illu/ration #ej ,! figure has be5 v>i\sly analyz$ ) a view to e/abli%+ num]ical ratios betwe5 its p>ts 7,illu/rations #dg1 #dh1 #di74 ,"s ( ^! are s simple & easily rememb]$ t !y h obta9$ a c]ta9 popul> curr5cy2 su* z t ! l5g? ( ! h& equals ! l5g? ( ! face2 t ! span ( ! horizontally ext5d$ arms equals ! height2 & ! well kn[n rule t twice ar\nd ! wri/ is once ar\nd ! neck1 & twice ar\nd ! neck is once ar\nd ! wai/4 ,! ,roman ar*itect ,vitruvius1 writ+ 9 ! age ( ,augu/us ,cs>1 =mulat$ ! important proportions ( ! /atues ( classical antiquity1 & except t he makes ! head small] ?an ! normal 7z x %\ld be 9 h]oic /atu>y71 ! ratios :i* he gives are ^? to :i* ! ideally p]fect male figure %\ld con=m4 ,among ! anci5ts ! foot 0 probably ! /&>d ( all l>ge measurem5ts1 be+ a m det]m9ate l5g? ?an t ( ! head or face1 & ! height 0 six l5g?s ( ! foot4 ,if ! head be tak5 z a unit1 ! ratio becomes #a3h1 & if ! face--#a3aj4 ,doctor ,rimm]1 9 8 ,art ,anatomy1 divides ! figure into f\r p>ts1 ?ree ( :i* are equal1 & correspond to ! l5g?s ( ! leg1 ! ?igh & ! trunk2 :ile ! f\r? "p1 :i* is two-?irds ( "o ( ^! ?irds1 ext5ds f ! /]num to ! cr[n ( ! head4 ,"o excell5ce ( su* a division aside f its simplicity1 consi/s 9 ! fact t x may be appli$ to ! face z well4 ,! l[e/ ( ! ?ree major divisions ext5ds f ! tip ( ! *9 to ! base ( ! nose1 ! next co9cides ) ! height ( ! nose 7its top be+ level ) ! eyebr[s71 & ! la/ ) ! height ( ! =ehead1 :ile ! rema9+ two-?irds ( "o ( ^! ?irds repres5ts ! horizontal projection f ! beg9n+ ( ! hair on ! =ehead to ! cr[n ( ! head4 ,! middle ( ! ?ree l>g] divisions locates ! e>s1 :i* are ! same height z ! nose 7,illu/rations #de1 #dg74 ,su* analyses ( ! figure1 h[ev] conduct$1 reveals an all-p]vasive h>mony ( p>ts1 betwe5 :i* def9ite num]ical relations are traceable1 & an appreh5sion ( ^! %\ld assi/ ! ar*itectural design] to arrive at beauty ( proportion by me?ods ( 8 own1 n p]haps 9 ! %ape ( rigid =mul1 b pres5t 9 ! consci\sness z a re/ra9+ influ5ce1 act+ & react+ ^u ! m9d ) a consci\s int5tion t[>d rhy?m & h>mony4 ,by means ( su* ex]cises1 he w approa* ne>] to an und]/&+ ( t great my/]y1 ! beauty & significance ( numb]s1 ( :i* my/]y music1 ar*itecture1 & ! human figure are equally pres5tm5ts--consid]$1 t is1 f ! /&po9t ( ! occulti/4 ,v ,,lat5t ,,geometry ,illu/ration #ea3 ,,! ,,hexagram ,,& ,,equilat]al ,,triangle ,,9 ,,nature ,x is a well kn[n fact t 9 ! microscopically m9ute ( nature1 units ev]y:]e t5d to arrange !mselves ) relation to c]ta9 simple geometrical solids1 among :i* are ! tetrah$ron1 ! cube1 & ! sph]e4 ,?is process gives rise to h>mony1 :i* may be def9$ z ! relation betwe5 p>ts & unity1 ! simplicity lat5t 9 ! inf9itely complex1 ! pot5tial complexity ( t :i* is simple4 ,proce$+ to ?+s visible & tangible1 ?is indwell+ h>mony1 rhy?m1 proportion1 :i* has its basis 9 geometry & numb]1 is se5 to exi/ 9 cry/als1 fl[] =ms1 leaf gr\ps1 & ! l1 :]e x is obvi\s2 & 9 ! m highly organiz$ _w ( ! animal k+dom also2 ?\gh "h ! geometry is lat5t r ?an pat5t1 elud+ ?\gh n q defy+ analysis1 & ?us augm5t+ beauty1 :i* l a woman is allur+ 9 proportion z %e eludes 7,illu/rations #ea1 #eb1 #ec74 ,illu/ration #eb3 ,,proportions ,,( ,,! ,,horse ,illu/ration #ec ,by ! true arti/1 9 ! cry/al mirror ( ^: m9d ! univ]sal h>mony is focus$ & reflect$1 ?is secret ( ! cause & s\rce ( rhy?m--t x dwells 9 a correlation ( p>ts bas$ on an ultimate simplicity--is in/9ctively appreh5d$4 ,a k ( x =m$ "p ( ! equipm5t ( ! pa9t]s :o made glori\s ! gold5 noon ( pictorial art 9 ,italy dur+ ! ,r5aissance4 ,! problem :i* preoccupi$ !m 01 z ,symonds says ( ,leon>do1 to submit ! free/ play ( =m to simple figures ( geometry 9 gr\p+4 ,alb]ti held t ! pa9t] %\ld above all ?+s h ma/]$ geometry1 & x is kn[n t ! /udy ( p]spective & k9dr$ subjects 0 widespread & popul>4 ,illu/ration #ed ,! fir/ pa9t] :o delib]ately r ?an in/9ctively bas$ 8 compositions on geometrical pr9ciples seems to h be5 ,fra ,b>tolommeo1 9 8 ,la/ ,judgm5t1 9 ! *ur* ( ,/4 ,m>ia ,nuova1 9 ,flor5ce4 ,symonds says ( ?is picture1 ,simple figures--! pyramid & triangle1 upright1 inv]t$1 & int]wov5 l ! rhymes ( a sonnet--=m ! basis ( ! composition4 ,?is sy/em 0 adh]$ to by ! ,fratre 9 all 8 subsequ5t works 7,illu/ration #ed74 ,raphael1 ) t p[] ( assimilation :i* di/+ui%es him among m5 ( g5ius1 le>n$ f ,fra ,b>tolommeo ?is me?od ( dispos+ figures & comb9+ !m 9 masses ) almo/ ma!matical precision4 ,x w\ld h be5 inde$ surpris+ if ,leon>do da ,v9ci1 9 :om ! arti/ & ! man ( sci5ce 7 s wond]fully unit$1 _h n be5 greatly preoccupi$ ) ! ma!matics ( ! art ( pa9t+4 ,8 ,madonna ( ! ,rocks1 & ,virg9 on ! ,lap ( ,sa9t ,anne1 9 ! ,l\vre1 exhibit ! v p]fection ( pyramidal composition4 ,x is h[ev] 9 8 ma/]piece1 ,! ,la/ ,supp]1 t he comb9es geometrical symmetry & precision ) p]fect naturalness & fre$om 9 ! gr\p+ ( individually int]e/+ & dramatic figures4 ,mi*ael ,angelo1 ,&rea del ,s>to1 & ! great ,v5etians1 9 ^: "w ! art ( pa9t+ may be said to h culm9at$1 recogniz$ & obey$ ^? ma!matical laws ( composition kn[n to _! imm$iate pr$ecessors1 & ! decad5ce ( ! art 9 ! ensu+ p]iod may be trac$ n alone to ! false s5tim5t & affectation ( ! times1 b also 9 ! ab&onm5t by ! arti/s ( ^? obscurely geometrical arrangem5ts & gr\p+s :i* 9 ! works ( ! greate/ ma/]s s satisfy ! eye & haunt ! memory ( ! behold] 7,illu/rations #ee1 #ef74 ,illu/ration #ee3 ,,! ,,employm5t ,,( ,,! ,,equilat]al ,,triangle ,,9 ,,r5aissance ,,pa9t+ ,illu/ration #ef3 ,,geometrical ,,basis ,,( ,,! ,,si/9e ,,ceil+ ,,pa9t+s ,illu/ration #eg3 ,,assyrian2 ,,greek ,illu/ration #eh3 ,,! ,,geometrical ,,basis ,,( ,,! ,,plan ,,9 ,,ar*itectural ,,design ,illu/ration #ei ,sculpture1 ev5 m ?an pa9t+1 is bas$ on geometry4 ,! colossi ( ,egypt1 ! bas-reliefs ( ,assyria1 ! figur$ p$im5ts & metopes ( ! temples ( ,greece1 ! c>v$ tombs ( ,rev5na1 ! ,della ,robbia lunettes1 ! sculptur$ tympani ( ,go?ic *ur* portals1 all alike l5d !mselves 9 great] or less degree to a geometrical synopsis 7,illu/ration #eg74 ,:5ev] sculpture suff]$ divorce f ar*itecture ! geometrical elem5t became less prom95t1 d\btless because ( all ! arts ar*itecture is ! mo/ cle>ly & closely relat$ to geometry4 ,inde$1 x may be said t ar*itecture is geometry made visible1 9 ! same s5se t music is numb] made audible4 ,a build+ is an aggregation ( ! commone/ geometrical =ms3 p>allelograms1 prisms1 pyramids & cones--! cyl9d] appe>+ 9 ! column1 & ! hemisph]e 9 ! dome4 ,! plans likewise ( ! _w's fam\s build+s r$uc$ to _! simple/ expression are discov]$ to resolve !mselves into a few simple geometrical figures4 7,illu/ration #eh74 ,?is is ! b$ rock ( all excell5t design4 ,illu/ration #fj3 ,,egyptian2 ,,greek2 ,,roman2 ,,m$i,,val ,illu/ration #fa3 ,,jeff]son',s ,,p5 ,,sket* ,,= ,,! ,,rotunda ,,( ,,! ,,univ]sity ,,( ,,virg9ia ,illu/ration #fb3 ,,application ,,( ,,! ,,equilat]al ,,triangle ,,to ,,! ,,ere*!um ,,at ,,a!ns ,illu/ration #fc ,illu/ration #fd3 ,,! ,,equilat]al ,,triangle ,,9 ,,roman ,,ar*itecture ,b ar*itecture is geometrical 9 ano!r & a high] s5se ?an ?is4 ,em]son says3 ,! pleasure a palace or a temple gives ! eye is t an ord] & a me?od has be5 communicat$ to /ones1 s t !y speak & geometrize1 become t5d] or sublime ) expression4 ,all truly great & beautiful works ( ar*itecture f ! ,egyptian pyramids to ! ca!drals ( ,ile-de-,france--are h>moni\sly proportion$1 _! pr9cipal & subsidi>y masses be+ relat$1 sometimes obvi\sly1 m (t5 obscurely1 to c]ta9 symmetrical figures ( geometry1 :i* ?\gh invisible to ! sight & n consci\sly pres5t 9 ! m9d ( ! behold]1 yet p]=m ! important function ( cord9at+ ! entire fabric into "o easily rememb]$ :ole4 ,^u "s su* pr9ciple is surely f\nd$ :at ,symonds calls t sev]e & l(ty art ( composition :i* seeks ! highe/ beauty ( design 9 ar*itectural h>mony supreme1 above ! melodies ( gracefulness ( detail4 ,illu/ration #fe3 ,,! ,,equilat]al ,,triangle ,,9 ,,italian ,,ar*itecture ,illu/ration #ff3 ,,! ,,hexagram ,,9 ,,go?ic ,,ar*itecture ,!re is abundant evid5ce 9 support ( ! !ory t ! build]s ( antiquity1 ! masonic guilds ( ! ,middle ,ages1 & ! ar*itects ( ! ,italian ,r5aissance1 knew & foll[$ c]ta9 rules1 b ?\gh ?is !ory be d5i$ or ev5 disprov$--if aft] all ^! m5 obta9$ _! results unconsci\sly--_! creations s l5d !mselves to a geometrical analysis t ! claim = ! exi/5ce ( c]ta9 canons ( proportion1 bas$ on geometry1 rema9s unimpea*$4 ,illu/ration #fg ,illu/ration #fh ,! plane figures pr9cipally employ$ 9 det]m9+ ar*itectural proportion are ! circle1 ! equilat]al triangle1 & ! squ>e--:i* also yields ! "r angl$ isosceles triangle4 ,x w be not$ t ^! are ! two dim5sional correlatives ( ! sph]e1 ! tetrah$ron & ! cube1 m5tion$ z be+ among ! det]m9+ =ms 9 molecul> /ructure4 ,! "q naturally arises1 :y ! circle1 ! equilat]al triangle & ! squ>e8 ,because1 aside f ! fact t !y are ( all plane figures ! mo/ elem5t>y1 !y are intimately relat$ to ! body ( man1 z has be5 %[n 7,illu/ration #de71 & ! body ( man is z x 7 ! ar*itectural ar*etype4 ,b ?is simply removes ! inquiry to a diff]5t field1 x is n an answ]4 ,:y is ! body ( man s con/ruct$ & relat$8 ,?is leads u1 z does e "q1 to ! ?re%old ( a my/]y ^u :i* !osophy alone is able to ?r[ light4 ,any ext5d$ elucidation w\ld be out ( place "h3 x is suffici5t to rem9d ! read] t ! circle is ! symbol ( ! univ]se2 ! equilat]al triangle1 ( ! high] tr9ity 7atma1 buddhi1 manas72 & ! squ>e1 ( ! l[] quat]n>y ( man's sev5fold nature4 ,illu/ration #fi ,illu/ration #gj ,! squ>e is pr9cipally us$ 9 prelim9>y plott+3 x is ! det]m9+ figure 9 _m ( ! palaces ( ! ,italian ,r5aissance2 ! ,arc de ,triomphe1 9 ,p>is is a mod]n example ( its use 7,illu/rations #ei1 #fj74 ,! circle is (t5 employ$ 9 conjunction ) ! squ>e & ! triangle4 ,9 ,?omas ,jeff]son's ,rotunda = ! ,univ]sity ( ,virg9ia1 a s+le great circle 0 ! det]m9+ figure1 z 8 orig9al p5 sket* ( ! build+ %[s 7,illu/ration #fa74 ,"s ( ! be/ ,roman triumphal ar*es submit !mselves to a circul> synopsis1 & a sy/em ( d\ble int]sect+ circles has be5 appli$1 ) int]e/+ results1 to faades z widely diff]5t z ^? ( ! ,p>!non & ! ,f>nese ,palace 9 ,rome1 ?\gh x w\ld be fatu\s to claim t ^! figures det]m9$ ! proportions ( ! faades4 ,by f> ! mo/ important figure 9 ar*itectural proportion1 consid]$ f ! /&po9t ( geometry1 is ! equilat]al triangle4 ,x w\ld seem t ! eye has an especial fondness = ?is figure1 j z ! e> has = c]ta9 relat$ s\nds4 ,inde$ x might n be too fanciful to ass]t t ! common *ord ( any key 7! tonic ) its ?ird & fif?7 is ! musical equival5t ( ! equilat]al triangle4 ,x is sc>cely necess>y to dwell ^u ! prop]ties & unique p]fection ( ?is figure4 ,( all regul> polygons x is ! simple/3 its ?ree equal sides subt5d equal angles1 ea* ( #fj degrees2 x trisects ! circumf]5ce ( a circle2 x is ! graphic symbol ( ! numb] ?ree1 & h5ce ( e ?reefold ?+2 d\bl$1 its g5]at+ arcs =m ! vesica piscis1 ( s frequ5t occurr5ce 9 e>ly ,*ri/ian art2 two symmetrically int]sect+ equilat]al triangles yield ! figure kn[n z ,solomon's ,seal1 or ! ,%ield ( ,david1 to :i* my/ic prop]ties h always be5 ascrib$4 ,x may be /at$ z a g5]al rule t :5ev] ?ree important po9ts 9 any ar*itectural composition co9cide 7approximately or exactly7 ) ! ?ree extremities ( an equilat]al triangle1 x makes = beauty ( proportion4 ,an anci5t & notable example occurs 9 ! pyramids ( ,egypt1 ! sides ( :i*1 9 _! orig9al condition1 are believ$ to h be5 equilat]al triangles4 ,x is a demon/rable fact t c]ta9 geometrical int]sections yield ! important proportions ( ,greek ar*itecture4 ,! p]fect little ,ere*!um w\ld seem to h be5 proportion$ by means ( ! equilat]al triangle & ! angle ( #fj degrees1 bo? 9 g5]al & 9 detail 7,illu/ration #fb74 ,! same angle1 erect$ f ! c5tral axis ( a column at ! po9t :]e x int]sects ! ar*itrave1 det]m9es bo? ! projection ( ! cornice & ! height ( ! ar*itrave 9 _m ( ! f9e/ ,greek & ,roman temples 7,illu/rations #fg-gj74 ,! equilat]al triangle us$ 9 conjunction ) ! circle & ! squ>e 0 employ$ by ! ,romans 9 det]m9+ ! proportions ( triumphal ar*es1 basilicas & ba?s4 ,t ! same figure 0 a factor 9 ! design+ ( ,go?ic ca!drals is suffici5tly indicat$ 9 ! accompany+ facsimile reproductions ( an illu/ration f ! ,como ,vitruvius1 publi%$ 9 ,milan 9 #aeba1 :i* %[s a v]tical section ( ! ,milan ca!dral & ! sy/em ( equilat]al triangles :i* det]m9$ its v>i\s p>ts 7,illu/ration #ga74 ,! vesica piscis 0 (t5 us$ to e/abli% ! two ma9 int]nal dim5sions ( ! ca!dral plan3 ! greate/ diamet] ( ! figure correspond+ ) ! wid? across ! transepts1 ! upp] apex m>k+ ! limit ( ! apse1 & ! l[]1 ! t]m9ation ( ! nave4 ,su* a proportion is se5 to be bo? subtle & simple1 & possesses ! advantage ( be+ easily laid out4 ,! ar*itects ( ! ,italian ,r5aissance d\btless inh]it$ c]ta9 ( ! ,roman canons ( ar*itectural proportion1 = !y seem v g5]ally to h recogniz$ !m z an ess5tial pr9ciple ( design4 ,illu/ration #ga ,nev]!less1 :5 all is said1 x is easy to exagg]ate ! importance ( ?is matt] ( geometrical proportion4 ,! design] :o seeks ! ultimate secret ( ar*itectural h>mony 9 ma!matics r ?an 9 ! tra9$ eye1 is foll[+ ! wrong road to success4 ,a happy inspiration is wor? all ! =mul 9 ! _w--if x be really happy1 ! arti/ w probably f9d t he has foll[$ ! rules )\t kn[+ !m4 ,ev5 :ile =mulat+ concepts ( art1 ! au?or mu/ reit]ate ,s*op5hau]'s dictum t ! concept is unfruitful 9 art4 ,! ma!matical analysis ( spatial beauty is an int]e/+ /udy1 & a useful "o to ! arti/2 b x c nev] take ! place ( ! creative faculty1 x c only supplem5t1 re/ra91 direct x4 ,! /udy ( proportion is to ! ar*itect :at ! /udy ( h>mony is to a musician--x helps 8 g5ius adequately to express itself4 ,,vi ,,! ,,ari?metic ,,( ,,beauty ,al?\gh ar*itecture is bas$ prim>ily ^u geometry1 x is possible to express all spatial relations num]ically3 = ari?metic1 n geometry1 is ! univ]sal sci5ce ( quantity4 ,! relation ( masses "o to ano!r--( voids to solids1 & ( heights & l5g?s to wid?s--=ms ratios2 & :5 su* ratios are simple & h>moni\s1 ar*itecture may be said1 9 ,walt] ,pat]'s fam\s phrase1 to aspire t[>ds ! condition ( music4 ,! tra9$ eye1 & n an ari?metical =mula1 det]m9es :at is1 & :at is n1 beautiful proportion4 ,nev]!less ! fact t ! eye in/9ctively rejects c]ta9 proportions z unpleas+1 & accepts o!rs z satisfactory1 is an indication ( ! exi/5ce ( laws ( space1 bas$ ^u numb]1 n unlike ^? :i* gov]n musical h>mony4 ,! secret ( ! deep reasonabl5ess ( su* selection by ! s5ses lies hidd5 9 ! v nature ( numb] itself1 = numb] is ! invisible ?read on :i* ! worlds are /rung--! univ]se ab/ractly symboliz$4 ,numb] is ! )9 ( all ?+s--! fir/ =m ( ,brahman4 ,x is ! measure ( "t & space2 x lurks 9 ! he>t-beat & is blazon$ ^u ! />r$ canopy ( night4 ,sub/ance1 9 a /ate ( vibration1 9 o!r words condition$ by numb]1 ceaselessly und]goes ! myriad transmutations :i* produce ph5om5al life4 ,elem5ts sep>ate & comb9e *emically accord+ to num]ical ratios3 ,moon1 plant1 gas1 cry/al1 are concrete geometry & numb]4 ,by ! ,py?agoreans & by ! anci5t ,egyptians sex 0 attribut$ to numb]s1 odd numb]s be+ conceiv$ ( z mascul9e or g5]at+1 & ev5 numb]s z fem99e or p>turitive1 on acc\nt ( _! inf9ite divisibility4 ,h>moni\s comb9ations 7 ^? involv+ ! m>riage ( a mascul9e & a fem99e--an odd & an ev5--numb]4 ,illu/ration #gb3 ,a ,,graphic ,,sy/em ,,( ,,notation ,numb]s progress f unity to inf9ity1 & return aga9 to unity z ! s\l1 def9$ by ,py?agoras z a self-mov+ numb]1 goes =? f1 & returns to ,god4 ,^! two acts1 "o ( projection & ! o!r ( recall2 ^! two =ces1 c5trifugal & c5tripetal1 are symboliz$ 9 ! op]ations ( addition & subtraction4 ,)9 !m is embrac$ ! :ole ( computation2 b because e numb]1 e aggregation ( units1 is also a new unit capable ( be+ add$ or subtract$1 !re are also ! op]ations ( multiplication & division1 :i* consi/s 9 "o case ( ! addition ( sev]al equal numb]s toge!r1 & 9 ! o!r1 ( ! subtraction ( sev]al equal numb]s f a great] until t is exhau/$4 ,9 ord] to ?9k correctly x is necess>y to consid] ! :ole ( num]ation1 computation1 & all ma!matical processes :atsoev] z ! division ( ! unit into its compon5t p>ts & ! e/abli%m5t ( relations betwe5 ^! p>ts4 ,illu/ration #gc ,illu/ration #gd ,! progression & retrogression ( numb]s 9 gr\ps express$ by ! multiplication table gives rise to :at may be t]m$ num]ical conjunctions4 ,^! are analog\s to a/ronomical conjunctions3 ! planets1 revolv+ ar\nd ! sun at diff]5t rates ( spe$1 & 9 widely sep>at$ orbits1 at c]ta9 times come into l9e ) "o ano!r & ) ! sun4 ,!y are !n said to be 9 conjunction4 ,simil>ly1 numb]s1 advanc+ t[>d inf9ity s+ly & 9 gr\ps 7express$ by ! multiplication table71 at c]ta9 /ages ( _! progression come into relation ) "o ano!r4 ,= example1 an important conjunction occurs 9 #ab1 = ( a s]ies ( twos x is ! six?1 ( ?rees ! f\r?1 ( f\rs ! ?ird1 & ( sixes ! second4 ,x /&s to #h 9 ! ratio ( #c3b1 & to #i1 ( #d3c4 ,x is relat$ to #g ?r\gh be+ ! product ( #c & #d1 ( :i* numb]s #g is ! sum4 ,! numb]s #aa & #ac are n conjunctive2 #ad is s 9 ! s]ies ( twos1 & sev5s2 #ae is s 9 ! s]ies ( fives & ?rees4 ,! next conjunction aft] #ab1 ( #c & #d & _! fir/ multiples1 is 9 #bd1 & ! next foll[+ is 9 #cf1 :i* numb]s are respectively ! two & ?ree ( a s]ies ( twelves1 ea* end be+ b a new beg9n+4 ,illu/ration #ge ,x w be se5 t ?is discov]y ( num]ical conjunctions consi/s m]ely ( resolv+ numb]s into _! prime factors1 & t a conjunctive numb] is a common multiple2 b by nam+ x s1 to dismiss ! entire subject z kn[n & exhau/$1 is to miss a s5se ( ! wond]1 beauty & rhy?m ( x all3 a m5tal impression analog\s to t made ^u ! eye by ! swift-glanc+ balls ( a juggl]1 ! evolutions ( drill+ troops1 or ! intricate figures ( a dance2 = ^! ?+s are numb] concrete & animate 9 "t & space4 ,illu/ration #gf ,! tru?s ( numb] are ( all tru?s ! mo/ int]ior1 ab/ract & difficult ( appreh5sion1 & s9ce k becomes cle> & def9ite to ! ext5t t x c be made to ent] ! m9d ?r\gh ! *annels ( physical s5se1 x is well to accu/om oneself to conceiv+ ( numb] graphically1 by means ( geometrical symbols 7,illu/ration #gb71 r ?an 9 t]ms ( ! famili> arabic notation :i* ?\gh admirable = purposes ( computation1 is ( too cond5s$ & arbitr>y a "* to reveal ! prop]ties ( individual numb]s4 ,to /ate1 = example1 t #d is ! fir/ squ>e1 & #h ! fir/ cube1 conveys b a vague idea to mo/ p]sons1 b if #d be repres5t$ z a squ>e enclos+ f\r small] squ>es1 & #h z a cube conta9+ eight small] cubes1 ! idea is appreh5d$ imm$iately & )\t ef=t4 ,! numb] #c is ( c\rse ! triangle2 ! irregul> & vital beauty ( ! numb] #e appe>s cle>ly 9 ! heptalpha1 or five-po9t$ />2 ! faultless symmetry ( #f1 its relation to #c & #b1 & its regul> division ( ! circle1 are portray$ 9 ! famili> hexagram kn[n z ! ,%ield ( ,david4 ,sev51 :5 repres5t$ z a compact gr\p ( circles reveals itself z a numb] ( s+ul> beauty & p]fection1 wor?y ( ! important place accord$ to x 9 all my/ical philosophy 7,illu/ration #gc74 ,x is a curi\s fact t :5 ask$ to ?9k ( any numb] less ?an #aj1 mo/ p]sons w *oose #g4 ,illu/ration #gg ,e =m ( art1 ?\gh prim>ily a vehicle = ! expression & transmission ( p>ticul> ideas & emotions1 has subsidi>y (fices1 j z a musical tone has h>monics :i* r5d] x m sweet4 ,pa9t+ reveals ! nature ( color2 music1 ( s\nd--9 wood1 9 brass1 & 9 /ret*$ /r+s2 ar*itecture %[s =? ! qualities ( light1 & ! /r5g? & beauty ( mat]ials4 ,all ( ! arts1 & p>ticul>ly music & ar*itecture1 portray 9 diff]5t mann]s & degrees ! tru?s ( numb]4 ,ar*itecture does ?is 9 two ways3 esot]ically z x 7 9 ! =m ( h>monic proportions2 & exot]ically 9 ! =m ( symbols :i* repres5t numb]s & gr\ps ( numb]s4 ,! fact t a s]ies ( ?rees & a s]ies ( f\rs mutually conjo9 9 #ab1 f9ds an ar*itectural expression 9 ! ,tuscan1 ! ,doric1 & ! ,ionic ord]s accord+ to ,vignole1 = 9 !m all ! /ylobate is f\r p>ts1 ! entablature #c1 & ! int]m$iate column #ab 7,illu/ration #gd74 ,! aff9ity betwe5 #d & #g1 reveal$ 9 ! fact t !y express 7v ne>ly7 ! ratio betwe5 ! base & ! altitude ( ! "r-angl$ triangle :i* =ms half ( an equilat]al1 & ! musical int]val ( ! dim9i%$ sev5?1 is ar*itecturally sugge/$ 9 ! ,palazzo ,giraud1 :i* is f\r /ories 9 height ) sev5 op5+s 9 ea* /ory 7,illu/ration #ge74 ,illu/ration #gh ,illu/ration #gi ,illu/ration #hj ,illu/ration #ha ,e build+ is a symbol ( "s numb] or gr\p ( numb]s1 & o!r ?+s be+ equal ! m p]fect ! numb]s involv$ ! m beautiful w be ! build+ 7,illu/rations #gf-hb74 ,! numb]s #e & #g--^? :i* occur (t5e/--are ! mo/ satisfactory because be+ ( small quantity1 !y are easily grasp$ by ! eye1 & be+ odd1 !y yield a c5t] or axis1 s necess>y 9 e ar*itectural composition4 ,next 9 value are ! l[e/ multiples ( ^! numb]s & ! lea/ common multiples ( any two ( !m1 because ! eye1 ) a little assi/ance1 is able to resolve !m into _! con/itu5t factors4 ,x is "p ( ! art ( ar*itecture to r5d] su* assi/ance1 = ! eye c\nts always1 consci\sly or unconsci\sly1 & :5 x is confront$ ) a numb] ( units great] ?an x c readily resolve1 x is refre%$ & re/$ if ^! units are s gr\p$ & arrang$ t !y reveal !mselves z factors ( "s high] quantity4 ,illu/ration #hb ,illu/ration #hc3 ,a ,,num]ical ,,analysis ,,( ,,go?ic ,,trac]y ,!re is a raison d'tre = /r+ c\rses o!r ?an to m>k ! position ( a floor on ! int]ior ( a build+1 & = quo9s & pila/]s o!r ?an to indicate ! pres5ce ( a transv]se wall4 ,^! sometimes s]ve ! useful purpose ( s subdivid+ a faade t ! eye e/imates ! numb] ( its op5+s )\t consci\s ef=t & consequ5t fatigue 7,illu/ration #hb74 ,! trac]y ( ,go?ic w9d[s =ms p]haps ! highe/ & f9e/ ar*itectural expression ( numb] 7,illu/ration #hc74 ,j z ?ir/ makes wat] m sweet1 s does ,go?ic trac]y confuse ! eye ) its complexity only ! m greatly to gratify ! sight by reveal+ ! inh]5t simplicity 9 :i* ?is complexity has its root4 ,sometimes1 z 9 ! case ( ! ,v5etian ,ducal ,palace1 ! numb]s involv$ are too great = c\nt+1 b o!r & diff]5t ari?metical tru?s are portray$2 = example1 ! multiplication ( ! fir/ arcade by #b 9 ! second1 & ?is by #c 9 ! cusp$ ar*es1 & by #d 9 ! quatrefoils imm$iately above4 ,illu/ration #hd3 ,,num]ation ,,9 ,,gr\ps ,,express$ ,,ar*itecturally ,illu/ration #he3 ,,ar*itectural ,,ornam5t ,,consid]$ ,,z ,,! ,,objectification ,,( ,,numb]4 ,,multiplication ,,9 ,,gr\ps ,,( ,,five2 ,,two2 ,,?ree2 ,,alt]nation ,,( ,,?ree ,,& ,,sev5 ,illu/ration #hf ,sev5 is prov]bially ! p]fect numb]4 ,x is ( a quantity suffici5tly complex to /imulate ! eye to resolve x1 & yet s simple t x c be analyz$ at a glance2 z a c5t] ) two equal sides1 x is possess$ ( symmetry1 & z ! sum ( an odd & ev5 numb] 7#c & #d7 x has vitality & v>iety4 ,all ^! prop]ties a "w ( ar*itecture c v>i\sly reveal 7,illu/ration #gg74 ,fifte51 also1 is a numb] ( great p]fection4 ,x is possible to arrange ! fir/ #i numb]s 9 ! =m ( a magic squ>e s t ! sum ( ea* l9e1 read v]tically1 horizontally or diagonally1 w be #ae4 ,?us3 #d #i #b #ae #c #e #g #ae #h #a #f #ae -- -- -- #ae #ae #ae ,its beauty is portray$ geometrically 9 ! accompany+ figure :i* expresses x1 be+ #ae triangles 9 ?ree gr\ps ( #e 7,illu/ration #hf74 ,few arrangem5ts ( op5+s 9 a faade bett] satisfy ! eye ?an ?ree sup]impos$ gr\ps ( five 7,illu/rations #gf-hj74 ,may n "o s\rce ( ?is satisfaction dwell 9 ! intr9sic beauty ( ! numb] #ae8 ,9 conclusion1 x is p]haps well t ! read] be aga9 rem9d$ t ^! are ! by-ways1 & n ! highways ( ar*itecture3 t ! highe/ beauty comes always1 n f beautiful numb]s1 nor f lik5esses to ,nature's et]nal patt]ns ( ! _w1 b f utility1 fitness1 economy1 & ! p]fect adaptation ( means to ends4 ,b along ) ?is tru? !re goes ano!r3 t 9 e excell5t "w ( ar*itecture1 9 addition to its obvi\s & individual beauty1 !re dwells an esot]ic & univ]sal beauty1 foll[+ z x does ! ar*etypal patt]n laid d[n by ! ,great ,ar*itect = ! build+ ( t temple :i* is ! _w :]e9 we dwell4 ,,vii ,,froz5 ,,music ,9 ! s]ies ( essays ( :i* ?is is ! f9al "o1 ! au?or has und]tak5 to en=ce ! tru? t evolution on any plane & on any scale proce$s accord+ to c]ta9 laws :i* are 9 reality only ramifications ( "o ubiquit\s & ev] op]ative law2 t ?is law regi/]s itself 9 ! ?+ evolv$1 leav+ /amp$ !reon z x 7 fossil footpr9ts by means ( :i* x may be kn[n4 ,9 ! arts ! creative _s ( man is at its free/ & f9e/1 & n[h]e among ! arts is x s free & s f9e z 9 music4 ,9 music accord+ly ! univ]sal law ( becom+ f9ds in/ant1 direct & p]fect self-expression2 music voices ! inn] nature ( ! w-to-live 9 all its moods & mom5ts2 9 x =m1 cont5t1 means & end are p]fectly fus$4 ,x is ?is fact :i* gives validity to ! be=e quot$ say+ t all ( ! arts aspire t[>d ! condition ( music4 ,all aspire to express ! law1 b music1 be+ lea/ encumb]$ by ! lead5 burd5 ( mat]iality1 expresses x mo/ easily & adequately4 ,?is be+ s !re is no?+ unreasonable 9 attempt+ to apply ! kn[n facts ( musical h>mony & rhy?m to any o!r art1 & s9ce ^! essays conc]n !mselves prim>ily ) ar*itecture1 ! f9al aspect 9 :i* t art w be pres5t$ "h is z froz5 music--pond]able =m gov]n$ by musical law4 ,music dep5ds prim>ily ^u ! equal & regul> division ( "t into beats1 & ( ^! beats into measures4 ,ov] ?is s\ndless & invisible w>p is wov5 an inf9itely v>i\s melodic patt]n1 made up ( tones ( diff]5t pit* & duration ari?metically relat$ & comb9$ accord+ to ! laws ( h>mony4 ,ar*itecture1 correspond+ly1 implies ! rhy?mical division ( space1 & ob$i5ce to laws num]ical & geometrical4 ,a c]ta9 id5tity !re=e exi/s betwe5 simple h>mony 9 music1 & simple proportion 9 ar*itecture4 ,by translat+ ! consonant tone-int]vals into numb]1 ! common d5om9ator1 z x 71 ( bo? arts1 x is possible to give ^! int]vals a spatial1 & h5ce an ar*itectural1 expression4 ,su* expression1 consid]$ z proportion only & divorc$ f ornam5t1 w prove pleas+ to ! eye 9 ! same way t its correlative is pleas+ to ! e>1 because 9 ei!r case x is n alone ! special organ ( s5se :i* is gratifi$1 b ! inn] ,self1 9 :i* all s5ses are "o4 ,conta9+ )9 itself ! my/]y ( numb]1 x ?rills responsive to e audible or visible pres5tm5t ( t my/]y4 ,illu/ration #hg ,if a vibrat+ /r+ yield+ a c]ta9 musical note be /opp$ 9 its c5t]1 t is1 divid$ by half1 x w !n s\nd ! octave ( t note4 ,! num]ical ratio :i* expresses ! int]val ( ! octave is !re=e #a3b4 ,if "o-?ird in/ead ( "o-half ( ! /r+ be /opp$1 & ! rema9+ two-?irds /ruck1 x w yield ! musical fif? ( ! orig9al note1 :i* ?us corresponds to ! ratio #b3c4 ,! l5g? repres5t$ by #c3d yields ! f\r?2 #d3e ! major ?ird2 & #e3f ! m9or ?ird4 ,^! comprise ! pr9cipal consonant int]vals )9 ! range ( "o octave4 ,! ratios ( inv]t$ int]vals1 s call$1 are f\nd by d\bl+ ! small] numb] ( ! orig9al int]val z giv5 above3 #b3c1 ! fif?1 gives #c3d1 ! f\r?2 #d3e1 ! major ?ird1 gives #e3h1 ! m9or six?2 #e3f1 ! m9or ?ird1 gives #f3aj1 or #c3e1 ! major six?4 ,illu/ration #hh3 ,,ar*itecture ,,z ,,h>mony ,( ^! v>i\s consonant int]vals ! octave1 fif?1 & major ?ird are ! mo/ important1 9 ! s5se ( be+ ! mo/ p]fect1 & !y are express$ by numb]s ( ! smalle/ quantity1 an odd numb] & an ev54 ,x w be not$ t all ! int]vals above giv5 are express$ by ! numb]s #a1 #b1 #c1 #d1 #e & #f1 except ! m9or six? 7#e3h71 & ?is is ! mo/ imp]fect ( all consonant int]vals4 ,! sub-m9or sev5?1 express$ by ! ratio #d3g ?\gh includ$ among ! dissonances1 =ms1 accord+ to ,helmholtz1 a m p]fect consonance ) ! tonic ?an does ! m9or six?4 ,a natural d$uction f ^! facts is t relations ( ar*itectural l5g? & bread?1 height & wid?1 to be musical %\ld be capable ( be+ express$ by ratios ( quantitively small numb]s1 pref]ably an odd numb] & an ev54 ,al?\gh g5]ally speak+ ! simpl] ! num]ical ratio ! m p]fect ! consonance1 yet ! int]vals ( ! fif? & major ?ird 7#b3c & #d3e71 are consid]$ to be m pleas+ ?an ! octave 7#a3b71 :i* is too obvi\sly a repetition ( ! orig9al note4 ,f ?is x is reasonable to assume 7& ! assumption is borne out by exp]i5ce71 t proportions1 ! num]ical ratios ( :i* ! eye resolves too readily1 become at la/ we>isome4 ,! relation %\ld be felt r ?an fa?om$4 ,!re %\ld be a p]ception ( id5tity1 & also ( diff]5ce4 ,z 9 music1 :]e dissonances are introduc$ to give value to consonances :i* foll[ !m1 s 9 ar*itecture simple ratios %\ld be employ$ 9 connection ) ^? m complex4 ,illu/ration #hi ,h>monics are ^? tones :i* s\nd )1 & re9=ce any musical note :5 x is s\nd$4 ,! di/+ui%able h>monics ( ! tonic yield ! ratios #a3b1 #b3c1 #c3d1 #d3e1 & #d3g4 ,a note & its h>monics =m a natural *ord4 ,!y may be comp>$ to ! wid5+ circles :i* appe> 9 /ill wat] :5 a /one is dropp$ into x1 = :5 a musical s\nd di/urbs ! quietude ( t pool ( sil5ce :i* we call ! air1 x ripples into ov]tones1 :i* becom+ fa9t] & fa9t]1 die away into sil5ce4 ,x w\ld seem reasonable to assume t ! comb9ation ( numb]s :i* express ^! ov]tones1 if translat$ into t]ms ( space1 w\ld yield proportions agreeable to ! eye1 & su* is ! fact1 z ! accompany+ examples suffici5tly indicate 7,illu/rations #hg-ij74 ,! int]val ( ! sub-m9or sev5? 7#d3g71 us$ 9 ?is way1 9 connection ) ! simpl] int]vals ( ! octave 7#a3b71 & ! fif? 7#b3c71 is p>ticul>ly pleas+ because x is nei!r too obvi\s nor too subtle4 ,?is ratio ( #d3g is important = ! reason t x expresses ! angle ( sixty degrees1 t is1 ! numb]s #d & #g repres5t 7v ne>ly7 ! ratio betwe5 "o-half ! base & ! altitude ( an equilat]al triangle3 also because !y =m "p ( ! num]ical s]ies #a1 #d1 #g1 #aj1 etc4 ,bo? are my/ic numb]s1 & 9 ,go?ic ar*itecture p>ticul>ly1 proportions 7 frequ5tly det]m9$ by numb]s to :i* a my/ic mean+ 0 atta*$4 ,accord+ to ,gwilt1 ! ,go?ic *apels ( ,w9dsor & ,ox=d are divid$ longitud9ally by f\r1 & transv]sely by sev5 equal p>ts4 ,! arcade above ! roses 9 ! faade ( ! ca!dral ( ,t\rs %[s sev5 pr9cipal units across ! front ( ! nave1 & f\r 9 ea* ( ! t[]s4 ,a di/+ui%+ *>act]i/ic ( ! s]ies ( ratios :i* repres5t ! consonant int]vals )9 ! compass ( an octave is t x advances by ! addition ( #a to bo? t]ms3 #a3b1 #b3c1 #c3d1 #d3e1 & #e3f4 ,su* a s]ies always approa*es unity1 j z1 repres5t$ graphically by means ( p>allelograms1 x t5ds t[>d a squ>e4 ,alb]ti 9 8 book pres5ts a design = a t[] %[+ 8 idea = its g5]al proportions4 ,x consi/s ( six /ories1 9 a sequ5ce ( ord]s4 ,! l[e/ /ory is a p]fect cube & ea* ( ! o!r /ories is #aa-ab?s ( ! /ory bel[1 dim9i%+ practically 9 ! proportion ( #h1 #g1 #f1 #e1 #d1 #c1 all[+ 9 ea* case = ! am\nt hidd5 by ! projection ( ! cornice bel[2 ea* ord] be+ accurate z reg>ds column1 entablature1 etc4 ,x is ( int]e/ to comp>e ?is ) ,rusk9's idea 9 8 ,sev5 ,lamps1 :]e he takes ! case ( a plant call$ ,alisma ,plantago1 9 :i* ! v>i\s bran*es dim9i% 9 ! proportion ( #g1 #f1 #e1 #d1 #c1 respectively1 & s c>ry out ! same idea2 on :i* ,rusk9 obs]ves t dim9ution 9 a build+ %\ld be aft] ! mann] ( ,nature4 ,illu/ration #ij3 ,,arcade ,,( ,,! ,,cancell]ia ,x w\ld be a pr(itless task to =mulate exact rules ( ar*itectural proportion bas$ ^u ! laws ( musical h>mony4 ,! two arts are too diff]5t f ea* o!r = t1 & moreov] ! la/ appeal mu/ always be to ! eye1 & n to a ma!matical =mula1 j z 9 music ! la/ appeal is to ! e>4 ,laws !re are1 b !y discov] !mselves to ! arti/ z he proce$s1 & are = ! mo/ "p incommunicable4 ,rules & =mul are useful & valuable n z a sub/itute = inspiration1 b z a guide3 n z w+s1 b z a tail4 ,9 ?is connection p]haps all t is necess>y = ! ar*itectural design] to be> 9 m9d is t important ratios ( l5g? & bread?1 height & wid?1 to be musical %\ld be express$ by quantitively small numb]s1 & t if possible !y %\ld obey "s simple law ( num]ical progression4 ,f ?is basic simplicity complexity w foll[1 b x w be an ord]$ & h>moni\s complexity1 l t ( a tree1 or ( a symphony4 ,illu/ration #ia3 ,,! ,,palazzo ,,v]zi ,,at ,,v]ona 7,,l[] ,,portion ,,only74 ,a ,,composition ,,f\nd$ ,,on ,,! ,,equal ,,& ,,regul> ,,division ,,( ,,space1 ,,z ,,music ,,is ,,f\nd$ ,,on ,,! ,,equal ,,& ,,regul> ,,division ,,( ,,"t4 ,illu/ration #ib3 ,,ar*itecture ,,z ,,rhy?m4 ,a ,,division ,,( ,,space ,,correspond+ ,,to #c_/d ,,& #d_/d ,,"t4 ,9 ! same way t a musical composition implies ! division ( "t into equal & regul> beats1 s a "w ( ar*itecture %\ld h = its basis "s unit ( space4 ,?is unit %\ld be n[h]e too obvi\s & may be v>i$ )9 c]ta9 limits1 j z musical "t is ret>d$ or accel]at$4 ,! und]ly+ rhy?m & symmetry w ?us give value & di/9ction to su* v>iation4 ,vas>i tells h[ ,brunelles*i4 ,bramante & ,leon>do da ,v9ci us$ to "w on pap] rul$ 9 squ>es1 describ+ x z a truly +5i\s ?+1 & ( great utility 9 ! "w ( design4 ,by ?is means !y develop$ proportions accord+ to a def9ite s*eme4 ,!y set to "w ) a division ( space analog\s to ! musician's division ( "t4 ,! examples giv5 h]e) indicate h[ close a p>allel may exi/ betwe5 music & ar*itecture 9 ?is matt] ( rhy?m 7,illu/rations #ia-ic74 ,illu/ration #ic ,x is a demon/rable fact t musical s\nds weave invisible patt]ns 9 ! air4 ,ar*itecture1 correspond+ly1 9 "o ( its aspects1 is geometric patt]n made fix$ & endur+4 ,:at c\ld be m ess5tially musical = example ?an ! sea arcade ( ! ,v5etian ,ducal ,palace8 ,! s& =ms trac$ by s\nd-waves on a musically vibrat+ /eel plate might easily sugge/ ar*itectural ornam5t did n ! diff]5ces ( scale & ( mat]ial t5d to confuse ! m9d4 ,! ar*itect %\ld occupy himself ) id5tities1 n diff]5ces4 ,if he w b be> 9 m9d t ar*itecture is patt]n 9 space1 j z music is patt]n 9 "t1 he w come to p]ceive ! ess5tial id5tity betwe51 say1 a ,greek rosette & a ,go?ic rose-w9d[2 an arcade & an egg & d>t m\ld+ 7,illu/ration #id74 ,all ar*itectural =ms & arrangem5ts :i* give endur+ pleasure are 9 _! ess5ce musical4 ,e well compos$ faade makes h>mony 9 ?ree dim5sions2 e good ro(-l9e s+s a melody aga9/ ! sky4 ,illu/ration #id3 ,,ar*itecture ,,z ,,patt]n ,,conclusion ,9 tak+ leave ( ! read] at ! end ( ?is excursion toge!r among ! by-ways ( a beautiful art1 ! au?or mu/ ne$s add a f9al ^w or two t\*+ ^u ! purpose & scope ( ^! essays4 ,ar*itecture 7l ev]y?+ else7 has two aspects3 x may be view$ f ! /&po9t ( utility1 t is1 z con/ruction2 or f ! /&po9t ( expressiv5ess1 t is1 z decoration4 ,no attempt has be5 made "h to deal ) its fir/ aspect1 & ( ! second 7:i* is aga9 tw(old71 only ! univ]sal1 n ! p>ticul> expressiv5ess has be5 s\ght4 ,! lit]ature ( ar*itecture is ri* 9 works deal+ ) ! utilit>ian & con/ructive side ( ! art3 inde$1 x may be said t to ?is side t lit]ature is almo/ exclusively devot$4 ,?is be+ s1 x has seem$ wor? :ile to attempt to %[ ! rev]se ( ! m$al1 ev5 ?\gh x be tails in/ead ( heads4 ,x w be not$ t ! inductive me?od has n1 9 ^! pages1 be5 honor$ by a due obs]vance4 ,x w\ld h be5 easy to h treat$ ! subject inductively1 amass+ facts & draw+ conclusions1 b to h done s ! au?or w\ld h be5 false to ! v pr9ciple ab\t :i* ! "w came into be+4 ,) ! acceptance ( ! ,anci5t ,wisdom1 ! inductive me?od becomes no long] necess>y4 ,facts are n useful 9 ord] to e/abli% a hypo!sis1 !y are us$ r to elucidate a kn[n & accept$ tru?4 ,:5 !osophical ideas %all h p]meat$ ! ?\ght ( mank9d1 ?is "w1 if x survives at all1 w be *iefly--p]haps solely--rem>kable by reason ( ! fact t x 0 among ! fir/ 9 :i* ! attempt 0 made aga9 to unify sci5ce1 art & religion1 z !y 7 unifi$ 9 ^? anci5t times & among ^? anci5t peoples :5 ! ,wisdom sway$ ! he>ts & m9ds ( m54