,,william ,,oughtr$ ,,william ,,oughtr$ ,a ,,great ,,sev5te5?-,,c5tury ,,tea*] ,,( ,,ma!matics ,,by ,,florian ,,cajori1 ,ph4,d4 ,pr(essor ( ,ma!matics ,colorado ,college ,,*icago ,,london ,,! ,,op5 ,,c\rt ,,publi%+ ,,company #aiaf ,copyright #aiaf ,by ,! ,op5 ,c\rt ,publi%+ ,co4 ,all ,rights ,res]v$ ,publi%$ ,septemb] #aiaf ,compos$ & ,pr9t$ ,by ,! ,univ]sity ( ,*icago ,press ,*icago1 ,ill9ois1 ,u4,s4,a4 ,,table ,,( ,,cont5ts ,,page ,introduction #a ,,*apt] ,i4 ,oughtr$'s ,life #c ,at ,s*ool & ,univ]sity #c ,z ,rector & ,amateur ,ma!matician #f ,8 ,wife #g ,9 ,dang] ( ,seque/ration #h ,8 ,tea*+ #i ,appe>ance & ,habits #ab ,alleg$ ,travel ,abroad #ad ,8 ,dea? #ae ,,ii4 ,pr9cipal ,works #ag ,clavis ma!maticae #ag ,circles ( ,proportion & ,trigonometrie #ce ,solution ( ,num]ical ,equations #ci ,log>i?ms #df ,inv5tion ( ! ,slide ,rule2 ,controv]sy on ,priority ( ,inv5tion #df ,,iii4 ,m9or ,works #ej ,,iv4 ,oughtr$'s ,influ5ce ^u ,ma!matical ,progress & ,tea*+ #eg ,oughtr$ & ,h>riot #eg ,oughtr$'s ,pupils #eh ,oughtr$1 ! 8,todhunt] ( ! ,sev5te5? ,c5tury0 #fj ,0 ,desc>tes ,indebt$ to ,oughtr$8 #fi ,! ,spread ( ,oughtr$'s ,notations #gc ,v4 ,oughtr$'s ,ideas on ! ,tea*+ ( ,ma!matics #hd ,g5]al ,/atem5t #hd ,ma!matics1 8a ,sci5ce ( ! ,eye0 #he ,rigor\s ,?9k+ & ! ,use ( ,in/rum5ts #hg ,newton's ,comm5ts on ,oughtr$ #id ,index #ig ,,introduction ,9 ! ye> #affj ! ,royal ,society 0 f\nd$ by royal favor 9 ,london1 al?\gh 9 reality its inception took place 9 #afde :5 ! ,philosophical ,society 7or1 z ,boyle call$ x1 ! 8,invisible ,college07 came into be+1 :i* held meet+s at ,gre%am ,college 9 ,london & lat] 9 ,ox=d4 ,x 0 dur+ ! second half ( ! sev5te5? c5tury t ,sir ,isaac ,newton1 surr\nd$ by a gr\p ( great m5--,wallis1 ,hooke1 ,b>r[1 ,halley1 ,cotes--c>ri$ on 8 epo*-mak+ rese>*es 9 ma!matics1 a/ronomy1 & physics4 ,b x is n ?is half-c5tury ( sci5ce 9 ,engl&1 nor any ( its great m51 t especially engage our att5tion 9 ?is monograph4 ,x is r ! half-c5tury prec$+1 an epo* ( prep>ation1 :5 9 ! e>ly times ( ! ,h\se ( ,/u>t ! sci5ces began to fl\ri% 9 ,engl&4 ,says ,dr4 ,a4 ,e4 ,%ipley3 8,:atev] 7 ! political & moral defici5cies ( ! ,/u>t k+s1 no "o ( !m lack$ intellig5ce 9 ?+s arti/ic & sci5tific40 ,x 0 at ?is "t t ma!matics1 & p>ticul>ly algebra1 began to be cultivat$ ) great] zeal1 :5 elem5t>y algebra ) its symbolism z we "k x n[ began to take its %ape4 ,biograph]s ( ,sir ,isaac ,newton make p>ticul> m5tion ( five ma!matical books :i* he read :ile a "y /ud5t at ,cambridge1 namely1 ,euclid's ,elem5ts1 ,desc>tes's ,gomtrie1 ,vieta's ,works1 ,van ,s*oot5's ,miscellanies1 & ,oughtr$'s ,clavis ma!maticae4 ,! la/ ( ^! books has be5 receiv+ increas+ att5tion f ! hi/orians ( algebra 9 rec5t ye>s4 ,we h prep>$ ?is sket* because we felt t !re 7 po9ts ( int]e/ 9 ! life & activity ( ,oughtr$ :i* h n receiv$ adequate treatm5t4 ,hi/orians h discuss$ 8 %>e 9 ! developm5t ( symbolic algebra1 b "s h fall5 into errors1 due to inability to exam9e ! orig9al editions ( ,oughtr$'s ,clavis ma!maticae1 :i* are q r>e & inaccessible to mo/ read]s4 ,moreov]1 hi/orians h fail$ utt]ly to recognize 8 inv5tions ( ma!matical in/rum5ts1 p>ticul>ly ! slide rule2 !y h completely ov]look$ 8 educational views & 8 ideas on ma!matical tea*+4 ,! mod]n read] may pause ) pr(it to consid] briefly ! c>e] ( ?is int]e/+ man4 ,oughtr$ 0 n a pr(essional ma!matician4 ,he did n make 8 livelihood z a tea*] ( ma!matics or z a writ]1 nor z an eng9e] :o applies ma!matics to ! control & use ( nature's =ces4 ,oughtr$ 0 by pr(ession a m9i/] ( ! gospel4 ,) him ! /udy ( ma!matics 0 a side issue1 a pleasure1 a recreation4 ,l ! great ,fr5* algebrai/1 ,vieta1 f :om he drew mu* ( 8 inspiration1 he 0 an amateur ma!matician4 ,! ^w 8amateur0 mu/ n be tak5 "h 9 ! s5se ( sup]ficial or un?or\gh4 ,great ,brita9 has _h _m m5 di/+ui%$ 9 sci5ce :o pursu$ sci5ce z amateurs4 ,( su* m5 ,oughtr$ is "o ( ! v e>lie/4 ,f4 ,c4 ,,*apt] ,i ,,oughtr$',s ,,life ,,at ,,s*ool ,,& ,,univ]sity ,william ,oughtr$1 or1 z he sometimes wrote 8 "n1 ,owtr$1 0 born at ,eton1 ! seat ( ,eton ,college1 ! ye> ( 8 bir? be+ v>i\sly giv5 z #aegc1 #aegd1 & #aege4 8,8 fa!r10 says ,aubrey1 8taught to write at ,eaton1 & 0 a scriv5]2 & und]/ood common ari?metique1 & 'twas no small helpe & fur!rance to 8 son to be in/ruct$ 9 x :5 a s*oole-boy40#a ,he 0 a boy at ,eton 9 ! ye> ( ! ,spani% ,armada4 ,at ?is fam\s s*ool1 :i* prep>$ boys = ! univ]sities1 "y ,oughtr$ receiv$ ?or\gh tra9+ 9 classical le>n+4 ,accord+ to in=mation receiv$ f ,f4 ,l4 ,cl>ke1 ,burs> & ,cl]k ( ,k+'s ,college1 ,cambridge1 ,oughtr$ 0 admitt$ at ,k+'s a s*ol> f ,eton on ,septemb] #a1 #aeib1 at ! age ( sev5te54 ,he 0 made ,fell[ at ,k+'s on ,septemb] #a1 #aeie1 :ile ,elizabe? 0 /ill on ! ?rone4 ,he receiv$ 9 #aeif ! degree ( ,ba*elor ( ,arts & 9 #afjj t ( ,ma/] ( ,arts4 ,he vacat$ 8 fell[%ip ab\t ! beg9n+ ( ,augu/1 #afjc4 ,8 c>e] at ! ,univ]sity ( ,cambridge we pres5t 9 8 own words4 ,he says3 ,next aft] ,eaton s*oole1 ,i 0 br$ up 9 ,cambridge 9 ,k+s ,coll$ge3 ( :i* society ,i 0 a memb] ab\t elev5 or twelve ye>es3 :]e9 h[ ,i behav$ my selfe1 go+ h& 9 h& ) ! re/ ( my ranke 9 ! ord9>y ,academicall /udies & ex]cises1 & ) :at approbation1 is well kn[ne & rememb]$ by _m3 ! "t :i* ov] & above ^? usuall /udies ,i employ$ ^u ! ,ma!maticall sci5ces1 ,i r$eem$ night by night f my naturall sleep1 defraud+ my body1 & inur+ x to wat*+1 cold1 & lab\r1 :ile mo/ o!rs tooke _! re/4 ,nei!r did ,i !re9 seek only my private cont5t1 b ! b5efit ( _m3 & by incit+1 assi/+1 & in/ruct+ o!rs1 br\ght _m into ! love & /udy ( ^? ,arts1 n only 9 our own1 b 9 "s o!r ,coll$ges also3 :i* "s at ?is "t 7m5 f> bett] ?an my selfe 9 le>n+1 degree1 & pref]m5t7 w mo/ lov+ly ackn[l$ge4#b ,^! words describe ! /ruggles :i* e y\? n end[$ ) ! highe/ g5ius mu/ make to a*ieve success4 ,!y %[1 moreov]1 ! k9dly feel+ t[>d o!rs & ! delight he took ?r\gh\t life 9 assi/+ anyone int]e/$ 9 ma!matics4 ,oughtr$'s passion = ?is /udy is ! m rem>kable z nei!r at ,eton nor at ,cambridge did x receive emphasis4 ,ev5 aft] 8 "t at ,cambridge ma!matical /udies & _! applications 7 neglect$ !re4 ,j]emiah ,horrox 0 at ,cambridge 9 #afcc-ce1 desir+ to make himself an a/ronom]4 8,b _m imp$im5ts10 says ,horrox1 8pres5t$ !mselves3 ! t$i\s difficulty ( ! /udy itself det]r$ a m9d n yet =m$2 ! want ( means oppress$1 & /ill oppresses1 ! aspirations ( my m9d3 b t :i* gave me mo/ conc]n 0 t !re 0 no "o :o c\ld in/ruct me 9 ! art1 :o c\ld ev5 help my endeav\rs by jo9+ me 9 ! /udy2 su* 0 ! slo? & languor :i* _h seiz$ all4 4 4 4 4 ,i f\nd t books mu/ be us$ in/ead ( tea*]s40#c ,"s att5tion 0 giv5 to ,greek ma!maticians1 b ! works ( ,italian1 ,g]man1 & ,fr5* algebrai/s ( ! latt] "p ( ! sixte5? & beg9n+ ( ! sev5te5? c5tury 7 q unkn[n at ,cambridge 9 ,oughtr$'s day4 ,x 0 "p ( 8 life-"w z a ma!matician to make algebra1 z x 0 be+ develop$ 9 8 "t1 accessible to ,engli% y\?s4 ,at ! age ( tw5ty-?ree ,oughtr$ inv5t$ 8 ,easy ,way ( ,del9eat+ ,sun-,dials by ,geometry1 :i*1 ?\gh n publi%$ until ab\t half a c5tury lat]1 9 ! fir/ ,engli% edition ( ,oughtr$'s ,clavis ma!maticae 9 #afdg1 0 9 ! meantime translat$ into ,lat9 by ,*ri/oph] ,wr51 !n a ,g5tleman ,common] ( ,wadham ,college1 ,ox=d1 n[ be/ kn[n ?r\gh 8 ar*itectural creations4 ,9 #afjj ,oughtr$ wrote a monograph on ! con/ruction ( sun-dials ^u a plane ( any incl9ation1 b t pap] 0 )held by him f publication until #afcb4 ,sun-dials 7 int]e/+ objects ( /udy1 s9ce wat*es & p5dulum clocks 7 !n /ill unkn[n4 ,all sorts ( sun-dials1 portable & non-portable1 7 us$ at t "t & long aft]w>d4 ,sev]al ( ! college build+s at ,ox=d & ,cambridge h sun-dials ev5 at ! pres5t "t4 ,,z ,,rector ,,& ,,amateur ,,ma!matician ,x 0 9 #afjd t ,oughtr$ ent]$ ^u 8 pr(essional life-"w z a prea*]1 be+ in/itut$ to ! vic>age ( ,%al=d 9 ,surrey4 ,9 #afaj he 0 made rector ( ,albury1 :]e he sp5t ! rema9d] ( 8 long life4 ,s9ce ! era ( ! ,re=mation two ( ! rectors ( ,albury obta9$ great celebrity f _! v>i$ tal5ts & acquirem5ts--our ,william ,oughtr$ & ,samuel ,horsley4 ,oughtr$ cont9u$ to devote 8 sp>e "t to ma!matics1 z he _h done 9 college4 ,a great ma!matical inv5tion made by a ,scot*man soon comm&$ 8 att5tion--! inv5tion ( log>i?ms4 ,an in=mant writes z foll[s3 ,"l ,napi]1 9 #afad1 publi%$ at ,ed9burgh 8 ,mirifici log>i?morum canonis descriptio4 4 4 4 4 ,x pres5tly fell into ! h&s ( ,mr4 ,briggs1 !n geometry-read] at ,gre%am ,college 9 ,london3 & t g5tleman1 =m+ a design to p]fect ,"l ,napi]'s plan1 consult$ ,oughtr$ ^u x2 :o probably wrote 8 ,treatise ( ,trigonometry ab\t ! same "t1 s9ce x is evid5tly =m$ ^u ! plan ( ,"l ,napi]'s ,canon4#d ,x w be %[n lat] t ,oughtr$ is v probably ! au?or ( an 8,app5dix0 :i* appe>$ 9 ! #afah edition ( ,edw>d ,wright's translation into ,engli% ( ,john ,napi]'s ,descriptio4 ,?is 8,app5dix0 relates to log>i?ms & is an able docum5t1 conta9+ sev]al po9ts ( hi/orical int]e/4 ,mr4 ,ar?ur ,hut*9son ( ,pembroke ,college in=ms me t 9 ! univ]sity libr>y at ,cambridge !re is a copy ( ,napi]'s ,con/ructio 7#afai7 b\nd up ) a copy ( ,kepl]'s ,*ilias log>i?morum 7#afbd71 t at ! beg9n+ ( ! ,con/ructio is a blank leaf1 & be=e ?is occurs ! title-page only ( ,napi]'s ,descriptio 7#afai71 at ! top ( :i* appe>s ,oughtr$'s autograph4 ,! hi/ory ( ?is int]e/+ signature is unkn[n4 ,,8 ,,wife ,9 #afjf he m>ri$ ,*ri/'sgift ,c>yll1 daught] ( ,c>yll1 ,esq41 ( ,tangley1 9 an adjo9+ p>i%4#e ,we "k v little ab\t ,oughtr$'s family life4 ,! records at ,k+'s ,college1 ,cambridge1#f m5tion a son1 b x is c]ta9 t !re 7 m *ildr54 ,a daught] 0 m>ri$ to ,*ri/oph] ,brookes4 ,b !re is no confirmation ( ,aubrey's /atem5ts1#g accord+ to :i* ,oughtr$ _h n9e sons & f\r daught]s4 ,ref]5ce to ! wife & *ildr5 is sometimes made 9 ! correspond5ce ) ,oughtr$4 ,9 #afaf ,j4 ,hales writes1 8,i pray let me be rememb]$1 ?\gh unkn[n1 to ,mi/ress ,oughtr$40#h ,z we %all see lat]1 ,oughtr$ _h a great _m "y m5 :o came to 8 h\se & rema9$ !re free ( *>ge to receive in/ruction 9 ma!matics1 :i* 0 likewise gratuit\s4 ,?is be+ ! case1 c]ta9ly great appreciation 0 due to ,mrs4 ,oughtr$1 ^u :om ! burd5 ( hospitality mu/ h fall54 ,yet *ronicl]s are s+ul>ly sil5t 9 reg>d to h]4 ,h]s 0 evid5tly a life ( obscurity & s]vice4 ,we greatly d\bt ! accuracy ( ! foll[+ item h&$ d[n by ,aubrey2 x _c be a true *>act]ization3 ,8 wife 0 a p5uri\s woman1 & w\ld n all[ him to burne c&le aft] supp]1 by :i* meanes _m a good notion is lo/1 & _m a probleme unsolv$2 s t ,mr4 ,?omas ,h5%awe1 :5 he 0 !re1 b\ght c&le1 :i* 0 a great com=t to ! old man4#i ,,9 ,,dang] ,,( ,,seque/ration ,oughtr$ sp5t 8 ye>s 9 8unremitt$ att5tion to 8 fav\rite /udy10 sometimes1 x has be5 :isp]$1 to ! neglect ( 8 rectorial duties4 ,says ,aubrey3 ,i h he>d 8 neighb\r m9i/]s say t he 0 a pittiful prea*]2 ! reason 0 because he nev] /udy$ x1 b b5t all 8 ?\ghts on ! ma!matiques2 b :5 he 0 9 dang] ( be+ seque/r$ = a royali/1 he fell to ! /udy ( div9ity1 & prea*t 7!y sayd7 admirably well1 ev5 9 8 old age4#aj ,?is rem>k on seque/ration br+s to m9d "o ( ! political & religi\s /ruggles ( ! "t1 ! episcopacy aga9/ ! indep5d5t movem5ts4 ,says ,mann+3 ,9 #afdf he 0 cit$ be=e ! ,committee = ,ecclesia/ical ,affairs1 :]e _m articles _h be5 depos$ aga9/ him2 b1 by ! fav\r ( ,sir ,bul/rode ,:itlock & o!rs1 :o1 at ! int]cession ( ,william ,lilye ! ,a/rolog]1 appe>$ 9 great numb]s on 8 behalf1 he _h a majority on 8 side1 & s escap$ a seque/ration4#aa ,n )\t int]e/ is ! acc\nt ( ?is matt] giv5 by ,lilly himself3 ,ab\t ?is ,"t1 ! mo/ fam\s ,ma!matician ( all ,europe1 7,mr4 ,william ,oughtr$1 ,p>son ( ,aldbury 9 ,surrey7 0 9 ,dang] ( ,seque/ration by ! ,committee ( or = plund]'d ,m9i/]s2 7,ambo-dext]s !y 727 sev]al inconsid]able ,articles 7 depos$ & sworn aga9/ him1 mat]ial en\gh to h seque/r$ him1 b t1 ^u 8 ,day ( he>+1 ,i appli$ my self to ,sir ,bol/rode ,:itlock1 & all my own old ,fri5ds1 :o 9 su* ,numb]s appe>$ 9 8 ,behalf1 t ?\gh ! ,*airman & _m o!r ,presbyt]ian ,memb]s 7 /iff aga9/ him1 yet he 0 cle>$ by ! major ,numb]4 ,! tru? is1 he _h a consid]able ,p>sonage1 & t only 0 en\gh to seque/] any mod]ate ,judgm5t3 ,he 0 also well kn[n to affect 8 ,maje/y ,*>les ,i4 ,9 ^! ,times _m wor?y ,m9i/]s lo/ _! ,liv+s or ,b5efices1 = n comply+ ) ! ,?ree-p5ny ,directory4#ab ,,8 ,,tea*+ ,oughtr$ _h few p]sonal enemies4 ,8 pupils held him 9 highe/ e/eem & %[$ deep gratitude2 only "o pupil mu/ be except$1 ,ri*>d ,delama94 ,aga9/ him arose a bitt] controv]sy :i* sadd5$ ! life ( ,oughtr$1 !n an old man4 ,x involv$1 z we %all see lat]1 ! priority ( inv5tion ( ! circul> slide rule & ( a horizontal in/rum5t or portable sun-dial4 ,9 def5se ( himself1 ,oughtr$ wrote 9 #afcc or #afcd ! ,apologeticall ,epi/le1 f :i* we quot$ above4 ,?is docum5t conta9s biographical details1 9 "p z foll[s3 ,ev] s9ce my dep>ture f ! ,vniv]sity1 :i* is ab\t ?irty ye>es1 ,i h liv$ ne]e to ! ,t[ne ( ,guild=d 9 ,surrey3 :]e1 :e!r ,i h tak5 s mu* lib]ty to ! losse ( "t1 & ! neglect ( my call+ ! :ole ,c\ntrey !reab\t1 bo? ,g5try & o!rs1 to :om ,i am full well kn[ne1 w quickely in=me him2 my h\se be+ n pa/ ?ree & tw5ty miles f ,london3 & yet ,i s hid my selve at home1 t ,i seldomly travell$ s f>re z ,london once 9 a ye>e4 ,inde$ ! life & m9d ( man _c endure )\t "s int]*angeabl5esse ( recreation1 & pawses f ! int5sive actions ( our sev]all call+s2 & e man is drawne ) 8 owne delight4 ,my recreations h be5 div]sity ( /udies3 & z (t z ,i 0 toyl$ ) ! lab\r ( my owne pr(ession1 ,i h allay$ t t$i\snesse by walk+ 9 ! pleasant & m !n ,elysian fields ( ! div]se & v>i\s p>ts ( humane le>n+1 & n ! ,ma!matics onely4 ,ev5 ! oppon5ts ( ,delama9 mu/ be grateful to him = hav+ be5 ! means ( draw+ f ,oughtr$ su* int]e/+ biographical details4 ,oughtr$ proce$s to tell h[1 ab\t #afbh1 he 0 induc$ to write 8 ,clavis ma!maticae1 ^u :i* 8 reputation z a ma!matician l>gely re/s3 ,ab\t five ye>es s9ce1 ! ,e>le ( ,arundell my mo/ hon\rable ,"l 9 a "t ( 8 private retir+ to 8 h\se 9 ! c\ntrey !n at ,we/ ,horsley1 f\re small miles f me 7?\gh s9ce he ha? a h\se 9 ,aldebury ! p>i% :]e ,i live7 he>+ ( me 7by :at meanes ,i "k n7 0 pleas$ to s5d = me3 & aft]w>d at ,london to appo9t mee a ,*amb] ( 8 owne h\se3 :]e1 at su* times1 & 9 su* mann] z x seem$ him good to imploy me1 & :5 ,i might n inconv5i5tly be sp>$ f my *>ge1 ,i h be5 mo/ ready to pres5t my selfe 9 all humble & affectionate s]vice3 ,i hope also )\t ! (f5ce ( ,god1 ! transgression ( ! good ,lawes ( ?is ,l&1 neglect ( my call+1 or ! des]v$ sc&all ( any good man4 4 4 4 4 ,& al?\gh ,i am no m]c5>y man1 nor make pr(ession to tea* any "o 9 ^! arts = ga9e & recomp5ce1 b z ,i s]ve at ! ,alt>1 s ,i live onely ( ! ,alt>3 yet 9 ^? int]ims t ,i am at ,london 9 my ,lords s]vice1 ,i h be5 /ill mu* frequ5t$ bo? by ,natives & ,/rang]s1 = my resolution & in/ruction 9 _m difficult poynts ( ,art2 & h mo/ freely & lov+ly imp>t$ my selfe & my skill1 su* z ,i _h1 to _! cont5tm5ts1 & mu* hon\rable ackn[l$gem5t ( _! obligation to my ,"l = br++ mee to ,london1 ha? be5e te/ify$ by _m4 ,( :i* my lib]allity & unwe>y$ read9esse to doe good to all1 sc>ce any "o c give m ample te/imony !n ,r4 ,d4 himselfe c3 w\ld he be b pleas$ to allay ! %ame ( ?is 8 hot & eag] cont5tion1 bl[ne up onely ) ! full bell[es ( int5d$ glory & ga9e2 4 4 4 4 !y ! subjects 9 :i* ,delama9 receiv$ assi/ance f ,oughtr$ 7 ! fir/ elem5ts ( ,a/ronomie conc]n+ ! second motions ( ! fix$ />res1 & ( ! ,sunne & ,moone2 !y 7 ! fir/ elem5ts ( ,conics1 to del9eate ^? sections3 !y 7 ! fir/ elem5ts ( ,optics1 ,catoptrics1 & ,dioptrics3 ( all :i* y knew no?+ at all4 ,^! la/ passages are in/ructive z %[+ :at topics 7 tak5 up = /udy ) "s ( 8 pupils4 ,! *ief subject ( int]e/ ) mo/ ( !m 0 algebra1 :i* at t "t 0 j beg9n+ to draw ! att5tion ( ,engli% lov]s ( ma!matics4 ,oughtr$ c>ri$ on an ext5sive correspond5ce on ma!matical subjects4 ,he 0 frequ5tly call$ ^u to assi/ 9 ! solution ( knotty problems--sometimes to 8 annoyance1 p]haps1 z is %[n by ! foll[+ lett] :i* he wrote 9 #afdb to a /rang]1 nam$ ,price3 ,x is true t ,i h be/[$ su* vacant "t1 z ,i c\ld ga9 f ! /udy ( div9ity1 7:i* is my call+17 ^u human kn[l$ges1 &1 among/ o!r1 ^u ! ma!matics1 :]e9 ! little skill ,i h atta9$1 be+ comp>$ ) o!rs ( my pr(ession1 :o = ! mo/ "p cont5t+ !mselves only ) _! own way1 refuse to tread ^! salebr\s & uneasy pa?s1 may p]adv5ture seem ! m4 ,b n[ be+ 9 ye>s & m9dful ( m9e end1 & hav+ paid de>ly = my =m] delights bo? 9 my heal? & /ate1 besides ! prejudice ( su*1 :o n consid]+ :at incessant lab\r may produce1 reckon s mu* want+ unto me 9 my prop] call+1 z !y ?9k ,i h acquir$ 9 o!r sci5ces2 by :i* op9ion 7n ( ! vulg> only7 ,i h suff]$ bo? disrespect1 & also h9d]ance 9 "s small p]f]m5ts ,i h aim$ at4 ,i h !re=e n[ le>n$ to sp>e myself1 & am n will+ to desc5d aga9 9 ar5am1 & to s]ve su* ungrateful muses4 ,yet1 sir1 at y\r reque/ ,i h p]us$ y\r problem4 4 4 4 4 ,y\r problem is easily wr\ght p] ,nicom$is con*oidem l9eam4#ac ,,appe>ance ,,& ,,habits ,aubrey gives in=mation ab\t ! appe>ance & habits ( ,oughtr$3 ,he 0 a little man1 _h black haire1 & blacke eies 7) a great deal ( _s74 ,8 head 0 always work+4 ,he w\ld drawe l9es & diagrams on ! du/4 4 4 4 4 ,he 8 olde/ son ,b5jam9 told me t 8 fa!r did use to lye a b$ till eleav5 or twelve a clock1 ) 8 d\blet on1 ev] s9ce he c rememb]4 ,/udy$ late at night2 w5t n to b$ till #aa a clock2 _h 8 t9d] box by him2 & on ! top ( 8 b$-/affe1 he _h 8 inke-horne fix't4 ,he slept b little4 ,sometimes he w5t n to b$ 9 two or ?ree nights1 & w\ld n come d[ne to meales till he _h f\nd out ! quaesitum4 ,he 0 m fam\s abroad = 8 le>n+1 & m e/eem$1 !n at home4 ,sev]all great ma!maticians came ov] into ,engl& on purpose to conv]se ) him4 ,8 c\ntrey neighb\rs 7?\gh !y und]/ood n 8 wor?7 knew t !re mu/ be extraord9>y wor? 9 him1 t he 0 s visit$ by =eign]s4 4 4 4 4 ,:5 le>n$ =eign]s came & sawe h[ privately he liv$1 !y did admire & blesse !mselves1 t a p]son ( s mu* wor? & le>n+ %\ld n be bett] provid$ =4 4 4 4 4 ,he has told bi%op ,w>d1 & ,mr4 ,elias ,a%mole 7:o 0 8 neighb\r71 t 8on ?is spott ( gr\nd0 7or 8lean+ aga9/ ?is oake0 or 8t a%e071 8! solution ( su* or su* a probleme came into my head1 z if infus$ by a div9e g5ius1 aft] ,i _h ?\ght on x )\t successe = a ye>e1 two1 or ?ree40 4 4 4 4 ,nicolaus ,m]cator1 ,holsatus 4 4 4 4 w5t to see him few ye>es be=e he dy$4 4 4 4 4 ,! "r honble ,?omas ,h[>d1 e>le ( ,arundel & ,surrey1 ,"l ,high ,m>%all ( ,engl&1 0 8 great patron1 & lov$ him intirely4 ,"o "t !y 7 l to h be5 kill$ toge!r by ! fall at ,albury ( a grott1 :i* fell d[ne b j z !y 7 come out4#ad ,oughtr$'s fri5ds convey ! impression t1 9 ! ma91 ,oughtr$ enjoy$ a com=table liv+ at ,albury4 ,only once appe> indications ( f9ancial emb>rassm5t4 ,ab\t #afcd "o ( 8 pupils1 ,w4 ,rob9son1 writes z foll[s3 ,i prote/ unto y s9c]ely1 7 ,i z able z "s1 at ^: h&s y h m]it$ exce$+ly1 or 7to speak m absolutely7 z able z will+1 ,i w\ld z freely give y #ejj l4 p] ann4 z #ejj p5ce2 & ,i _c b be a/oni%$ at ?is our age1 :]e9 pelf & dross is made _! summum bonum1 & ! be/ "p ( man1 ) ! true ornam5ts !re(1 sci5ce & k1 are s slight$4 4 4 4 4#ae ,9 8 lett]s ,oughtr$ compla9s sev]al times ( ! limitations = "w & ! infirmities due to 8 advanc+ old age4 ,! impression he made ^u o!rs 0 q diff]5t4 ,says "o biograph]3 ,he sometimes amus$ himself ) ar*]y1 & sometimes practis$ z a surveyor ( l&4 4 4 4 4 ,he 0 sprightly & active1 :5 m ?an eighty ye>s ( age4#af ,ano!r in=mant says t ,oughtr$ 0 z faceti\s 9 ,greek & ,lat9e z solid 9 ,ari?metique1 ,a/ronomy1 & ! sph]e ( all ,measures1 ,musick1 etc42 exact 9 8 /yle z 9 8 judgm5t2 h&l+ 8 ,cube1 & o!r ,in/rum5ts at eighty1 z /eadily1 z o!rs did at ?irty2 ow+ ?is1 he said1 to temp]ance & ,ar*]y2 pr9cipl+ 8 p ) pla9 & solid tru?s1 z he did ! _w ) great & useful ,arts2 advanc+ new ,inv5tions 9 all ?+s b ,religion4 ,:i* 9 its old ord] & dec5cy he ma9ta9$ secure 9 8 privacy1 prud5ce1 meekness1 simplicity1 resolution1 pati5ce1 & cont5tm5t4#ag ,,alleg$ ,,travel ,,abroad ,accord+ to c]ta9 s\rces ( in=mation1 ,oughtr$ travel$ on ! ,european ,cont95t & 0 invit$ to *ange 8 abode to ! ,cont95t4 ,we h se5 no /atem5t f ,oughtr$ himself on ?is matt]4 ,he seldom ref]r$ to himself 9 8 books & lett]s4 ,! autobiography conta9$ 9 8 ,apologeticall ,epi/le 0 writt5 a qu>t] ( a c5tury be=e 8 dea?4 ,aubrey gives ! foll[+3 ,9 ! "t ( ! civill w>res ! duke ( ,flor5ce invit$ him ov]1 & (f]$ him #ejj li4 p] annum2 b he w\ld n accept x1 because ( 8 religion4#ah ,a portrait ( ,oughtr$1 pa9t$ 9 #afdf by ,holl> & ins]t$ 9 ! ,engli% edition ( ! ,clavis ( #afdg1 conta9s und]nea? ! foll[+ l9es3 8,haec e/ ,oughtr$i s5io labantis imago ,itala quam cupiit1 ,t]ra ,britanna tulit40 ,9 ! sket* ( ,oughtr$ by ,ow5 ,mann+ x is confess$ t 8x is n kn[n to :at ?is alludes2 b possibly he might h be5 9 ,italy ) 8 patron1 ! ,e>l ( ,arundel40#ai ,x w\ld seem q c]ta9 ei!r t ,oughtr$ travel$ 9 ,europe or t he receiv$ "s sort ( an (f] to settle 9 ,italy4 ,9 view ( ,aubrey's explicit /atem5t & ( ,oughtr$'s well-kn[n habit ( conf9+ himself to 8 duties & /udies 9 8 own p>i%1 seldom go+ ev5 z f> z ,london1 we /rongly incl9e to ! op9ion t he did n travel on ! ,cont95t1 b t he receiv$ an (f] f "s patron ( ! sci5ces--possibly "s di/+ui%$ visitor--to settle 9 ,italy4 ,,8 ,,dea? ,he di$ at ,albury1 ,june #cj1 #affj1 ag$ ab\t eighty-six ye>s4 ,( 8 la/ days & dea?1 ,aubrey speaks z foll[s3 ,be=e he dy$ he burn$ a _w ( pap]s1 & sayd t ! _w 0 n wor?y ( !m2 he 0 s sup]b4 ,he burn$ also sev]all pr9t$ bookes1 & w\ld n /irre1 till !y 7 consum$4 4 4 4 4 ,i myselfe h 8 ,pitiscus1 imbeli%$ ) 8 excell5t m>g9all notes1 :i* ,i e/eeme z a great r>ity4 ,i wi% ,i c\ld also h got 8 ,bil+sley's ,euclid1 :i* ,john ,coll9s sayes 0 full ( 8 annotations4 4 4 4 4 ,ralph ,greatrex1 8 great fri5d1 ! ma!maticall in/rum5t-mak]1 say$ he conceiv$ he dy$ ) joy = ! come+-9 ( ! k+1 :i* 0 ! #bi? ( ,may be=e4 8,& are yee sure he is re/or$80--8,!n give me a glasse ( sack to dr9ke 8 sacr$ maje/ie's heal?40 ,8 spirits 7 !n q ^u ! w+ to fly away4 4 4 4 4#bj ,9 ?is passage1 z 9 o!rs1 due all[ance mu/ be made = ,aubrey's lack ( discrim9ation4 ,he 0 n 9 ! habit ( sift+ facts f m]e gossip4 ,t ,oughtr$ %\ld h decl>$ t ! _w 0 n wor?y ( 8 pap]s or manuscripts is n 9 consonance ) ! sweetness ( disposition ord9>ily attribut$ to him4 ,m probable 0 ! feel+ t ! pap]s he burn$--possibly old s]mons--7 ( no p>ticul> value to ! _w4 ,t he did n de/roy a l>ge mass ( ma!matical manuscripts is evid5t f ! fact t a consid]able numb] ( !m came aft] 8 dea? into ! h&s ( ,sir ,*>les ,sc>bor\gh1 ,m4,d41 "u ^: sup]vision "s ( !m 7 c>efully revis$ & publi%$ at ,ox=d 9 #afgg "u ! title ( ,opuscula ma!matica hact5us in$ita4 ,aubrey's /ory ( ,oughtr$'s mode ( dea? has be5 z widely circulat$ 9 e mod]n biographical sket* z has 8 sl&] ( ,mrs4 ,oughtr$ by claim+ t %e 0 s p5uri\s t %e w\ld d5y him ! use ( c&les to read by4 ,oughtr$ di$ on ,june #cj2 ! ,re/oration occurr$ on ,may #bi4 ,no d\bt ,oughtr$ rejoic$ ov] ! ,re/oration1 b ! /ory ( 8 dr9k+ 8a glass ( sack0 to 8 ,maje/y's heal?1 & !n dy+ ( joy is surely apocryphal4 ,de ,morgan humor\sly rem>ks1 8,x %\ld be add$1 by way ( excuse1 t he 0 eighty-six ye>s old40#ba ,,*apt] ,,ii ,,pr9cipal ,,works 8,,clavis ,,ma!maticae0 ,pass+ to ! consid]ation ( ,oughtr$'s ma!matical books1 we beg9 ) ! obs]vation t he %[$ a m>k$ dis9cl9ation to give 8 writ+s to ! press4 ,8 fir/ pap] on sun-dials 0 writt5 at ! age ( tw5ty-?ree1 b we are n aw>e t m ?an "o brief ma!matical manuscript 0 pr9t$ be=e 8 fifty-sev5? ye>4 ,9 e in/ance1 publication 9 pr9t$ =m seems to h be5 due to pressure ex]t$ by "o or m ( 8 patrons1 pupils1 or fri5ds4 ,"s ( 8 manuscripts 7 l5t out to 8 pupils1 :o prep>$ copies = _! own use4 ,9 "s in/ances !y urg$ ^u him ! desirability ( publication & assi/$ 9 prep>+ copy = ! pr9t]4 ,! e>lie/ & be/-kn[n book ( ,oughtr$ 0 8 ,clavis ma!maticae1 to :i* repeat$ allusion has already be5 made4 ,z he himself in=ms u1 he 0 employ$ by ! ,e>l ( ,arundel ab\t #afbh to in/ruct ! ,e>l's son1 ,"l ,william ,h[>d 7aft]w>d ,visc\nt ,/af=d7 9 ! ma!matics4 ,= ! use ( ?is "y man ,oughtr$ compos$ a treatise on algebra :i* 0 publi%$ 9 ,lat9 9 ! ye> #afca at ! urg5t reque/ ( a k9sman ( ! "y man1 ,*>les ,cav5di%1 a patron ( le>n+4 ,! ,clavis ma!maticae1#bb 9 its fir/ edition ( #afca1 0 a booklet ( only #hh small pages4 ,yet x conta9$ 9 v cond5s$ =m ! ess5tials ( ari?metic & algebra z kn[n at t "t4 ,aside f ! addition ( f\r tracts1 ! #afca edition und]w5t "s *anges 9 ! editions ( #afdg & #afdh1 :i* two are mu* alike4 ,! tw5ty *apt]s ( #afca are r$uc$ to n9ete5 9 #afdg & 9 all ! lat] editions4 ,num]\s m9ute alt]ations f ! #afca edition occur 9 all p>ts ( ! books ( #afdg & #afdh4 ,! mat]ial ( ! la/ ?ree *apt]s ( ! #afca edition is re>rang$1 ) "s slight additions "h & !re4 ,! #afdh edition has no preface4 ,9 ! pr9t ( #afeb !re are only slight alt]ations f ! #afdh edition2 aft] t ! book und]w5t h>dly any *anges1 except = ! numb] ( tracts app5d$1 & brief explanatory notes add$ at ! close ( ! *apt]s 9 ! ,engli% editions ( #afid & #agjb4 ,! #afeb & #affg editions 7 se5 ?r\gh ! press by ,john ,wallis2 ! #afih impression conta9s on ! title-page ! words3 ,ex ,recognitione ,d4 ,johannis ,wallis1 ,s4,t4,d4 ,geometriae ,pr(essoris ,saviliani4 ,! co/ ( publi%+ may be a matt] ( "s int]e/4 ,:5 arrang+ = ! pr9t+ ( ! #affg edition ( ! ,clavis1 ,wallis wrote ,coll9s3 8,i told y 9 my la/ :at price %e ,mrs4 ,li*field expects = x1 z ,i h =m]ly und]/ood f h]1 viz41 #dj = ! impression1 :i* is ab\t #i;d4 a book40#bc ,z comp>$ ) o!r contempor>y works on algebra1 ,oughtr$'s di/+ui%es itself = ! am\nt ( symbolism us$1 p>ticul>ly 9 ! treatm5t ( geometric problems4 ,extraord9>y emphasis 0 plac$ ^u :at he call$ 9 ! ,clavis ! 8analytical art40#bd ,by t t]m he did n mean our mod]n analysis or analytical geometry1 b ! art 89 :i* by tak+ ! ?+ s\ght z kn[ne1 we f9de out t we seeke40#be ,he meant to express by x cond5s$ processes ( rigid1 logical d$uction express$ by appropriate symbols1 z contra/$ ) m]e description or elucidation by passages fraught ) v]bosity4 ,9 ! preface to ! fir/ edition 7#afca7 he says3 ,9 ?is little book ,i make kn[n 4 4 4 4 ! rules relat+ to fundam5tals1 collect$ toge!r1 j l a bundle1 & adapt$ to ! explanation ( z _m problems z possible4 ,z /at$ 9 ?is preface1 "o ( 8 reasons = publi%+ ! book1 is 4 4 4 4 t l ,ariadne ,i might (f] a ?read to ma!matical /udy by :i* ! my/]ies ( ?is sci5ce might be reveal$1 & direction giv5 to ! be/ au?ors ( antiquity1 ,euclid1 ,ar*im$es1 ! great geometrician ,apollonius ( ,p]ga1 & o!rs1 s z to be easily & ?or\ghly und]/ood1 _! !orems be+ add$1 n only because to _m !y are ! height & dep? ( ma!matical sci5ce 7,i ignore ! w\ld-be ma!maticians :o occupy !mselves only ) ! s-call$ practice1 :i* is 9 reality m]e juggl]'s tricks ) in/rum5ts1 ! surface s to speak1 pursu$ ) a disreg>d ( ! great art1 a contemptible picture71 b also to %[ ) :at ke5ness !y h p5etrat$1 ) :at mass ( equations1 comp>isons1 r$uctions1 conv]sions & disquisitions ^! h]oes h ornam5t$1 increas$ & inv5t$ ?is mo/ beautiful sci5ce4 ,! ,clavis op5s ) an explanation ( ! ,h9du-,arabic notation & ( decimal fractions4 ,notewor?y is ! abs5ce ( ! words 8million10 8billion10 etc4 ,?\gh us$ on ! ,cont95t by c]ta9 ma!matical writ]s long be=e ?is1 ^! words did n become curr5t 9 ,engli% ma!matical books until ! eighte5? c5tury4 ,! au?or 0 a great admir] ( decimal fractions1 b fail$ to introduce ! notation :i* 9 lat] c5turies came to be univ]sally adopt$4 ,oughtr$ wrote #j4ef 9 ?is mann] #jef2 ! po9t he us$ to designate ratio4 ,?us #c3d 0 writt5 by him #cd4 ,! decimal po9t 7or comma7 0 fir/ us$ by ! inv5tor ( log>i?ms1 ,john ,napi]1 z e>ly z #afaf & #afag4 ,al?\gh ,oughtr$ _h ma/]$ ! !ory ( log>i?ms soon aft] _! publication 9 #afad & 0 a great admir] ( ,napi]1 he pref]r$ to use ! dot = ! designation ( ratio4 ,?is notation ( ratio is us$ 9 all 8 ma!matical books1 except 9 two in/ances4 ,! two dots 737 occur z symbols ( ratio 9 "s p>ts ( ,oughtr$'s po/hum\s "w1 ,opuscula ma!matica hact5us in$ita1 ,ox=d1 #afgg1 b may h be5 due to ! editors & n to ,oughtr$ himself4 ,!n aga9 ! two dots 737 are us$ to designate ratio on ! la/ two pages ( ! tables ( ! ,lat9 edition ( ,oughtr$'s ,trigonometria ( #afeg4 ,9 all o!r p>ts ( t book ! dot 77 is us$4 ,probably someone :o sup]vis$ ! pr9t+ ( ! tables introduc$ ! 737 on ! la/ two pages1 foll[+ ! log>i?mic tables1 :]e me?ods ( int]polation are expla9$4 ,! probability ( ?is conjecture is ! /rong]1 because 9 ! ,engli% edition ( ! ,trigonometrie1 br\ght out ! same ye> 7#afeg7 b aft] ! ,lat9 edition1 ! notation 737 at ! end ( ! book is replac$ by ! usual 771 except t 9 "s copies ( ! ,engli% edition ! explanations at ! end are omitt$ altoge!r4 ,oughtr$ introduces an int]e/+1 & at ! same "t new1 feature ( an abbreviat$ multiplication & an abbreviat$ division ( decimal fractions4 ,on ?is po9t he took a position f> 9 advance ( 8 "t4 ,! "p on abbreviat$ multiplication 0 rewritt5 9 slightly enl>g$ =m & ) "s unimportant alt]ations 9 ! lat] edition ( ! ,clavis4 ,we give x z x occurs 9 ! revision4 ,f\r cases are giv54 ,9 f9d+ ! product ( #bdfiad & #cebg1 8if y w\ld h ! ,product )\t any ,p>ts0 7)\t any decimal "p71 8set ! place ( ,unity ( ! less] "u ! place ( ,unity 9 ! great]3 z 9 ! ,example10 writ+ ! figures ( ! less] numb] 9 inv]se ord]4 ,f ! example x w be se5 t he beg9s by multiply+ by #c1 ! "r-h& digit ( ! multipli]4 ,9 ! fir/ edition ( ! ,clavis he began ) #g1 ! left digit4 ,obs]ve also t he 8c>ries0 ! ne>e/ t5s 9 ! product ( ea* l[] digit & ! upp] digit "o place to its "r4 ,= in/ance1 he takes #gdbh & c>ries #c1 !n he f9ds #gbcag & writes d[n #ag4 #b #d #fi #a #d #g #be #c ------- #g #d #j #g #a #b #c #e #d #i #a #g ------- #h #g #j #h ,! second case supposes t 8y w\ld h ! ,product ) "s places ( p>ts0 7decimals71 say #d3 8,set ! place ( ,unity ( ! less] ,numb] "u ! ,f\r? place ( ! ,p>ts ( ! great]40 ,! multiplication ( #bdfiad by #cebg is n[ p]=m$ ?us3 #b #d #fi #a #d #g #be #c --------------- #g #d #j #g #d #b #j #j #a #b #c #d #e #g #j #j #d #i #c #h #b #h #a #g #b #h #d #j --------------- #h #g #j #hf #e #f #h ,9 ! ?ird & f\r? cases are consid]$ factors :i* appe> z integ]s1 b are 9 reality decimals2 = in/ance1 ! s9e ( #ed is giv5 9 ! tables z #hjijb :5 9 reality x is 4#hjijb4 ,( int]e/ z reg>ds ! use ( ! ^w 8p>abola0 is ! foll[+3 8,! ,numb] f\nd by ,division is call$ ! ,quoti5t1 or also ,p>abola1 because x arises out ( ! ,application ( a pla9 ,numb] to a giv5 ,longitude1 t a congru\s ,latitude may be f\nd40#bf ,?is is 9 h>mony ) etymological diction>ies :i* speak ( a p>abola z ! application ( a giv5 area to a giv5 /raight l9e4 ,! divid5d or product is ! area2 ! divisor or factor is ! l9e4 ,oughtr$ gives two processes ( long division4 ,! fir/ is id5tical ) ! mod]n process1 except t ! divisor is writt5 bel[ e rema9d]1 ea* digit ( ! divisor be+ cross$ out z soon z x has be5 us$ 9 ! p>tial multiplication4 ,! second me?od ( long division is "o ( ! sev]al types ( ! old 8scrat* me?od40 ,?is antiquat$ process held its place by ! side ( ! mod]n me?od 9 all editions ( ! ,clavis4 ,! au?or divides #dfgjbc by #cegjibfdbe1 giv+ ! foll[+ in/ructions3 8,take z _m ( ! fir/ ,figures ( ! ,divisor z are necess>y1 = ! fir/ ,divisor1 & !n 9 e foll[+ p>ticul> ,division drop "o ( ! ,figures ( ! ,divisor t[>ds ! ,left ,h&1 till y h got a compet5t ,quoti5t40 ,he does n expla9 abbreviat$ division z ?or\ghly z abbreviat$ multiplication4 #ag #cjc #bhjc #ajiicj #cegjibfdbe7 #dfgjbc 7#acjghj #cegjic #ajgabg #bejj #bhf ,oughtr$ does n exam9e ! degree ( reliability or accuracy ( 8 processes ( abbreviat$ multiplication & division4 ,"h z 9 o!r places he gives 9 cond5s$ /atem5t ! mode ( proc$ure1 )\t fur!r discussion4 ,he does n attempt to e/abli% ! rules = ! addition1 subtraction1 multiplication1 & division ( positive & negative numb]s4 8,if ! ,signs are bo? alike1 ! ,product w be affirmative1 if unlike1 negative02 !n he proce$s to applications4 ,?is attitude is sup]ior to t ( _m writ]s ( ! eighte5? & n9ete5? c5turies1 on p$agogical z well z logical gr\nds3 p$agogically1 because ! beg9n] 9 ! /udy ( algebra is n 9 a position to appreciate an ab/ract tra9 ( ?\ght1 z e tea*] well kn[s1 & d]ives bett] intellectual ex]cise f ! applications ( ! rules to problems2 logically1 because ! rule ( signs 9 multiplication does n admit ( rigor\s pro(1 unless "s o!r assumption is fir/ made :i* is no less arbitr>y ?an ! rule itself4 ,x is well kn[n t ! pro(s ( ! rule ( signs giv5 by eighte5?-c5tury writ]s are invalid4 ,some:]e !y involve "s surreptiti\s assumption4 ,?is criticism applies ev5 to ! pro( giv5 by ,laplace1 :i* tacitly assumes ! di/ributive law 9 multiplication4 ,a ^w %\ld be said on ,oughtr$'s def9ition ( & -4 ,he recognizes _! d\ble function 9 algebra by say+ 7,clavis1 #afca1 p4 #b73 8,signum additionis1 sive affirmationis1 e/ plus0 & 8,signum subductionis1 sive negationis e/ - m9us40 ,!y are symbols :i* indicate ! quality ( numb]s 9 "s in/ances & op]ations ( addition or subtraction 9 o!r in/ances4 ,9 ! #afid edition ( ! ,clavis1 ?irty-f\r ye>s aft] ! dea? ( ,oughtr$1 ^! symbols are def9$ z signify+ op]ations only1 b are actually us$ to signify ! quality ( numb]s z well4 ,9 ?is respect ! #afid edition m>ks a recrudesc5ce4 ,! *>act]i/ic 9 ! ,clavis t is mo/ /rik+ to a mod]n read] is ! total abs5ce ( indexes or expon5ts4 ,!re is mu* discussion 9 ! lead+ treatises ( ! latt] "p ( ! sixte5? & ! e>ly "p ( ! sev5te5? c5tury on ! !ory ( indexes1 b ! mod]n expon5tial notation1 a1 is ( lat] date4 ,! mod]n notation1 = positive integral expon5ts1 fir/ appe>s 9 ,desc>tes' ,gomtrie1 #afcg2 fractional & negative expon5ts 7 fir/ us$ 9 ! mod]n =m by ,sir ,isaac ,newton1 9 8 ann\ncem5t ( ! b9omial =mula1 9 a lett] writt5 9 #afgf4 ,?is total abs5ce ( our mod]n expon5tial notation 9 ,oughtr$'s ,clavis gives x a /range aspect4 ,l ,vieta1 ,oughtr$ uses ord9>ily ! capital lett]s1 ,a1 ,b1 ,c1 4 4 4 4 to designate giv5 numb]s2 ,a is writt5 ,aq1 ,a is writt5 ,ac2 = ,a1 ,a1 ,a he has1 respectively1 ,aqq1 ,aqc1 ,acc4 ,only on r>e occasions1 usually :5 "s p>allelism 9 notation is aim$ at1 does he use small lett]s#bg to repres5t numb]s or magnitudes4 ,p[]s ( b9omials or polynomials are m>k$ by prefix+ ! capital lett]s ,q 7= squ>e71 ,c 7= cube71 ,,qq 7= ! f\r? p[]71 ,,qc 7= ! fif? p[]71 etc4 ,oughtr$ does n express aggregation by 774 ,p>5!ses _h be5 us$ by ,gir>d1 & by ,clavius z e>ly z #afji1bh b did n come into g5]al use 9 ma!matical language until ! "t ( ,leibniz & ! ,b]n\llis4 ,oughtr$ indicates aggregation by writ+ a colon 737 at bo? ends4 ,?us1 ,q3,a-,e3 means ) him 7,a-,e74 ,simil>ly1 q3,a,e3 means 7,a,e74 ,! two dots at ! end are frequ5tly omitt$ :5 ! "p affect$ includes all ! t]ms ( ! polynomial to ! end4 ,?us1 ,c3,a,b-,e44 means 7,a,b-,e744 ,!re are /ill fur!r dep>tures f ?is notation1 b !y occur s seldom t we incl9e to ! int]pretation t !y are simply pr9t]'s errors4 ,= proportion ,oughtr$ uses ! symbol 73374 ,! proportion a3bc3d appe>s 9 8 notation ab33cd4 ,app>5tly1 a proportion 0 n fully recogniz$ 9 ?is day z be+ ! expression ( an equality ( ratios4 ,t probably expla9s :y he did n use "h z 9 ! notation ( ord9>y equations4 ,yet ,oughtr$ mu/ h be5 v close to ! int]pretation ( a proportion z an equality2 = he says 9 8 ,elem5ti decimi ,euclidis decl>atio1 8proportio1 sive ratio aequalis 330 ,t he introduc$ ?is extra symbol :5 ! "o = equality 0 suffici5t is a mis=tune4 ,simplicity dem&s t no unnecess>y symbols be introduc$4 ,h[ev]1 ,oughtr$'s symbolism is c]ta9ly sup]ior to ^? :i* prec$$4 ,consid] ! notation ( ,clavius4#bi ,he wrote #bj3fjd3x1 x#ab1 ?us3 8#bjfjd8 fiunt #ab40 ,! insuffici5cy ( su* a notation 9 ! m involv$ expressions frequ5tly aris+ 9 algebra is readily se54 ,h5ce ,oughtr$'s notation 7337 0 e>ly adopt$ by ,engli% ma!maticians4 ,x 0 us$ by ,john ,wallis at ,ox=d1 by ,samuel ,fo/] at ,gre%am ,college1 by ,james ,gregory ( ,ed9burgh1 by ! translators into ,engli% ( ,rahn's algebra1 & by _m o!r e>ly writ]s4 ,oughtr$ has be5 cr$it$ g5]ally ) ! introduction ( ,/4 ,&rew's cross z ! symbol = multiplication 9 ! ,clavis ( #afca4 ,we h discov]$ t ?is symbol1 or r ! lett] x :i* closely resembles x1 occurs z ! sign ( multiplication ?irte5 ye>s e>li] 9 an anonym\s 8,app5dix to ! ,log>i?mes1 %ew+ ! practise ( ! ,calculation ( ,triangles etc40 to ,edw>d ,wright's translation ( ,john ,napi]'s ,descriptio1 publi%$ 9 #afah4cj ,lat] we %all give our reasons = believ+ t ,oughtr$ is ! au?or ( t 8,app5dix40 ,! has surviv$ z a symbol ( multiplication4 ,ano!r symbol introduc$ by ,oughtr$ & f\nd 9 mod]n books is 1 express+ diff]5ce2 ?us ,c,d signifies ! diff]5ce betwe5 ,c & ,d1 ev5 :5 ,d is ! l>g] numb]4#ca ,?is symbol 0 us$ by ,john ,wallis 9 #afeg4cb ,oughtr$ repres5t$ 9 symbols also c]ta9 composite expressions1 z = in/ance ,a,e,z1 ,a-,e,x1 :]e ,a is great] ?an ,e4 ,he repres5t$ by a symbol also ea* ( ! foll[+3 ,a,e1 ,a,e1 ,a-,e1 ,a-,e4 ,oughtr$ practically translat$ ! t5? book ( ,euclid f its pond]\s rhetorical =m into t ( brief symbolism4 ,an appeal to ! eye 0 a passion ) ,oughtr$4 ,! pres5t writ] has collect$ ! diff]5t ma!matical symbols us$ by ,oughtr$ & has f\nd m ?an "o hundr$ & fifty ( !m4 ,! diff]5ces betwe5 ! sev5 diff]5t editions ( ! ,clavis lie ma9ly 9 ! special p>ts app5d$ to "s editions & dropp$ 9 ! late/ editions4 ,! "p :i* orig9ally con/itut$ ! ,clavis 0 n mat]ially alt]$1 except 9 two or ?ree ( ! orig9al tw5ty *apt]s4 ,^! *anges 7 made 9 ! editions ( #afdg & #afdh4 ,aft] ! fir/ edition1 great /ress 0 laid ^u ! !ory ( indices ^u ! v fir/ page1 z also 9 passages f>!r on4 ,( c\rse1 ,oughtr$ did n h our mod]n notation ( indices or expon5ts1 b _! !ory _h be5 a "p ( algebra & ari?metic = "s "t4 ,oughtr$ incorporat$ ?is !ory 9 8 brief exposition ( ! ,h9du-,arabic notation & 9 8 explanation ( log>i?ms4 ,z previ\sly po9t$ out1 ! la/ ?ree *apt]s ( ! #afca edition 7 consid]ably re>rang$ 9 ! lat] editions & comb9$ into two *apt]s1 s t ! ,clavis prop] _h n9ete5 *apt]s in/ead ( tw5ty 9 ! additions aft] ! fir/4 ,^! *apt]s consi/$ ( applications ( algebra to geometry & 7 s fram$ z to con/itute a sev]e te/ ( ! /ud5t's grip ( ! subject4 ,! v la/ problem deals ) ! division ( angles into equal p>ts4 ,he d]ives ! cubic equation ^u :i* ! trisection dep5ds algebraically1 also ! equations ( ! fif? degree & sev5? degree ^u :i* ! divisions ( ! angle into #e & #g equal p>ts dep5d1 respectively4 ,! exposition 0 sev]ely brief1 yet accurate4 ,he did n believe 9 conduct+ ! read] along level pa?s or along slight incl9es4 ,he 0 a guide = m\nta9-climb]s1 & woe unto him :o lack$ n]ve4 ,oughtr$ lays great /ress ^u expansions ( p[]s ( a b9omial4 ,he makes use ( ^! expansions 9 ! solution ( num]ical equations4 ,to "o :o does n specialize 9 ! hi/ory ( ma!matics su* expansions may create surprise1 = did n ,newton inv5t ! b9omial !orem aft] ! dea? ( ,oughtr$8 ,z a matt] ( fact1 ! expansions ( positive integral p[]s ( a b9omial 7 kn[n long be=e ,newton1 n only to sev5te5?-c5tury b ev5 to elev5?-c5tury ma!maticians4 ,oughtr$'s ,clavis ( #afca gave ! b9omial coeffici5ts = all p[]s up to & includ+ ! t5?4 ,:at ,newton really accompli%$ 0 ! g5]alization ( ! b9omial expansion :i* makes x applicable to negative & fractional expon5ts & conv]ts x into an inf9ite s]ies4 ,z a specim5 ( ,oughtr$'s /yle ( writ+ we quote 8 solution ( quadratic equations1 accompani$ by a translation into ,engli% & into mod]n ma!matical symbols4 ,z a prelim9>y /ep#cc he lets ,z,a,e & ,a,e2 he lets also ,x,a-,e4 ,f ^! relations he obta9s id5tities :i*1 9 mod]n notation1 are ,z-,,ae7,z-,e7,x4 ,n[1 if we "k ,z & ,,ae1 we c f9d ,x4 ,!n 7,z,x7,a1 & 7,z-,x7,e1 & ,a,z7,z-,,ae74 ,hav+ e/abli%$ ^! prelim9>ies1 he proce$s ?us3 ,datis igitur l9ea inaequalit] secta ,z 7#aj71 rectangulo sub segm5tis ,,ae 7#ba7 qui gnomon e/3 datur semidiff]5tia segm5torum ,x3 p] consequ5s ipsa segm5ta4 ,nam ponatur alt]utrum segm5tum ,a3 alt]um erit ,z-,a3 ,rectangulum auctem e/ ,,za-,aq,,ae4 ,et quia dantur ,z ,,ae3 e/que ,zq-,,ae,xq3 p] #e;c4 #ah1 ,z,x,a3 ,z-,x,e3 ,aequatio sic resoluetur3 ,zq3,zq-,,ae3,a maius segm5t_/m9us segm5t4 ,itaque proposita equatione1 9 qua sunt tres species aequalit] 9 ord9e tabellae adsc5d5tes1 altissima autem species ponitur negata3 ,magnitudo data coeffici5s m$iam speciem e/ l9ea bisec&a3 magnitudo absoluta data1 ad quam sit aequatio1 e/ rectangulum sub segm5tis inaequalibus1 s9e gnomon3 vt ,,za-,aq,,ae3 9 num]is autem #ajl-lq#ba3 ,e/que ,a1 vel #al1 alt]utrum segm5tum inaequale4 ,inu5itur autem sic3 ,dimidiata coeffici5s m$ian speciem e/ ,z_/#b 7#e72 cuius quadratum e/ ,zq_/#d 7#be73 ex hoc tolle ,,ae 7#ba7 absolutum3 eritque ,zq_/#d-;,,ae 7#d7 quadratum semidiff]5tiae segm5torum3 latus huius quadratum 7#b7 e/ semidiff]5tia3 quam si addas ad ,z_/#b 7#e7 semissem coeffici5tis1 sive l9eae bisec&ae1 erit maius segm5t42 s9 detrahas1 erit m9us segm5t3 ,dico ,z_/#bq3,zq_/#d-;,,ae3,a maius segm5tum_/m9us segm5tum4 ,we translate ! ,lat9 passage1 us+ ! mod]n expon5tial notation & p>5!ses1 z foll[s3 ,giv5 !re=e an unequally divid$ l9e ,z 7#aj71 & a rectangle b5ea? ! segm5ts ,,ae 7#ba7 :i* is a gnomon4 ,half ! diff]5ce ( ! segm5ts ,x is giv51 & consequ5tly ! segm5t itself4 ,=1 if "o ( ! two segm5ts is plac$ equal to ,a1 ! o!r w be ,z-,a4 ,moreov]1 ! rectangle is ,,za-,a,,ae4 ,& because ,z & ,,ae are giv51 & !re is ,z-,,ae,x1 & by #e;c4#ah1 ,z,x,a1 & ,z-,x,e1 ! equation w be solv$ ?us3 ,z7,z-,,ae7,a major segm5t_/m9or segm5t4 ,& s an equation hav+ be5 propos$ 9 :i* ?ree species 7t]ms7 are 9 equally asc5d+ p[]s1 ! highe/ species1 moreov]1 be+ negative1 ! giv5 magnitude :i* con/itutes ! middle species is ! l9e to be bisect$4 ,& ! giv5 absolute magnitude to :i* x is equal is ! rectangle b5ea? ! unequal segm5ts1 )\t gnomon4 ,z ,,za-,a,,ae1 or 9 numb]s1 #ajx-x#ba4 ,& ,a or x is "o ( ! two unequal segm5ts4 ,x may be f\nd ?us3 ,! half ( ! middle species is ,z_/#b 7#e71 its squ>e is ,z_/#d 7#be74 ,f x subtract ! absolute t]m ,,ae 7#ba71 & ,z_/#d-;,,ae 7#d7 w be ! squ>e ( half ! diff]5ce ( ! segm5ts4 ,! squ>e root ( ?is1 7,z_/#b7-;,,ae 7#b71 is half ! diff]5ce4 ,if y add x to half ! coeffici5t ,z_/#b 7#e71 or half ! l9e to be bisect$1 ! long] segm5t is obta9$2 if y subtract x1 ! small] segm5t is obta9$4 ,i say3 ,z_/#b7,z_/#d-;,,ae7,a major segm5t_/m9or segm5t4 ,! quadratic equation ,aq,,za,,ae receives simil> treatm5t4 ,?is & ! prec$+ equation1 ,,za-,aq,,ae1 con/itute toge!r a solution ( ! g5]al quadratic equation1 xaxb1 provid$ t ,e or ,z are n re/rict$ to positive values1 b admit ( be+ ei!r positive or negative1 a case n adequately treat$ by ,oughtr$4 ,imag9>y numb]s & imag9>y roots receive no consid]ation :atev]4 ,a notation sugge/$ by ,vieta & favor$ by ,gir>d made v[els /& = unkn[ns & consonants = kn[ns4 ,?is conv5tionality 0 adopt$ by ,oughtr$ 9 p>ts ( 8 algebra1 b n ?r\gh\t4 ,ne> ! beg9n+ he us$ ,q to designate ! unkn[n1 ?\gh usually ?is lett] /ood ) him = ! 8squ>e0 ( ! expression aft] x4#cd ,x is ( "s int]e/ t ,oughtr$ us$ _/ to signify ! ratio ( ! circumf]5ce to ! diamet] ( a circle4 ,v probably ?is notation is ! =]unn] ( ! #c4adaei 4 4 4 4 us$ 9 #agjf by ,william ,jones4 ,oughtr$ fir/ us$ _/ 9 ! #afdg edition ( ! ,clavis ma!maticae4 ,9 ! #afeb edition he says1 8,si 9 circulo sit #g4bb3333aac4cee3;erit 33#b ,r4,p3 p]iph40 ,?is notation 0 adopt$ by ,isaac ,b>r[1 :o us$ x ext5sively4 ,david ,gregory#ce us$ _/ 9 #afig1 & ,de ,moivre#cf us$ c_/r ab\t #afig1 to designate ! ratio ( ! circumf]5ce to ! radius4 ,we quote ! description ( ! ,clavis t 0 giv5 by ,oughtr$'s greate/ pupil1 ,john ,wallis4 ,x conta9s additional in=mation ( int]e/ to u4 ,wallis devotes *ap4 xv ( 8 ,treatise ( ,algebra1 ,london1 #afhe1 pp4 #fg-fi1 to ,mr4 ,oughtr$ & 8 ,clavis1 say+3 ,mr4 ,william ,oughtr$ 7our ,c\ntry-man7 9 8 ,clavis ,ma!maticae1 7or ,key ( ,ma!maticks17 fir/ publi%$ 9 ! ,ye> #afca1 foll[s ,vieta 7z he did ,diophantus7 9 ! use ( ! ,cossick ,d5om9ations2 omitt+ 7z he _h done7 ! names ( ,sursolids1 & cont5t+ himself ) ^? ( ,squ>e & ,cube1 & ! ,comp\nds ( ^!4 ,b he do? abridge ,vieta's ,*>act]s or ,species1 us+ only ! lett]s q1 c1 c4 :i* 9 ,vieta are express$ 7at l5g?7 by ,quadrate1 ,cube1 c4 ,= ?\gh :5 ,vieta fir/ introduc$ ?is way ( ,speci\s ,ari?metick1 x 0 m necess>y 7! ?+ be+ new17 to express x 9 words at l5g?3 ,yet :5 ! ?+ 0 once receiv$ 9 practise1 ,mr4 ,oughtr$ 7:o affect$ brevity1 & to deliv] :at he taught z briefly z might be1 & r$uce all to a %ort view17 cont5t$ himself ) s+le ,lett]s in/ead ( ^? words4 ,?us :at ,vieta w\ld h writt5 ,a ,quadrate1 into ,b ,cube1 ------------------------ ,equal to ,,fg ,plane1 ,,cde ,solid1 w\ld ) him be ?us express$ ,aq ,bc ------- ,,fg4 ,c ,d ,e ,& ! bett] to di/+ui% ^u ! fir/ view1 :at quantities 7 ,kn[n1 & :at ,unkn[n1 he do? 7usually7 d5ote ! ,kn[n to ,consonants1 & ! ,unkn[n by ,v[els2 z ,vieta 7= ! same reason7 _h done be=e him4 ,he do? also 7to v great advantage7 make use ( sev]al ,ligatures1 or ,comp5di\s ,notes1 to signify ,summs1 ,diff]5ces1 & ,rectangles ( sev]al ,quantities4 ,z = in/ance1 ,( two ,quantities ,a 7! ,great]71 & ,e 7! ,less]71 ! ,sum he calls ,z1 ! ,diff]5ce ,x1 ! ,rectangle ,,ae4 4 4 4 4 ,:i* be+ ( 7almo/7 a con/ant signification ) him ?r\gh\t1 d save a great circumlocution ( words1 7ea* ,lett] s]v+ in/ead ( a ,def9ition27 & are also made use ( 7) v great advantage7 to discov] ! true nature ( div]s intricate ,op]ations1 aris+ f ! v>i\s compositions ( su* ,p>ts1 ,sums1 ,diff]5ces1 & ,rectangles2 7( :i* !re is great pl5ty 9 8 ,clavis1 ,cap4 #aa1 #af1 #ah1 #ai4 & else:]e17 :i* )\t su* ,ligatures1 or ,comp5di\s ,notes1 w\ld n be easily discov]$ or appreh5d$4 4 4 4 4 ,i "k !re are :o f9d fault ) 8 ,clavis1 z too obscure1 because s %ort1 b )\t cause2 = 8 words be always full1 b n ,r$undant1 & ne$ only a little att5tion 9 ! ,read] to weigh ! =ce ( e ^w1 & ! ,syntax ( x2 4 4 4 4 ,& ?is1 :5 once appreh5d$1 is mu* m easily reta9$1 ?an if x 7 express$ ) ! prolixity ( "s o!r ,writ]s2 :]e a ,read] mu/ fir/ be at ! pa9s to we$ out a great deal ( sup]flu\s ,language1 t he may h a %ort prospect ( :at is mat]ial2 :i* is "h contract$ = him 9 a %ort ,synopsis4 4 4 4 4 ,mr4 ,oughtr$ 9 8 ,clavis1 cont5ts himself 7= ! mo/ "p7 ) ! solution ( ,quadratick ,equations1 )\t proce$+ 7or v sp>+ly7 to ,cubick ,equations1 & ^? ( ,high] ,p[]s2 hav+ design$ t ,"w = an ,introduction into ,algebra s f>1 leav+ ! ,discussion ( ,sup]ior ,equations = ano!r "w4 4 4 4 4 ,he cont5ts himself likewise 9 ,resolv+ ,equations1 to take notice ( ! ,affirmative or ,positive ,roots2 omitt+ ! ,negative or ,ablative ,roots1 & su* z are call$ ,imag9>y or ,impossible ,roots4 ,& ( ^? :i*1 he calls ,ambigu\s ,equations1 7z hav+ m ,affirmative ,roots ?an "o17 he do? n 7t ,i rememb]7 any :]e take notice ( m ?an ,two ,affirmative ,roots3 7,because 9 ,quadratick ,equations1 :i* are ^? he h&le?1 !re are inde$ no m47 ,:]eas yet 9 ,cubick ,equations1 !re may be ,?ree1 & 9 ^? ( ,high] ,p[]s1 yet m4 ,:i* ,vieta 0 well aw>e (1 & m5tione? 9 "s ( 8 ,writ+s2 & ( :i* ,mr4 ,oughtr$ c\ld n be ignorant4 8,,circles ,,( ,,proportion0 ,,& 8,,trigonometrie0 ,oughtr$ wrote & _h publi%$ ?ree important ma!matical books1 ! ,clavis1 ! ,circles ( ,proportion1#cg & a ,trigonometrie4#ch ,?is la/ appe>$ 9 ! ye> #afeg at ,london1 9 bo? ,lat9 & ,engli%4 ,x is claim$ t ! trigonometry 0 8nei!r f9i%$ nor publi%$ by himself1 b collect$ out ( 8 scatt]$ pap]s2 & ?\gh he conniv$ at ! pr9t+ x1 yet imp]fectly done1 z appe>s by 8 ,,mss42 & "o ( ! pr9t$ ,books1 correct$ by 8 own ,h&40#ci ,d\btless m accurate on ?is po9t is a lett] ( ,ri*>d ,/okes :o saw ! book ?r\gh ! press3 ,i h procur$ y\r ,trigonometry to be writt5 ov] 9 a fair h&1 :i* :5 f9i%$ ,i w s5d to y1 to "k if x be accord+ to y\r m9d2 = ,i int5d 7s9ce y 7 pleas$ to give y\r ass5t7 to endeav\r to pr9t x ) ,mr4 ,briggs 8 ,tables1 & s soon z ,i c get ! ,prut5ic ,tables ,i w turn ^? ( ! sun & moon1 & s5d !m to y4#dj ,9 ! preface to ! ,lat9 edition ,/okes writes3 ,s9ce ?is trigonometry 0 writt5 = private use )\t ! int5tion ( hav+ x publi%$1 x pleas$ ! ,rev]5d ,au?or1 be=e all[+ x to g to press1 to expunge "s ?+s1 to *ange o!r ?+s & ev5 to make "s additions & ins]t m lucid me?ods ( exposition4 ,?is mu* is c]ta91 ! ,trigonometry be>s ! impress *>act]i/ic ( ,oughtr$4 ,l all 8 ma!matical writ+s1 ! book 0 v cond5s$4 ,aside f ! tables1 ! text cov]$ only #cf pages4 ,plane & sph]ical triangles 7 tak5 up toge!r4 ,! treatise is kn[n 9 ! hi/ory ( trigonometry z among ! v e>lie/ works to adopt a cond5s$ symbolism s t equations involv+ trigonometric functions c\ld be easily tak5 9 by ! eye4 ,9 ! "w ( #afeg1 contractions are giv5 z foll[s3 ss9e1 ttang5t1 sesecant1 s cocos9e 7s9e complem5t71 t cocotang5t1 se cocosecant1 loglog>i?m1 ,z crusum ( ! sides ( a rectangle or "r angle1 ,x crudiff]5ce ( ^! sides4 ,x has be5 g5]ally ov]look$ by hi/orians t ,oughtr$ us$ ! abbreviations ( trigonometric functions1 nam$ above1 a qu>t] ( a c5tury e>li]1 9 8 ,circles ( ,proportion1 #afcb1 #afcc4 ,moreov]1 he us$ sometimes also ! abbreviations :i* are curr5t at ! pres5t "t1 namely s9s9e1 tantang5t1 secsecant4 ,we "k t ! ,circles ( ,proportion exi/$ 9 manuscript _m ye>s be=e !y 7 publi%$4 ,! symbol sv = s9us v]sus occurs 9 ! ,clavis ( #afca4 ,! great importance ( well-*os5 symbols ne$s no emphasis to read]s ( ! pres5t day4 ,) ref]5ce to ,oughtr$'s trigonometric symbols4 ,augu/us ,de ,morgan said3 ,?is is s v important a /ep1 simple z x is1 t ,eul] is ju/ly held to h greatly advanc$ trigonometry by its introduction4 ,nobody t we "k ( has notic$ t ,oughtr$ 0 ma/] ( ! improvem5t1 & will+ to h taught x1 if p w\ld h le>nt4#da ,we f9d1 h[ev]1 t ev5 ,oughtr$ _c be giv5 ! :ole cr$it 9 ?is matt]4 ,by or be=e #afca sev]al o!r writ]s us$ abbreviations ( ! trigonometric functions4 ,z e>ly z #afbd ! contractions s9 = s9e & tan = tang5t appe> on ! draw+ repres5t+ ,gunt]'s scale1 b ,gunt] did n use !m 9 8 books1 except 9 ! draw+ ( 8 scale4#db ,a clos] competitor = ! honor ( fir/ us+ ^! trigonometric abbreviations is ,ri*>d ,norwood 9 8 ,trigonometrie1 ,london1 #afca1 :]e s /&s = s9e1 t = tang5t1 sc = s9e complem5t 7cos9e71 tc = tang5t complem5t 7cotang5t71 & sec = secant4 ,norwood 0 a tea*] ( ma!matics 9 ,london & a well-kn[n writ] ( books on navigation4 ,aside f ! abbreviations j cit$ ,norwood did n use ne>ly z mu* symbolism 9 8 ma!matics z did ,oughtr$4 ,m5tion %\ld be made ( trigonometric symbols us$ ev5 e>li] ?an any ( ! prec$+1 9 8,an ,app5dix to ! ,log>i?mes1 %ew+ ! practise ( ! ,calculation ( ,triangles1 etc410 pr9t$ 9 ,edw>d ,wright's edition ( ,napi]'s ,a ,description ( ! ,admirable ,table ( ,log>i?mes1 ,london1 #afah4 ,we ref]r$ to ?is 8,app5dix0 9 trac+ ! orig9 ( ! sign 4 ,x conta9s1 on p4 #d1 ! foll[+ passage3 8,= ! ,log>i?me ( an ar* or an angle ,i set be=e 7s71 = ! antilog>i?me or complim5t !re( 7s997 & = ! ,diff]5tial 7t740 ,9 fur!r explanation ( ?is r unsatisfactory passage1 ! au?or 7,oughtr$87 says1 8,z = example3 s,b,,bc,,ca4 t is1 ! ,log>i?me ( an angle ,b4 at ! ,base ( a plane "r-angl$ triangle1 increas$ by ! addition ( ! ,log>i?m ( ,,bc1 ! hypo!nuse !re(1 is equall to ! ,log>i?me ( ,,ca ! ca!tus40 ,"h 8log>i?me ( an angle ,b0 evid5tly means 8log s9 ,b10 j z ) ,napi]1 8,log>i?ms ( ! arcs0 signifies really 8,log>i?ms ( ! s9es ( ! angles40 ,9 ,napi]'s table1 ! numb]s 9 ! column m>k$ 8,diff]5tiae0 signify log s9e m9us log cos9e ( an angle2 t is1 ! log>i?ms ( ! tang5ts4 ,?is expla9s ! contraction 7t7 9 ! 8,app5dix40 ,! conclusion ( all ?is is t z e>ly z #afah ! signs s1 s991 t 7 us$ = s9e1 cos9e1 & tang5t1 respectively4 ,john ,speidell1 9 8 ,breefe ,treatise ( ,spha]icall ,triangles1 ,london1 #afbg1 uses ,si4 = s9e1 ,t4 & ,tan = tang5t1 ,se4 = secant1 ,si4 ,co4 = cos9e1 ,se4 ,co4 = cosecant1 ,t4 ,co4 = cotang5t4 ,! innovation ( designat+ ! sides & angles ( a triangle by ,a1 ,b1 ,c1 & a1 b1 c1 s t ,a 0 opposite a1 ,b opposite b1 & ,c opposite c1 is attribut$ to ,leon>d ,eul] 7#agec71 b 0 fir/ us$ by ,ri*>d ,rawl9son ( ,que5's ,college1 ,ox=d1 sometimes aft] #afee & be=e #affh4 ,oughtr$ did n use ,rawl9son's notation4#dc ,9 trigonometry ,engli% writ]s ( ! fir/ half ( ! sev5te5? c5tury us$ contractions m freely ?an _! cont95tal contempor>ies2 ev5 m freely1 inde$1 ?an ,engli% writ]s ( a lat] p]iod4 ,von ,braunmhl1 ! great hi/orian ( trigonometry1 gives ,oughtr$ mu* praise = 8 trigonometry1 & po9ts out t half a c5tury lat] ! army ( writ]s on trigonometry _h h>dly yet rea*$ ! /&>d set by ,oughtr$'s analysis4#dd ,oughtr$ mu/ be cr$it$ also ) ! fir/ complete pro( t 0 giv5 to ! fir/ two ( 8,napi]'s analogies40 ,8 trigonometry conta9s sev5-place tables ( s9es1 tang5ts1 & secants1 & six-place tables ( log>i?mic s9es & tang5ts2 also sev5-place log>i?mic tables ( numb]s4 ,at ! "t ( ,oughtr$ !re 0 "s agitation 9 favor ( a wid] introduction ( decimal sy/ems4 ,?is movem5t is reflect$ 9 ^? tables :i* conta9 ! c5tesimal division ( ! degree1 a practice :i* is urg$ = g5]al adoption 9 our own day1 p>ticul>ly by ! ,fr5*4 ,,solution ,,( ,,num]ical ,,equations ,9 ! solution ( num]ical equations ,oughtr$ does n m5tion ! s\rces f :i* he drew1 b ! me?od is sub/antially t ( ! great ,fr5* algebrai/ ,vieta1 z expla9$ 9 a publication :i* appe>$ 9 #afjj 9 ,p>is "u ! title1 ,de num]osa pote/atum pur>um atque adfect>um ad exeges9 resolutione tractatus4 ,9 view ( ! fact t ,vieta's process has be5 describ$ inaccurately by lead+ mod]n hi/orians includ+ ,h4 ,hankel#de & ,m4 ,cantor1#df x may be wor? :ile to g into "s detail4#dg ,by !m x is made to appe> z id5tical ) ! proc$ure giv5 lat] by ,newton4 ,! two are n ! same4 ,! diff]5ce lies 9 ! divisor us$4 ,:at is n[ call$ 8,newton's me?od0 is ,newton's me?od z modifi$ by ,joseph ,raphson4#dh ,! ,newton-,raphson me?od ( approximation to ! roots ( an equation f7x7#j is usually giv5 ! =m a-f7a7_/f7a71 :]e a is an approximate value ( ! requir$ root4 ,x w be se5 t ! divisor is f7a74 ,vieta's divisor is diff]5t2 x is f7as7-f7a7-s1 :]e f7x7 is ! left ( ! equation f7x7k1 n is ! degree ( equation1 & s is a unit ( ! d5om9ation ( ! digit next to be f\nd4 ,?us 9 x#dbjjjjx#bdgfeagac1 x c be %[n t #dag is approximately a root2 suppose t a has be5 tak5 to be #djj1 !n s#aj2 b if1 at ! next /ep ( approximation1 a is tak5 to be #daj1 !n s#a4 ,9 ?is example1 tak+ a#djj1 ,vieta's divisor w\ld h be5 #iabjjjj2 ,newton's divisor w\ld h be5 #ijjjjj4 ,a comp>ison ( ,vieta's me?od ) ! ,newton-,raphson me?od reveals ! fact t ,vieta's divisor is m reliable1 b labors "u ! v great disadvantage ( requir+ a mu* l>g] am\nt ( computation4 ,! latt] divisor is accurate en\gh & easi] to compute4 ,altoge!r ! ,newton-,raphson process m>ks a decid$ advance ov] t ( ,vieta4 ,z already /at$1 x is ! me?od ( ,vieta t ,oughtr$ expla9s4 ,! ,engli%man's exposition is an improvem5t on t ( ,vieta1 pr9t$ =ty ye>s e>li]4 ,nev]!less1 ,oughtr$'s explanation is f> f easy to foll[4 ,! !ory ( equations 0 at t "t /ill 9 its primitive /age ( developm5t4 ,algebraic notation 0 n suffici5tly develop$ to enable ! argum5t to be cond5s$ into a =m easily survey$4 ,s complicat$ does ,vieta's process ( approximation appe> t ,m4 ,cantor fail$ to recognize t ,vieta possess$ a uni=m mode ( proc$ure4 ,b :5 "o has 9 m9d ! g5]al expression = ,vieta's divisor :i* we gave above1 "o w recognize t !re 0 m>k$ uni=mity 9 ,vieta's approximations4 ,oughtr$ all[s himself tw5ty-eight sections 9 :i* to expla9 ! process & at ! close _c =be> rem>k+ t #bh is a 8p]fect0 numb] 7be+ equal to ! sum ( its divisors1 #a1 #b1 #d1 #g1 #ad74 ,! e>ly "p ( 8 exposition %[s h[ an equation may be trans=m$ s z to make its roots #aj1 #ajj1 #ajjj1 or #ajm times small]4 ,?is simplifies ! task ( 8locat+ a root02 t is1 ( f9d+ betwe5 :at integ]s ! root lies4 ,tak+ "o ( ,oughtr$'s equations1 x-#gbx#bchfjjx#hgbehae1 ^u divid+ #gbx by #aj1 #bchfjjx by #ajjj1 & #hgbehae by #aj1jjj1 we obta9 x-#gbx#bchfx#hgbe4 ,divid+ bo? sides by x1 we obta9 x#bchf-gbxx7#hgbe4 ,lett+ x#d1 we h #fdbchf-aaebahgd4 ,b #d7hgbe7baha2 #d is too small4 ,next let x#e1 we h #abebchf-ahjahcf4 ,b #e7hgbe7agde2 #e is too l>ge4 ,we take ! less] value1 x#d1 or 9 ! orig9al equation1 x#dj4 ,?is me?od may be us$ to f9d ! second digit 9 ! root4 ,oughtr$ divides bo? sides ( ! equation by x1 & obta9s xx7#bchfjj-gbxx7#hgbehae4 ,he tries x#dg & x#dh1 & f9ds t x#dg4 ,he expla9s also h[ ! la/ computation may be done by log>i?ms4 ,!reby he e/abli%$ = himself ! record ( be+ ! fir/ to use log>i?ms 9 ! solution ( affect$ equations4 ,z an illu/ration ( ,oughtr$'s me?od ( approximation aft] ! root s\ght has be5 locat$1 we h *os5 = brevity a cubic 9 pref]5ce to a qu>tic4 ,we select$ ! equation x#dbjjjjx#bdgfeagac4 ,by ! process expla9$ above a root is f\nd to lie betwe5 x#djj & x#ejj4 ,f ?is po9t on1 ! approximation z giv5 by ,oughtr$ is z %[n on p4 #dc4 ,9 fur!r explanation ( ?is process1 obs]ve t ! giv5 equation is ( ! =m ,lc,cq,l,dc1 :]e ,lc is our x1 ,cq#dbjjjj1 ,dc#bdgfeagac4 ,9 ! fir/ /ep ( approximation1 let ,l,a,e1 :]e ,a#djj & ,e is1 z yet1 undet]m9$4 ,we h ,lc7,a,e7,a#c;,a,e#c;,,ae,e & ,cq,l#dbjjjj7;,a,e74 ,subtract f #bdgfeagac ! sum ( ! kn[n t]ms ,a 78 ,ac7 & #dbjjjj ,a 78 ,cq,a74 ,?is sum is #bcbjjjjjj ! rema9d] is #aefeagac4 8,exemplum ,,ii #a;c#dbjjjjl#bdgfeagac ,hoc e/1 ,lc,cq,l,dc #b #d #g #f #e #a #g #a #c 7 #d #a #g -------------------------------- #d #b #j #j #j #j ,cq -------------------------------- #f #d ,ac #a #f #h #j #j #j #j ,cq ,a -------------------------------- #b #c #b #j #j #j #j ,ablatit4 ,r #a #e #f #e #a #g #a #c -------------------------------- #d #h #c ,aq #a #b #c ,a #d #b #j #j #j #j ,cq -------------------------------- #i #a #b #j #j #j ,divisor4 -------------------------------- #d #h #c ,aq ,e #a #b #c ,a ,eq #a ,ec #d #b #j #j #j #j ,cq ,e -------------------------------- #i #a #b #a #j #j ,ablatit4 ,r #f #e #c #j #g #a #c #d #a -------------------------------- ------------ #e #j #d #c #c ,aq #a #b #c #c ,a #a #f #h #d #b #j #j #j #j ,cq #a -------------------------------- ------------ #i #b #e #e #c #j ,divisor4 #a #f #h #a -------------------------------- #c #e #c #j #a #c ,aq ,e #f #j #b #g #c ,a ,eq #c #d #c ,ec #b #i #d #j #j #j #j ,cq ,e -------------------------------- #f #e #c #j #g #a #c ,ablatit40 ,next1 he evaluates ! coeffici5ts ( ,e 9 #c;,a,e & #dbjjjj;,e1 also #c;,a1 ! coeffici5t ( ,e4 ,he obta9s #c;,a#dhjjjj1 #c;,a#abjj1 ,cq#dbjjjj4 ,he int]prets #c;,a & ,cq z t5s1 #c;,a z hundr$s4 ,accord+ly1 he obta9s z _! sum #iabjjjj1 :i* is ! divisor = f9d+ ! second digit 9 ! approximation4 ,obs]ve t ?is divisor is ! value ( f7as7-f7a7-s 9 our g5]al expression1 :]e a#djj1 s#aj1 n#c1 f7x7x#dbjjjjx4 ,divid+ ! rema9d] #aefeagac by #iabjjjj1 he obta9s ! integ] #a 9 t5's place2 ?us ,e#aj1 approximately4 ,he n[ computes ! t]ms #c;,a,e1 #c;,,ae & ,e to be1 respectively1 #dhjjjjj1 #abjjjj1 #ajjj4 ,_! sum is #iabajjj4 ,subtract+ x f ! previ\s rema9d]1 #aefeagac1 leaves ! new rema9d]1 #fecjgac4 ,f "h on ea* /ep is a repetition ( ! prec$+ /ep4 ,! new ,a is #daj1 ! new ,e is to be det]m9$4 ,we h n[ 9 clos] approximation1 ,l,a,e4 ,?is "t we d n subtract ,a & ,cq,a1 because ?is subtraction is already affect$ by ! prec$+ "w4 ,we f9d ! second trial divisor by comput+ ! sum ( #c;,a1 #c;,a & ,cq2 t is1 ! sum ( #ejdcjj1 #abcj1 #dbjjjj1 :i* is #ibeecj4 ,aga91 ?is divisor c be comput$ by our g5]al expression = divisors1 by tak+ a#daj1 s#a1 n#c4 ,divid+ #fecjgac by #ibeecj yields ! integ] #g4 ,?us ,e#g4 ,comput+ #c;,a,e1 #c;,,ae1 ,e & subtract+ _! sum1 ! rema9d] is #j4 ,h5ce #dag is an exact root ( ! giv5 equation4 ,s9ce ! extraction ( a cube root is m]ely ! solution ( a pure cubic equation1 xn1 ! process giv5 above may be utiliz$ 9 f9d+ cube roots4 ,?is is precisely :at ,oughtr$ does 9 *ap4 xiv ( 8 ,clavis4 ,if ! =ego+ computation is modifi$ by putt+ ,cq#j1 ! process w yield ! approximate cube root ( #bdgfeagac4 ,oughtr$ solves #af examples by ! process ( approximation "h expla9$4 ,( ^!1 #i are cubics1 #e are qu>tics1 & #b are qu9tics4 ,9 all cases he f9ds only "o or two real roots4 ,( ! roots s\ght1 five are irrational1 ! rema9+ are rational & are comput$ to _! exact values4 ,?ree ( ! comput$ roots h #b figures ea*1 #i roots h #c figures ea*1 #d roots h #d figures ea*4 ,:ile no attempt is made to secure all ! roots--me?ods ( comput+ complex roots 7 inv5t$ mu* lat]--he computes roots ( equations :i* involve l>ge coeffici5ts & "s ( !m are ( a degree z high z ! fif?4 ,9 view ( ! fact t _m editions ( ! ,clavis 7 issu$1 "o impression z late z #agjb1 x contribut$ probably m ?an any o!r book to ! popul>ization ( ,vieta's me?od 9 ,engl&4 ,be=e ,oughtr$1 ,?omas ,h>riot & ,william ,milb\rn are ! only ,engli%m5 kn[n to h solv$ num]ical equations ( high] degrees4 ,milb\rn publi%$ no?+4 ,h>riot slightly modifi$ ,vieta's process by simplify+ some:at ! =mation ( ! trial divisor4 ,?is me?od ( approximation 0 ! be/ 9 exi/5ce 9 ,europe until ! publication by ,wallis 9 #afhe ( ,newton's me?od ( approximation4 ,x %\ld be /at$ t1 be=e ! "t ( ,newton1 ! be/ me?od ( approximation to ! roots ( num]ical equations exi/$1 n 9 ,europe1 b 9 ,*9a4 ,z e>ly z ! ?irte5? c5tury ! ,*9ese possess$ a me?od :i* is almo/ id5tical ) :at is kn[n today z 8,horn]'s me?od40 ,,log>i?ms ,oughtr$'s treatm5t ( log>i?ms is q 9 accordance ) ! m rec5t practice4#di ,he expla9s ! f9d+ ( ! 8index0 7our 8*>act]i/ic072 he /ates t 8! sum ( two ,log>i?ms is ! ,log>i?m ( ! ,product ( _! ,valors2 & _! diff]5ce is ! ,log>i?m ( ! ,quoti5t10 t 8! ,log>i?m ( ! side #dcf drawn ^u ! ,index numb] #b ( dim5sions ( any ,pote/as is ! log>i?m ( ! same ,pote/as0 #dcf1 t 8! log>i?m ( any ,pote/as #dcf divid$ by ! numb] ( its dim5sions #b af=de? ! ,log>i?m ( its ,root #dcf40 ,^! /atem5ts ( ,oughtr$ occur = ! fir/ "t 9 ! ,key ( ! ,ma!maticks ( #afdg2 ! ,clavis ( #afca conta9s no treatm5t ( log>i?ms4 ,if ! *>act]i/ic ( a log>i?m is negative1 ,oughtr$ indicates ?is fact by plac+ ! - above ! *>act]i/ic4 ,he sep>ates ! *>act]i/ic & mantissa by a comma1 b /ill uses ! sign to indicate decimal fractions4 ,he uses ! contraction 8log40 ,,inv5tion ,,( ,,! ,,slide ,,rule2 ,,controv]sy ,,on ,,priority ,,( ,,inv5tion ,oughtr$'s mo/ orig9al l9e ( sci5tific activity is ! "o lea/ kn[n to ! pres5t g5]ation4 ,augu/us ,de ,morgan1 9 speak+ ( ,oughtr$1 :o 0 sometimes call$ 8,oughtr$ ,aeton5sis10 rem>ks3 8,he is an animal ( ext9ct race1 an ,eton ma!matician4 ,few ,eton m51 ev5 ( ! m9ority :i* kn[s :at a slid+ rule is1 are aw>e t ! inv5tor 0 ( _! own s*ool & college40#ej ,! inv5tion ( ! slide rule has1 until rec5tly1#ea be5 a matt] ( dispute2 x has be5 errone\sly ascrib$ to ,edmund ,gunt]1 ,edmund ,w+ate1 ,se? ,p>tridge1 & o!rs4 ,we h be5 able to e/abli% t ,william ,oughtr$ 0 ! fir/ inv5tor ( slide rules1 ?\gh n ! fir/ to publi% !reon4 ,we %all see t ,oughtr$ inv5t$ slide rules ab\t #afbb1 b ! descriptions ( 8 in/rum5ts 7 n put into pr9t be=e #afcb & #afcc4 ,mean:ile "o ( 8 own pupils1 ,ri*>d ,delama91 :o probably inv5t$ ! circul> slide rule indep5d5tly1 publi%$ a description 9 #afcj1 at ,london1 9 a pamphlet ( #cb pages entitl$ ,grammelogia2 or ! ,ma!maticall ,r+4 ,9 editions ( ?is pamphlet :i* appe>$ dur+ ! foll[+ ?ree or f\r ye>s1 v>i\s p>ts 7 add$ on1 & "s p>ts ( ! fir/ & second editions elim9at$4 ,?us ,delama9 ant$ates ,oughtr$ two ye>s 9 ! publication ( a description ( a circul> slide rule4 ,b ,oughtr$ _h inv5t$ also a rectil9e> slide rule1 a description ( :i* appe>$ 9 #afcc4 ,to ! inv5tion ( ?is ,oughtr$ has a cle> title4 ,a bitt] controv]sy sprang up betwe5 ,delama9 on "o h&1 & ,oughtr$ & "s ( 8 pupils on ! o!r1 on ! priority & indep5d5ce ( inv5tion ( ! circul> slide rule4 ,few inv5tors & sci5tific m5 are s =tunate z to escape conte/s4 ,! read] ne$s only to recall ! disputes :i* h aris51 involv+ ! rese>*es ( ,sir ,isaac ,newton & ,leibniz on ! diff]5tial & integral calculus1 ( ,?omas ,h>riot & ,r5 ,desc>tes relat+ to ! !ory ( equations1 ( ,rob]t ,may]1 ,h]mann von ,helmholtz1 & ,j\le on ! pr9ciple ( ! cons]vation ( en]gy1 or ( ,rob]t ,morse1 ,joseph ,h5ry1 ,gauss & ,web]1 & o!rs on ! telegraph1 to see t que/ions ( priority & indep5d5ce are n uncommon4 ,! controv]sy betwe5 ,oughtr$ & ,delama9 embitt]$ ,oughtr$'s life = _m ye>s4 ,he ref]s to x 9 pr9t on m ?an "o occasion4 ,we %all conf9e ourselves at pres5t to ! /atem5t t x is by no means cle> t ,delama9 /ole ! inv5tion f ,oughtr$2 ,delama9 0 probably an indep5d5t inv5tor4 ,moreov]1 x is highly probable t ! controv]sy w\ld nev] h aris51 _h n "s ( ,oughtr$'s pupils urg$ & =c$ him into x4 ,william ,=/] /at$ 9 ! preface to ! ,circles ( ,proportion ( #afcb t :ile he _h be5 c>efully prep>+ ! manuscript = ! press1 8ano!r to :om ! ,au?or ,oughtr$ 9 a l\+ confid5ce disc\]$ ?is int5t1 us+ m ha/ !n good spe$1 w5t ab\t to preocupate40 ,x 0 ?is passage :i* />t$ ! conflagration4 ,ano!r pupil1 ,w4 ,rob9son1 wrote to ,oughtr$1 :5 ! latt] 0 prep>+ 8 ,apologeticall ,epi/le z a reply to ,delama9's c\nt]*>ges3 8,good sir1 let me be behold5 to y = y\r ,apology :5soev] x comes =?1 & 7if ,i speak n too late7 let me entreat y1 :ip ignorance well on ! bl9d side1 & we may turn him r\nd1 & see :at "p ( him is free40#eb ,z /at$ previ\sly1 ,oughtr$'s circul> slide rule 0 describ$ by him 9 8 ,circles ( ,proportion1 ,london1 #afcb1 :i* 0 translat$ f ,oughtr$'s ,lat9 manuscript & !n se5 ?r\gh ! press by 8 pupil1 ,william ,=/]4 ,9 #afcc appe>$ ,an ,addition vnto ! ,vse ( ! ,in/rvm5t call$ ! ,circles ( ,proportion :i* conta9$ at ! end 8,! ,decl>ation ( ! two ,rul]s = ,calculation10 giv+ a description ( ,oughtr$'s rectil9e> slide rule4 ,?is ,addition 0 b\nd ) ! ,circles ( ,proportion z "o volume4 ,ab\t ! same "t ,oughtr$ describ$ a modifi$ =m ( ! rectil9e> slide rule1 to be us$ 9 ,london = gaug+4#ec ,,*apt] ,,iii ,,m9or ,,works ,among ! m9or works ( ,oughtr$ mu/ be rank$ 8 booklet ( =ty pages to :i* ref]5ce has already be5 made1 entitl$1 ,! ,new ,artificial ,gaug+ ,l9e or ,rod1 ,london1 #afcc4 ,8 diff]5t designs ( slide rules & 8 inv5tions ( sun-dials z well z 8 exposition ( ! mak+ ( wat*es %[ t he display$ unusual int]e/ & tal5t 9 ! v>i\s ma!matical in/rum5ts4 ,a %ort tract on wat*mak+ 0 br\ght out 9 ,london z an app5dix to ! ,horological ,dialogues ( a clock- & wat*mak] :o sign$ himself 8,j4 ,s40 7,john ,smi?874 ,oughtr$'s tract appe>$ ) its own title-page1 b ) pag9ation cont9u$ f ! prec$+ "p1 z ,an ,app5dix :]e9 is conta9$ a ,me?od ( ,calculat+ all ,numb]s = ,wat*es4 ,writt5 orig9ally by t fam\s ,ma!matician ,mr4 ,william ,oughtr$1 & n[ made ,publick4 ,by ,j4 ,s4 ( ,london1 ,clock-mak]4 ,london1 #afge4 8,j4 ,s40 says 9 8 preface3 ,! me?od foll[+ 0 _m ye>s s9ce ,compil$ by ,mr4 ,oughtr$ = ! use ( "s ,+5i\s ,g5tlem5 8 fri5ds1 :o = recreation at ! ,univ]sity1 /udi$ to f9d out ! reason & ,k ( ,wat*-"w1 :i* seem$ also to be a ?+ ) :i* ,mr4 ,oughtr$ himself 0 mu* affect$1 z may 9 "p appe> by 8 putt+ out ( 8 own ,son to ! same ,trade1 = ^: use 7z ,i am in=m$7 he did compile a l>g] tract1 b :at became ( x _c be kn[n4 ,not)/&+ ,oughtr$'s m>k$ activity 9 ! design ( ma!matical in/rum5ts1 & 8 use ( survey+ in/rum5ts1 he always spoke 9 deprecat+ t]ms ( _! importance & _! educational value4 ,9 8 epi/le aga9/ ,delama9 he says3 ,! ,in/rum5ts ,i doe n value or weigh "o s+le p5ny4 ,if ,i _h be5 ambiti\s ( praise1 or _h ?\ght !m 7or bett] !n !y7 wor?y1 at :i* to h tak5 my rise1 out ( my secure & quiet obscuritie1 to m\nt up into glory1 & ! k ( m53 ,i c\ld h done x _m ye>es be=e4 4 4 4 4 ,long agoe1 :5 ,i 0 a "y /ud5t ( ! ,ma!maticall ,sci5ces1 ,i try$ _m wayes & devices to fit my selve ) "s good ,diall or ,in/rum5t portable = my pocket1 to f9de ! h\re1 & try o!r conclusions by1 & accord+ly fram$ = t my purpose bo? ,quadrants1 & ,r+s1 & ,cyl9d]s1 & _m o!r composures4 ,yet n to my full cont5t & satisfaction2 = ei!r !y p]=m$ b little1 or els 7 pat*$ up ) a div]sity ( l9es by an unnaturall & =c$ contexture4 ,at la/ ,i 4 4 4 4 f\nd :at ,i _h be=e ) mu* /udie & pa9es 9 va9e s\ght =4#ed ,m5tion has be5 made 9 ! previ\s pages ( two ( 8 pap]s on sun-dials1 prep>$ 7z he says7 :5 he 0 9 8 tw5ty-?ird ye>4 ,! fir/ 0 publi%$ 9 ! ,clavis ( #afdg4 ,! second pap] appe>$ 9 8 ,circles ( ,proportion4 ,bo? be=e & aft] ! "t ( ,oughtr$ mu* 0 writt5 on sun-dials4 ,su* in/rum5ts 7 set up aga9/ ! walls ( prom95t build+s1 mu* z ! faces ( clocks 9 our "t4 ,! inscriptions t 7 put ^u sun-dials are (t5 v clev]3 8,i c\nt only ! h\rs ( sun%9e10 8,alas1 h[ fleet+40 ,a sun-dial on ! gr\nds ( ,m]*i/on ,ca/le1 9 ,ed9burgh1 :]e ! inv5tor ( log>i?ms1 ,john ,napi]1 liv$ = _m ye>s1 be>s ! inscription1 8,ere "t be t9t1 tak t5t ( "t0 7,ere "t be lo/1 take he$ ( "t74 ,portable sun-dials 7 sometimes c>ri$ 9 pockets1 z we c>ry wat*es4 ,?us ,%akespe>e1 9 ,z ,y ,l ,x1 ,act ,,ii1 sc4 vii3 8,& !n he drew a diall f 8 poke40 ,wat*es 7 fir/ made = c>ry+ 9 ! pocket ab\t #afeh4 ,because ( ?is lit]>y1 sci5tific1 & practical int]e/ 9 me?ods ( indicat+ "t x is n surpris+ t ,oughtr$ devot$ himself to ! ma/]y & ! advancem5t ( me?ods ( "t-measurem5t4 ,besides ! acc\nts previ\sly not$1 !re came f 8 p53 ,! ,description & ,use ( ! d\ble ,horizontall ,dyall3 ,:]eby n onely ! h[] ( ! day is %ewne2 b also ! ,m]idian ,l9e is f\nd3 ,& mo/ ,a/ronomical ,que/ions1 :i* may be done by ! ,globe1 are resolv$4 ,inv5t$ & writt5 by ,w4 ,o41 ,london1 #afcf4 ,! 8,horizontall ,dyall0 & 8,horologicall ,r+0 appe>$ aga9 z app5dixes to ,oughtr$'s translation f ! ,fr5* ( a book on ma!matical recreations4 ,! f\r? ,fr5* edition ( t "w appe>$ 9 #afbg at ,p>is1 "u ! title ( ,recreations ma!matiqve1 writt5 by 8,h5ry van ,ett510 a pseudonym = ! ,fr5* ,jesuit ,jean ,leure*on 7#aeia-afij74 ,engli% editions appe>$ 9 #afcc1 #afec1 & #afgd4 ,! full title ( ! #afec edition conveys an idea ( ! cont5ts ( ! text3 ,ma!matical ,recreations1 or1 ,a ,collection ( _m ,problemes1 extract$ out ( ! ,anci5t & ,mod]n ,philosoph]s1 z ,secrets & ,exp]im5ts 9 ,ari?metick1 ,geometry1 ,cosmographie1 ,horologiographie1 ,a/ronomie1 ,navigation1 ,musick1 ,opticks1 ,ar*itecture1 ,/atick1 ,me*anicks1 ,*emi/ry1 ,wat]-works1 ,fire-works1 c4 ,n vulg>ly manife/ till n[4 ,writt5 fir/ 9 ,greek & ,lat91 lately compil'd 9 ,fr5*1 by ,h5ry ,van ,ett51 & n[ 9 ,engli%1 ) ! ,exam9ations & ,augm5tations ( div]s ,mod]n ,ma!maticians4 ,:]eunto is add$ ! ,description & ,use ( ! ,g5]all ,horologicall ,r+4 ,& ,! ,d\ble ,horizontall ,diall4 ,inv5t$ & writt5 by ,william ,oughtr$4 ,london1 ,pr9t$ = ,william ,leake1 at ! ,signe ( ! ,cr[n 9 ,fleet-/reet1 betwe5 ! two ,temple-,gates4 ,,mdcliii4 ,! graphic solution ( sph]ical triangles by ! accurate draw+ ( ! triangles on a sph]e & ! measurem5t ( ! unkn[n p>ts 9 ! draw+ 0 expla9$ by ,oughtr$ 9 a %ort tract :i* 0 publi%$ by 8 son-9-law1 ,*ri/oph] ,brookes1 "u ! foll[+ title3 ,! ,solution ( all ,spha]ical ,triangles bo? "r & oblique ,by ! ,planispha]e3 ,:]eby two ( ! ,spha]ical p>tes s\ght1 are at "o position mo/ easily f\nd out4 ,publi%$ ) cons5t ( ! ,au?or1 ,by ,*ri/oph] ,brookes1 ,ma!matique ,in/rum5t-mak]1 & ,manciple ( ,wadham ,coll$ge1 9 ,ox=d4 ,brookes says 9 ! preface3 ,i h (t5times se5 my ,rev]5d fri5d ,mr4 ,w4 ,o4 9 8 resolution ( all spha]icall triangles bo? "r & oblique1 to use a planispha]e1 )\t ! t$i\s lab\r ( ,trigonometry by ! ord9>y ,canons3 :i* planispha]e he _h del9eat$ ) 8 own h&s1 & us$ 9 8 calculations m ?an ,=ty ye>s be=e4 ,int]e/+ z "o ( our s\rces f :i* ,oughtr$ obta9$ 8 k ( ! conic sections is 8 /udy ( ,mydorge4 ,a tract :i* he wrote !reon 0 publi%$ by ,jonas ,moore1 9 8 ,ari?metick 9 two books 4 4 4 4 conta9+ also ! two fir/ books ( ,mydorgius 8 conical sections analyz$ by t rev]5d dev9e ,mr4 ,w4 ,oughtr$1 ,engli%$ & complet$ ) cuts4 ,london1 #affj4 ,ano!r edition be>s ! date #afhh4 ,to be not$ among ! m9or works ( ,oughtr$ are 8 po/hum\s pap]s4 ,he left a consid]able numb] ( ma!matical pap]s :i* 8 fri5d ,sir ,*>les ,sc>bor\gh _h revis$ "u 8 direction & publi%$ at ,ox=d 9 #afgf 9 "o volume "u ! title1 ,gulielmi ,oughtr$i1 ,eton5sis1 quondam ,collegii ,regalis 9 ,cantabrigia ,socii1 ,opuscula ,ma!matica hact5us in$ita4 ,its n9e tracts are ( little int]e/ to a mod]n read]4 ,"h we wi% to give our reasons = our belief t ,oughtr$ is ! au?or ( an anonym\s tract on ! use ( log>i?ms & on a me?od ( log>i?mic int]polation :i*1 z previ\sly not$1 appe>$ z an 8,app5dix0 to ,edw>d ,wright's translation into ,engli% ( ,john ,napi]'s ,descriptio1 "u ! title1 ,a ,description ( ! ,admirable ,table ( ,log>i?mes1 ,london1 #afah4 ,! 8,app5dix0 be>s ! title1 8,an ,app5dix to ! ,log>i?mes1 %[+ ! practise ( ! ,calculation ( ,triangles1 & also a new & ready way = ! exact f9d+ out ( su* l9es & ,log>i?mes z are n precisely to be f\nd 9 ! ,canons40 ,x is an able tract4 ,a natural guess is t ! editor ( ! book1 ,samuel ,wright1 a son ( ,edw>d ,wright1 compos$ ?is 8,app5dix40 ,m probable is ! conjecture :i* 7,dr4 ,j4 ,w4 ,l4 ,glai%] in=ms me7 0 made by ,augu/us ,de ,morgan1 attribut+ ! au?or%ip to ,oughtr$4 ,two reasons 9 support ( ?is are advanc$ by ,dr4 ,glai%]1 ! use ( x 9 ! 8,app5dix0 z ! sign ( multiplication 7to ,oughtr$ is g5]ally attribut$ ! introduction ( ! cross = multiplication 9 #afca71 & ! !n unusual designation 8ca!tus0 = ! v]tical leg ( a "r triangle1 a t]m appe>+ 9 ,oughtr$'s books4 ,we are able to advance a ?ird argum5t1 namely1 ! occurr5ce 9 ! 8,app5dix0 ( 7,s997 z ! notation = s9e complem5t 7cos9e71 :ile ,se? ,w>d1 an e>ly pupil ( ,oughtr$1 9 8 ,idea trigonometriae demon/ratae1 ,ox=d1 #afed1 us$ a simil> notation 7,s'74 ,x has be5 /at$ else:]e t ,oughtr$ claim$ ,se? ,w>d's exposition ( trigonometry z virtually 8 own4 ,att5tion %\ld be call$ also to ! fact t1 9 8 ,trigonometria1 p4 #b1 ,oughtr$ uses 7'7 to designate #ahj-;angle4 ,dr4 ,j4 ,w4 ,l4 ,glai%] is ! fir/ to call att5tion to o!r po9ts ( int]e/ 9 ?is 8,app5dix40 ,! int]polations are effect$ ) ! aid ( a small table conta9+ ! log>i?ms ( #gb s9es4 ,except = ! omission ( ! decimal po9t1 ^! log>i?ms are natural log>i?ms--! fir/ ( _! k9d ev] publi%$4 ,9 ?is table we f9d log #ajbcjbehd2 9 mod]n notation1 ?is is /at$1 loge #ajb4cjbehd4 ,! fir/ m ext5d$ table ( natural log>i?ms ( numb]s 0 publi%$ by ,john ,speidell 9 ! #afbb impression ( 8 ,new ,log>i?mes1 :i* conta9s1 besides trigonometric tables1 ! log>i?ms ( ! numb]s #a-ajjj4 ,! 8,app5dix0 conta9s also ! fir/ acc\nt ( a me?od ( comput+ log>i?ms1 call$ ! 8radix me?od10 :i* is usually attribut$ to ,briggs :o appli$ x 9 8 ,ari?metica log>i?mica1 #afbd4 ,9 g5]al1 ?is me?od consi/s 9 multiply+ or divid+ a numb]1 ^: log>i?m is s\ght1 by a suitable factor & resolv+ ! result into factors ( ! =m #ax_/#aj4 ,! log>i?m ( ! numb] is !n obta9$ by add+ ! previ\sly calculat$ log>i?ms ( ! factors4 ,! me?od has be5 repeat$ly r$iscov]$1 by ,fl[] 9 #agga1 ,atwood 9 #aghf1 ,leonelli 9 #ahjb1 ,mann+ 9 #ahjf1 ,w$dle 9 #ahde1 ,he>n 9 #ahdg1 & ,or*>d 9 #ahdh4 ,we conclude ) ! words ( ,dr4 ,j4 ,w4 ,l4 ,glai%]3 ,! ,app5dix 0 an int]e/+ & rem>kable contribution to ma!matics1 = 9 its sixte5 small pages x conta9s 7#a7 ! fir/ use ( ! sign 2 7#b7 ! fir/ abbreviations1 or symbols1 = ! s9e1 tang5t1 cos9e1 & cotang5t2 7#c7 ! inv5tion ( ! radix me?od ( calculat+ log>i?ms2 7#d7 ! fir/ table ( hyp]bolic log>i?ms4#ee ,,*apt] ,,iv ,,oughtr$',s ,,influ5ce ,,^u ,,ma!matical ,,progress ,,& ,,tea*+ ,,oughtr$ ,,& ,,h>riot ,oughtr$'s ,clavis ma!maticae 0 ! mo/ influ5tial ma!matical publication 9 ,great ,brita9 :i* appe>$ 9 ! int]val betwe5 ,john ,napi]'s ,mirifici log>i?morum canonis descriptio1 ,ed9burgh1 #afad1 & ! "t1 =ty ye>s lat]1 :5 ,john ,wallis began to publi% 8 important rese>*es at ,ox=d4 ,! ye> #afca is ( int]e/ z ! date ( publication1 n only ( ,oughtr$'s ,clavis1 b also ( ,?omas ,h>riot's ,artis analyticae praxis4 ,we h no evid5ce t ^! two ma!maticians ev] met4 ,?r\gh _! writ+s !y did n influ5ce ea* o!r4 ,h>riot di$ t5 ye>s be=e ! appe>ance ( 8 magnum opus1 or t5 ye>s be=e ! publication ( ,oughtr$'s ,clavis4 ,/rangely1 ,oughtr$1 :o surviv$ ,h>riot ?irty-n9e ye>s1 nev] m5tions him4 ,!re is no d\bt t1 ( ! two1 ,h>riot 0 ! m orig9al m9d1 m capable ( p5etrat+ into new fields ( rese>*4 ,b he _h ! mis=tune ( hav+ a /rong competitor 9 ,r5 ,desc>tes 9 ! developm5t ( algebra1 s t no s+le algebraic a*ievem5t /&s out /rongly & conspicu\sly z ,h>riot's own contribution to algebraic sci5ce4 ,z a text to s]ve z an introduction to algebra1 ,h>riot's ,artis analyticae praxis 0 inf]ior to ,oughtr$'s ,clavis4 ,! =m] 0 a mu* l>g] book1 n z conv5i5tly portable1 compil$ aft] ! au?or's dea? by o!rs1 & n prep>$ ) ! c>e 9 ! developm5t ( ! details1 nor ) ! coh]5ce & unity & ! pr(\nd p$agogic insight :i* di/+ui% ! "w ( ,oughtr$4 ,nor 0 ,h>riot's position 9 life su* z to be surr\nd$ by s wide a circle ( pupils z 0 ,oughtr$4 ,to be sure1 ,h>riot _h su* foll[]s z ,torporley1 ,william ,l[]1 & ,pro!roe 9 ,wales1 b ?is gr\p is small z comp>$ ) ,oughtr$'s4 ,,oughtr$',s ,,pupils ,!re 0 a l>ge numb] ( di/+ui%$ m5 :o1 9 _! y\?1 ei!r visit$ ,oughtr$'s home & /udi$ "u 8 ro( or else read 8 ,clavis & s\ght 8 assi/ance by correspond5ce4 ,we p]mit ,aubrey to enum]ate "s ( ^! pupils 9 8 own gossipy /yle3 ,se? ,w>d1 ,m4,a41 a fell[ ( ,sydney ,coll$ge 9 ,cambridge 7n[ bi%op ( ,s>um71 came to him1 & liv$ ) him halfe a ye>e 7& he w\ld n take a f>?+ = 8 diet71 & le>n$ all 8 ma!matiques ( him4 ,sir ,jonas ,m 0 ) him a good :ile1 & le>n't2 he 0 b an ord9>y logi/ be=e4 ,sir ,*>les ,sc>bor\gh 0 8 s*ol>2 s ,dr4 ,john ,wallis 0 8 s*ol>2 s 0 ,*ri/oph] ,wr5 8 s*ol>1 s 0 ,mr4 4 4 4 4 ,sme?wyck1 ,regiae ,societatis ,socius4 ,"o ,mr4 ,au/9 7a mo/ +5iose man7 0 8 s*ol>1 & /udy$ s mu* t he became mad1 fell a laugh+1 & s dy$1 to ! great griefe ( ! old g5tleman4 ,mr4 4 4 4 4 ,/okes1 ano!r s*ol>1 fell mad1 & dream't t ! good old g5tleman came to him1 & gave him good advice1 & s he recov]$1 & is /ill well4 ,mr4 ,?omas ,h5%awe1 ,regiae ,societatis ,socius1 0 8 s*ol> 7!n a "y g5tleman74 ,b he did n s mu* l any z ^? t tugg$ & tooke pa9es to worke out que/ions4 ,he taught all free4 ,he c\ld n endure to see a s*ol> write an ill h&2 he taught !m all pres5tly to m5d _! h&s4#ef ,_h ,oughtr$ be5 ! means ( guid+ ! ma!matical /udies ( only ,john ,wallis & ,*ri/oph] ,wr5--"o ! greate/ ,engli% ma!matician betwe5 ,napi] & ,newton1 ! o!r "o ( ! greate/ ar*itects ( ,engl&--he w\ld h e>n$ pr(\nd gratitude4 ,b ! =ego+ li/ embraces n9e m51 mo/ ( !m di/+ui%$ 9 _! day4 ,& yet ,aubrey's li/ is v incomplete4 ,x is easy to m ?an d\ble x by add+ ! names ( ,william ,=/]1 :o translat$ f ,lat9 into ,engli% ,oughtr$'s ,circles ( ,proportion2 ,ar?ur ,haughton1 :o br\ght out ! #affj ,ox=d edition ( ! ,circles ( ,proportion2 ,rob]t ,wood1 an educator & politician1 :o assi/$ ,oughtr$ 9 ! translation ( ! ,clavis f ,lat9 into ,engli% = ! edition ( #afdg2 ,w4 ,gascoigne1 a man ( promise1 :o fell 9 #afdd at ,m>/on ,moor2 ,john ,twysd51 :o 0 active z a publi%]2 ,william ,sudell1 ,n4 ,ew>t1 ,ri*>d ,%uttlewor?1 ,william ,rob9son1 & ,william ,h[>d1 ! son ( ! ,e>l ( ,arundel1 = ^: in/ruction ,oughtr$ orig9ally prep>$ ! manuscript treatise t 0 publi%$ 9 #afca z ! ,clavis ma!maticae4 ,nor mu/ we ov]look ! names ( ,lawr5ce ,rooke 7:o 8did admirably well read 9 ,gre%am ,coll4 on ! six? *apt4 ( ! said book10 ! ,clavis72 ,*ri/oph] ,brookes 7a mak] ( ma!matical in/rum5ts :o m>ri$ a daught] ( ! fam\s ma!matician72 ,william ,lee* & ,william ,bre>ly 7:o ) ,rob]t ,wood 8h be5 ready & helpfull inc\rag]s ( me ,oughtr$ 9 ?is lab\r0 ( prep>+ ! ,engli% ,clavis ( #afdg71 & ,?omas ,:>ton1 :o /udi$ ! ,clavis & assi/$ 9 ! edit+ ( ! edition ( #afdg4 ,! devotion ( ^! pupils (f]s eloqu5t te/imony1 n only ( ,oughtr$'s ability z a ma!matician1 b also ( 8 p[] ( draw+ "y m5 to him--( 8 p]sonal magnetism4 ,nor %\ld we omit f ! li/ ,ri*>d ,delama91 a tea*] ( ma!matics 9 ,london1 :o un=tunately _h a bitt] controv]sy ) ,oughtr$ on ! priority & indep5d5ce ( ! inv5tion ( ! circul> slide rule & a =m ( sun-dial4 ,delama9 became lat] a tutor 9 ma!matics to ,k+ ,*>les ,i1 & p]i%$ 9 ! civil w>1 be=e #afde4 ,,oughtr$1 ,,! 8,,todhunt] ,,( ,,! ,,sev5te5? ,,c5tury0 ,to af=d a cle>] view ( ,oughtr$ z a tea*] & ma!matical expositor we quote "s passages f v>i\s writ]s & f 8 correspond5ce4 ,an?ony ,wood#eg gives an int]e/+ acc\nt ( h[ ,se? ,w>d & ,*>les ,sc>bor\gh w5t f ,cambridge ,univ]sity to ! obscure home ( ! c\ntry ma!matician to be initiat$ into ! my/]ies ( algebra3 ,mr4 ,*a4 ,sc>bor\gh1 !n an +5i\s "y /ud5t & fell[ ( ,caius ,coll4 9 ! same univ]sity1 0 8 ,se? ,w>d's great acqua9tance1 & bo? be+ equally /ud5ts 9 t faculty & desir\s to p]fect !mselves1 !y took a j\rney to ,mr4 ,w4 ,oughtr$ liv+ !n at ,albury 9 ,surrey1 to be in=m$ 9 _m ?+s 9 8 ,clavis ma!matica :i* seem$ at t "t v obscure to !m4 ,mr4 ,oughtr$ treat$ !m ) great humanity1 be+ v mu* pleas$ to see su* +5i\s "y m5 apply !mselves to ^! /udies1 & 9 %ort "t he s5t !m away well satisfi$ 9 _! desires4 ,:5 !y return$ to ,cambridge1 !y aft]w>ds read ! ,clav4 ,ma?4 to _! pupils1 :i* 0 ! fir/ "t t book 0 read 9 ! said univ]sity4 ,mr4 ,laur4 ,rook1 a disciple ( ,oughtr$1 ,i ?9k1 & ,mr4 ,w>d's fri5d1 did admirably well read 9 ,gre%am ,coll4 on ! six? *ap4 ( ! said book1 :i* obta9$ him great repute f "s & great] f ,mr4 ,w>d1 :o ev] aft] _h an especial fav\r = him4 ,an?ony ,wood makes a simil> /atem5t ab\t ,?omas ,h5%aw3 ,:ile he rema9$ 9 t coll4 ,univ]sity ,college1 ,ox=d :i* 0 five ye>s 4 4 4 4 he made an excursion = ab\t #i mon?s to ! fam\s ma!matician ,w4 ,oughtr$ p>son ( ,aldbury 9 ,surrey1 by :om he 0 initiat$ 9 ! /udy ( ma!matics1 & aft]w>ds retir+ to 8 coll4 = a "t1 he at l5g? w5t to ,london1 0 ent]$ a /ud5t 9 ! ,middle ,temple4#eh ,extracts f lett]s ( ,w4 ,gascoigne to ,oughtr$1 ( ! ye>s #afdj & #afda1 ?r[ "s light ^u ma!matical tea*+ ( ! "t3 ,among/ ! ma!matical r>ities ^! times h af=d$1 !re are none ( t small numb] ,i 7a late intrud] into ^! /udies7 h yet view$1 :i* s fully demon/rates _! au?ors' great abilities z y\r ,clavis1 n ri*] 9 augm5tations1 ?an valuable = contraction2 4 4 4 4 ,y\r belief t !re is 9 all inv5tions aliquid div9um1 an infusion beyond human cogitations1 ,i am confid5t w appe> notably /r5g!n$1 if y please to af=d ?is tru? belief1 t ,i ent]$ ^u ^! /udies accid5tally aft] ,i betook myself to ! c\ntry1 hav+ nev] _h s mu* aid z to be taught addition1 nor ! disc\rse ( an arti/ 7hav+ left bo? ,ox=d & ,london be=e ,i knew :at any proposition 9 geometry meant7 to in=m me :at 7 ! be/ au?ors4#ei ,! foll[+ extracts f two lett]s by ,w4 ,rob9son1 writt5 be=e ! appe>ance ( ! #afdg ,engli% edition ( ! ,clavis1 express ! feel+ ( _m read]s ( ! ,clavis on its extreme concis5ess & brevity ( explanation3 ,i %all long exce$+ly till ,i see y\r ,clavis turn$ into a pick-lock2 & ,i besee* y enl>ge x1 & expla9 x :at y c1 = we %all n ne$ to fe> ei!r tautology or sup]fluity2 y are naturally concise1 & y\r cle> judgm5t makes y bo? me?odical & pi?y2 & y\r analytical way is inde$ ! only way4 4 4 4 4 ,i w once aga9 e>ne/ly entreat y1 t y be r diffuse 9 ! sett+ =? ( y\r ,engli% ma!matical ,clavis1 ?an concise1 consid]+ t ! wise/ ( m5 not$ ( old1 & said /ultorum inf9itus e/ num]us1 ^! arts _c be made too easy1 !y are s ab/ruse ( !mselves1 & m5 ei!r s lazy or dull1 t _! fa/idi\s wits take a loa?+ at ! v entrance ( ^! /udies1 unless x be sweet5$ on ) pla9ness & facility4 ,brevity may well argue a le>n$ au?or1 t )\t any excess or r$undance1 ei!r ( matt] or words1 c give ! v sub/ance & ess5ce ( ! ?+ treat$ (2 b x seldom makes a le>n$ s*ol>2 & if "o be capable1 tw5ty are n2 & if ! ma/] sum up 9 brief ! pi? ( 8 own long lab\rs & travails1 x is n easy to imag9e t s*ol>s c ) less lab\r ?an x co/ _! ma/]s dive into ! dep?s !re(4#fj ,"h is ! judgm5t ( ano!r ( ,oughtr$'s fri5ds3 4 4 4 4 ) ! "* ,i receiv$ f y\r & my noble fri5d ,sir ,*>les ,cav5di%1 !n at ,p>is1 ( y\r second edition ( ! same piece1 made me at my return into ,engl& spe$ily to get1 & dilig5tly p]use ! same4 ,nei!r truly did ,i f9d my expectation deceiv$2 hav+ ) admiration (t5 consid]$ h[ x 0 possible 7ev5 9 ! h>de/ ?+s ( geometry7 to deliv] s mu* matt] 9 s few words1 yet ) su* demon/rative cle>ness & p]spicuity3 & ha? (t5 put me 9 m9d ( le>n$ ,m]s5nus 8 judgm5t 7s9ce dead7 ( x1 t !re 0 m matt] compreh5d$ 9 t little book ?an 9 ,diophantus1 & all ! anci5ts4 4 4 4 4#fa ,oughtr$'s own feel+ 0 aga9/ diffus5ess 9 textbook writ+4 ,9 8 revisions ( 8 ,clavis ! orig9al "* ( t book 0 n alt]$4 ,9 8 reply to ,w4 ,rob9son1 ,oughtr$ said3 4 4 4 4 ,b my art = all su* ma!matical inv5tions ,i h set d[n 9 my ,clavis ,ma!matica1 :i* !re=e 9 my title ,i say is tum logi/icae cum analyticae adeoque totius ma!maticae quasi clavis1 :i* if any "o ( a ma!matical g5ius w c>efully /udy1 7& inde$ x mu/ be c>efully /udi$17 he w n admire o!rs1 b himself d wond]s4 ,b ,i 7su* is my t5uity7 h en\gh fungi vice cotis1 acutum r$d]e quae f]rum valet1 exsors ipsa sec&i1 or l ! t\*/one1 :i* be+ b a /one1 base & little wor?1 c %ew ! excell5ce & ri*es ( gold4#fb ,john ,wallis held ,oughtr$'s ,clavis 9 high reg>d4 ,:5 9 correspond5ce ) ,john ,coll9s conc]n+ plans = a new edition1 ,wallis wrote 9 #afff-fg1 six ye>s aft] ! dea? ( ,oughtr$3 4 4 4 4 ,b = ! goodness ( ! book 9 itself1 x is t 7,i confess7 :i* ,i look ^u z a v good book1 & :i* do? 9 z little room deliv] z mu* ( ! fundam5tal & useful "p ( geometry 7z well z ( ari?metic & algebra7 z any book ,i "k2 & :y x %\ld n be n[ acceptable ,i d n see4 ,x is true1 t z 9 o!r ?+s s 9 ma!matics1 fa%ions w daily alt]1 & t :i* ,mr4 ,oughtr$ design$ by great lett]s may be n[ by o!rs be design$ by small2 b a ma!matician w1 ) ! same ease & advantage1 und]/& ,ac1 & a or aaa4 4 4 4 4 ,& ! l ,i judge ( ,mr4 ,oughtr$'s ,clavis1 :i* ,i look ^u 7z ^? pieces ( ,vieta :o fir/ w5t 9 t way7 z la/+ books & classic au?ors 9 ?is k9d2 to :i*1 not)/&+1 e day may make new additions4 4 4 4 4 ,b ,i confess1 z to my own judgm5t1 ,i am n = mak+ ! book bigg]1 because x is contr>y to ! design ( x1 be+ int5d$ = a manual or contract2 :]eas comm5ts1 by enl>g+ x1 d r de/roy x4 4 4 4 4 ,b x 0 by him int5d$1 9 a small epitome1 to give ! sub/ance ( :at is by o!rs deliv]$ 9 l>g] volumes4 4 4 4 4#fc ,t !re cont9u$ to be a gr\p ( /ud5ts & tea*]s :o desir$ a full] exposition ?an is giv5 by ,oughtr$ is evid5t f ! appe>ance1 ov] fifty ye>s aft] ! fir/ publication ( ! ,clavis1 ( a booklet by ,gilb]t ,cl>k1 entitl$ ,oughtr$us ,explicatus1 ,london1 #afhb4 ,a review ( ?is appe>$ 9 ! ,acta ,eruditorum 7,leipzig1 #afhd71 on p4 #afh1 :]e9 ,oughtr$ is nam$ 8cl>issimus ,angliae ma!maticus40 ,john ,coll9s wrote ,wallis 9 #afff-fg t ,cl>k1 8:o lives ) ,sir ,ju/9ian ,i%am1 )9 sev5 miles ( ,nor?ampton1 4 4 4 4 intimates he wrote a comm5t on ! ,clavis1 :i* lay long 9 ! h&s ( a pr9t]1 by :om he 0 abus$1 mean+ ,leyb\rne40#fd ,we %all h occasion bel[ to ref] to ,oughtr$'s inability to secure a copy ( a not$ ,italian ma!matical "w publi%$ a few ye>s be=e4 ,9 ^? days ! condition ( ! book trade 9 ,engl& mu/ h be5 some:at extraord9>y4 ,dr4 ,j4 ,w4 ,l4 ,glai%] ?r[s "s light ^u ?is subject4#fe ,he f\nd 9 ! ,cal5d> ( ,/ate ,pap]s1 ,dome/ic ,s]ies1 #afcg1 a petition to ,ar*bi%op ,laud 9 :i* x is set =? t :5 ,hooganhuys51 a ,dut*man1 8h]et(ore compla9$ ( 9 ! ,high ,commission = import+ books pr9t$ beyond ! seas10 _h be5 b\nd 8n to br+ 9 any m10 "o ,vlacq 7! comput] & publi%] ( log>i?mic tables7 8kept up ! same ag5cy & sold books 9 8 /ead4 4 4 4 4 ,vlacq is n[ prep>+ to g beyond ! seas to avoid answ]+ 8 late br++ ov] n9e bales ( books contr>y to ! decree ( ! ,/> ,*amb]40 ,judgm5t 0 pass$ t1 8,consid]+ ! ill-consequ5ce & sc&al t w\ld arise by /rang]s import+ & v5t+ 9 ?is k+dom books pr9t$ beyond ! seas10 c]ta9 importations be prohibit$1 & seiz$ if br\ght ov]4 ,?is want ( easy int]communication ( results ( sci5tific rese>* 9 ,oughtr$'s "t is reveal$ 9 ! foll[+ lett]1 writt5 by ,oughtr$ to ,rob]t ,keylway1 9 #afde3 ,i speak ?is ! r1 & am induc$ to a bett] confid5ce ( y\r p]=mance1 by reason ( a geometric-analytical art or practice f\nd out by "o ,cavali]i1 an ,italian1 ( :i* ab\t ?ree ye>s s9ce ,i receiv$ in=mation by a lett] f ,p>is1 :]e9 0 praelibat$ only a small ta/e !re(1 yet s t ,i div9e great enl>gem5t ( ! b\nds ( ! ma!matical empire w ensue4 ,i 0 !n v desir\s to see ! au?or's own book :ile my spirits 7 m free & lightsome1 b ,i c\ld n get x 9 ,france4 ,s9ce1 be+ m /ept into ye>s1 daunt$ & brok5 ) ! suff]+s ( ^! disa/r\s times1 ,i mu/ cont5t myself to keep home1 & n put out to any =eign discov]ies4#ff ,x 0 9 #afee1 :5 ,oughtr$ 0 ab\t eighty ye>s old1 t ,john ,wallis1 ! great =]unn] ( ,newton 9 ,great ,brita91 began to publi% 8 great rese>*es on ! ari?metic ( inf9ites4 ,oughtr$ rejoic$ ov] ! a*ievem5ts ( 8 =m] pupil4 ,9 #afee1 ,oughtr$ wrote ,john ,wallis z foll[s3 ,i h ) unspeakable delight1 s f> z my necess>y bus9esses1 ! infirmness ( my heal?1 & ! greatness ( my age 7approa*+ n[ to an end7 w\ld p]mit1 p]us$ y\r mo/ le>n$ pap]s1 ( sev]al *oice argum5ts1 :i* y s5t me3 :]e9 ,i d fir/ ) ?ankfulness ackn[l$ge to ,god1 ! ,fa!r ( lights1 ! great light he ha? giv5 y2 & next ,i congratulate y1 ev5 ) admiration1 ! cle>ness & p]spicacity ( y\r und]/&+ & g5ius1 :o h n only gone1 b also op5$ a way into ^! pr(\nde/ my/]ies ( art1 unkn[n & n ?\ght ( by ! anci5ts4 ,) :i* y\r my/]i\s inv5tions ,i am ! m affect$1 because full tw5ty ye>s ago1 ! le>n$ patron ( le>n+1 ,sir ,*>les ,cav5di%1 %ew$ me a pap] writt51 :]e9 7 "s few excell5t new !orems1 wr\ght by ! way1 z ,i suppose1 ( ,cavali]i1 :i* ,i wr\ght ov] aga9 m agreeably to my way4 ,! pap]1 :]e9 ,i wr\ght x1 ,i %ew$ to _m1 :]e( "s took copies1 b my own ,i _c f9d4 ,i m5tion x = ?is1 because ,i saw !re9 a light break+ out = ! discov]y ( wond]s to be reveal$ to mank9d1 9 ?is la/ age ( ! _w3 :i* light ,i did salute z af> (f1 & n[ at a ne>] di/ance embrace 9 y\r prosp]\s beg9n+s4 ,sir1 t y are pleas$ to m5tion my "n 9 y\r nev] dy+ pap]s1 t is y\r noble fav\r to me1 :o c add no?+ to y\r glory1 b only my applause4 4 4 4 4#fg ,! la/ s5t5ce has ref]5ce to ,wallis' appreciative & eulogi/ic ref]5ce to ,oughtr$ 9 ! preface4 ,x is ( int]e/ to secure ! op9ion ( lat] ,engli% writ]s :o knew ,oughtr$ only ?r\gh 8 books4 ,john ,locke wrote 9 8 j\rnal "u ! date1 ,june #bd1 #afha1 8! be/ algebra yet extant is ,outr$'s40#fh ,john ,coll9s1 :o is kn[n 9 ! hi/ory ( ma!matics *iefly ?r\gh 8 v ext5sive correspond5ce ) ne>ly all ma!maticians ( 8 day1 0 incl9$ to be m critical4 ,he wrote ,wallis ab\t #affg3 ,x 0 n my int5t to disp>age ! au?or1 ?\gh ,i "k _m t did lightly e/eem him :5 liv+1 "s :]e( are at re/1 z ,mr4 ,fo/] & ,mr4 ,gibson4 4 4 4 4 ,y grant ! au?or is brief1 & !re=e obscure1 & ,i say x is b a collection1 :i*1 if himself knew1 he _h done well to h quot$ 8 au?ors1 :]eto ! read] might h repair$4 ,y d n l ^? words ( ,vieta 9 8 !orems1 ex adjunctione plano solidi1 plus quadrato quadrati1 etc41 & ?9k ,mr4 ,oughtr$ ! fir/ t abridg$ ^? expressions by symbols2 b ,i diss5t1 & tell y 'twas done be=e by ,cataldus1 ,geysius1 & ,camillus ,gloriosus1#fi :o 9 8 fir/ decade ( ex]cises1 7n ! fir/ tract17 pr9t$ at ,naples 9 #afbg1 :i* 0 f\r ye>s be=e ! fir/ edition ( ! ,clavis1 propose? ?is equation j z ,i "h give x y1 viz4 #a;ccc#afqcc#daqqc-#bcjd;cc-#ahcfdqc-#ac cjjjqq-#edeje;c#cgbhq#hjfd ,n aequatur #dfjh1 f9ds ,n or a root ( x to be #bd1 & compose? ! :ole out ( x = pro(1 j 9 ,mr4 ,oughtr$'s symbols & me?od4 ,cataldus on ,vieta came out fifte5 ye>s be=e1 & ,i _c quote t1 z n hav+ x by me4 4 4 4 4 ,& z = ,mr4 ,oughtr$'s me?od ( symbols1 ?is ,i say to x2 x may be prop] = y z a comm5tator to foll[ x1 b div]s ,i "k1 m5 ( inf]ior rank t h good skill 9 algebra1 t nei!r use nor approve x4 4 4 4 4 ,is n ,a soon] wrote ?an ,aqc8 ,let ,a be #b1 ! cube ( #b is #h1 :i* squ>$ is #fd3 "o ( ! que/ions betwe5 ,maghet ,grisio & ,gloriosus is :e!r #fd;,acc or ,aqc4 ,! ,c>tesian me?od tells y x is ,a1 & decides ! d\bt4 4 4 4 4#gj ,!re is "s gr\nd = ! criticisms pass$ by ,coll9s4 ,to be sure1 ! fir/ edition ( ! ,clavis is dat$ #afca--six ye>s be=e ,desc>tes sugge/$ ! expon5tial notation :i* came to be adopt$ z ! symbolism 9 our mod]n algebra4 ,b ! second edition ( ! ,clavis1 #afdg1 appe>$ t5 ye>s aft] ,desc>tes' innovation4 ,_h ,oughtr$ se5 fit to adopt ! new expon5tial notation 9 #afdg1 ! /ep w\ld h be5 epo*-mak+ 9 ! tea*+ ( algebra 9 ,engl&4 ,we h se5 no indication t ,oughtr$ 0 famili> ) ,desc>tes' ,gomtrie ( #afcg4 ,! ye> prec$+ ,oughtr$'s dea? ,mr4 ,john ,twysd5 express$ himself z foll[s 9 ! preface to 8 ,miscellanies3 ,x rema9s t ,i %\ld adde some?+ t\*+ ! beg9n+1 & use ( ^! ,sci5ces4 4 4 4 4 ,i %all only1 to _! hon\rs1 "n "s ( our own ,nation yet liv+1 :o h happily lab\r$ ^u bo? /ages4 ,t succe$+ ages may und]/& t 9 ?is ( ours1 !re yet rema9$ "s :o 7 nei!r ignorant ( ^! ,arts1 z if !y _h held !m va91 nor condemn !m z sup]flu\s4 ,among/ !m all let ,mr4 ,william ,oughtr$1 ( ,aeton1 be nam$ 9 ! fir/ place1 a ,p]son ( v5]able grey haires1 & exempl>y piety1 :o inde$ exce$s all praise we c be/[ ^u him4 ,:o by an easie me?od1 & admirable ,key1 ha? unlock$ ! hidd5 ?+s ( geometry4 ,:o by an accurate ,trigonometry & furniture ( ,in/rum5ts1 ha? inri*$1 z well geometry1 z ,a/ronomy4 ,let ,d4 ,john ,wallis1 & ,d4 ,se? ,w>d1 succe$ 9 ! next place1 bo? fam\s ,p]sons1 & ,doctors 9 ,div9ity1 ! "o ( geometry1 ! o!r ( a/ronomy1 ,savilian ,pr(essors 9 ! ,univ]sity ( ,ox=d4#ga ,! a/ronom] ,edmund ,halley1 9 8 preface to ! #afid ,engli% edition ( ! ,clavis1 speaks ( ?is book z "o ( 8s e/abli%$ a reputation1 t x 7 ne$less to say any?+ !re(10 ?\gh 8! concise ,brevity ( ! au?or is su*1 z 9 _m places to ne$ ,explication1 to r5d] x ,intelligible to ! less kn[+ ,ma!matical matt]s40 ,9 clos+ ?is "p ( our monograph1 we quote ! te/imony ( ,rob]t ,boyle1 ! exp]im5tal physici/1 z giv5 ,may #h1 #afdg1 9 a lett] to ,mr4 ,h>tlib3 ,! ,engli%+ (1 & additions to ,oughtr$'s ,clavis ma!matica does mu* cont5t me1 ,i hav+ =m]ly sp5t mu* /udy on ! orig9al ( t algebra1 :i* ,i h long s9ce e/eem$ a mu* m in/ructive way ( logic1 ?an t ( ,ari/otle4#gb ,,0 ,,desc>tes ,,indebt$ ,,to ,,oughtr$8 ,?is "q fir/ arose 9 ! sev5te5? c5tury1 :5 ,john ,wallis1 ( ,ox=d1 9 8 ,algebra 7! ,engli% edition ( #afhe1 & m p>ticul>ly ! ,lat9 edition ( #afic71 rais$ ! issue ( ,desc>tes' indebt$ness to ! ,engli% sci5ti/s1 ,?omas ,h>riot & ,william ,oughtr$4 ,9 discuss+ matt]s ( priority betwe5 ,h>riot & ,desc>tes1 relat+ to ! !ory ( equations1 ,wallis is g5]ally held to h %[n m>k$ p>tiality to ,h>riot4 ,less att5tion has be5 giv5 by hi/orians ( ma!matics to ,desc>tes' indebt$ness to ,oughtr$4 ,yet ?is "q is ( importance 9 trac+ ,oughtr$'s influ5ce ^u 8 "t4 ,on ,janu>y #h1 #afhh-hi1 ,samuel ,morl& address$ a lett] ( inquiry to ,john ,wallis1 conta9+ a passage :i* we translate f ! ,lat93 ,"s "t ago ,i read 9 ! elegant & truly preci\s book t y h writt5 on ,algebra1 ab\t ,desc>tes1 ?is philosoph] s extoll$ above all = hav+ arriv$ at a v p]fect sy/em by 8 own p[]s1 )\t ! aid ( o!rs1 ?is ,desc>tes1 ,i say1 :o has receiv$ 9 geometry v great light f our ,oughtr$ & our ,h>riot1 & has foll[$ _! track ?\gh he c>efully suppress$ _! names4 ,i /at$ ?is 9 a conv]sation ) a pr(essor 9 ,utre*t 7:]e ,i reside at pres5t74 ,he reque/$ me to indicate to him ! page-numb]s 9 ! two au?ors :i* ju/ifi$ ?is accusation4 ,i admitt$ t ,i c\ld n d s4 ,! ,gomtrie ( ,desc>tes is n suffici5tly famili> to me1 al?\gh ) ,oughtr$ ,i am fairly famili>4 ,i pray y !re=e t y w assume ?is burd54 ,give me at lea/ ^? ref]5ces to passages ( ! two au?ors f ! comp>ison ( :i* ! plagi>ism by ,desc>tes is ! mo/ /rik+4#gc ,foll[+ ,morl&'s lett] 9 ! ,de algebra tractatus1 is pr9t$ ,wallis' reply1 dat$ ,m>* #ab1 #afhh 78,/ilo ,angliae071 :i* is1 9 "p1 z foll[s3 ,i n[h]e give him ! "n ( a plagi>i/2 ,i w\ld n appe> s impolite4 ,h[ev] ?is ,i say1 ! major "p ( 8 algebra 7if n all7 is f\nd be=e him 9 o!r au?ors 7notably 9 our ,h>riot7 :om he does n designate by "n4 ,t algebra may be appli$ to geometry1 & t x is 9 fact s appli$1 is no?+ new4 ,pass+ ! anci5ts 9 sil5ce1 we /ate t ?is has be5 done by ,vieta1 ,ghetaldi1 ,oughtr$ & o!rs1 be=e ,desc>tes4 ,!y h resolv$ by algebra & speci\s ari?metic lit]al ari?metic _m geometrical problems4 4 4 4 4 ,b ! "q is n z to application ( algebra to geometry 7a ?+ q old71 b ( ! ,c>tesian algebra consid]$ by itself4 ,wallis !n indicates 9 ! #afei edition ( ,desc>tes' ,gomtrie :]e ! subjects treat$ on ! fir/ six pages are f\nd 9 ! writ+s ( e>li] algebrai/s1 p>ticul>ly ( ,h>riot & ,oughtr$4 ,= example1 :at is f\nd on ! fir/ page ( ,desc>tes1 relat+ to addition1 subtraction1 multiplication1 division1 & root extraction1 is decl>$ by ,wallis to be drawn f ,vieta1 ,ghetaldi1 & ,oughtr$4 ,x is true t ,desc>tes makes no m5tion ( mod]n writ]s1 except once ( ,c>dan4 ,b x 0 n ! purpose ( ,desc>tes to write a hi/ory ( algebra4 ,to be sure1 ref]5ces to su* ( 8 imm$iate pr$ecessors z he _h read w\ld n h be5 out ( place4 ,nev]!less1 ,wallis fails to %[ t ,desc>tes made illegitimate use ( any?+ he may h se5 9 ,h>riot or ,oughtr$4 ,! fir/ inquiry to be made is1 ,did ,desc>tes possess copies ( ! books ( ,h>riot & ,oughtr$8 ,x is only 9 rec5t "t t ?is "q has be5 answ]$ z to ,h>riot4 ,z to ,oughtr$1 x is /ill unansw]$4 ,x is n[ kn[n t ,desc>tes _h se5 ,h>riot's ,artis analyticae praxis 7#afca74 ,desc>tes wrote a lett] to ,con/ant9 ,huyg5s 9 :i* he /ates t he is s5d+ ,h>riot's book4#gd ,an able discussion ( ! "q1 :at effect1 if any1 ,oughtr$'s ,clavis ma!maticae ( #afca _h ^u ,desc>tes'#ge ,gomtrie ( #afcg1 is giv5 by ,h4 ,bosmans 9 a rec5t article4 ,accord+ to ,bosmans no evid5ce has be5 f\nd t ,desc>tes possess$ a copy ( ,oughtr$'s book1 or t he _h exam9$ x4 ,bosmans believes nev]!less t ,desc>tes 0 influ5c$ by ! ,clavis1 ei!r directly or indirectly4 ,he says3 ,if ,desc>tes did n read x c>efully1 :i* is n prov$1 he 0 none ! less well in=m$ ) reg>d to x4 ,no "o d5ies 8 intimate k ( ! intellectual movem5t ( 8 "t4 ,! ,clavis ma!matica enjoy$ a rapid success4 ,x is impossible t1 at lea/ indirectly1 he did n "k ! m orig9al ideas :i* x conta9$4 ,f> f belittl+ ,desc>tes1 z ,i mu* desire to repeat1 ?is r makes him ! great]4#gf ,we ourselves w\ld h>dly g z f> z does ,bosmans4 ,unless ,desc>tes actually exam9$ a copy ( ,oughtr$ x is n likely t he 0 influ5c$ by ,oughtr$ 9 appreciable degree4 ,book reviews 7 q unkn[n 9 ^? days4 ,no evid5ce has yet be5 adduc$ to %[ t ,desc>tes obta9$ a k ( ,oughtr$ by correspond5ce4 ,a mo/ /rik+ feature ab\t ,oughtr$'s ,clavis is its notation4 ,no trace ( ! ,engli%man's symbolism has be5 po9t$ out 9 ,desc>tes' ,gomtrie ( #afcg4 ,only six ye>s int]v5$ betwe5 ! publication ( ! ,clavis & ! ,gomtrie4 ,x took long] ?an ?is p]iod = ! ,clavis to %[ evid5ce ( its influ5ce ^u ma!matical books publi%$ 9 ,engl&2 x is n probable t abroad ! contact 0 m imm$iate ?an at home4 ,our /udy ( sev5te5?-c5tury algebra has l$ u to ! conviction t ,oughtr$ des]ves a high] place 9 ! developm5t ( ?is sci5ce ?an is usually accord$ to him2 b t x took sev]al dec5nia = 8 influ5ce fully to develop4 ,,! ,,spread ,,( ,,oughtr$',s ,,notations ,an idea ( ,oughtr$'s influ5ce ^u ma!matical ?\ght & tea*+ c be obta9$ f ! spread ( 8 symbolism4 ,?is /udy indicates t ! adoption 0 n imm$iate4 ,! e>lie/ use t we h be5 able to f9d ( ,oughtr$'s notation = proportion1 ,a4,b33,c4,d1 occurs n9ete5 ye>s aft] ! ,clavis ma!maticae ( #afca4 ,9 #afej ,john ,k]sey br\ght out 9 ,london an edition ( ,edmund ,w+ates' ,ari?metique made easie1 9 :i* ?is notation is us$4 ,aft] ?is date publications employ+ x became frequ5t1 "s ( !m be+ ! productions ( pupils ( ,oughtr$4 ,we h se5 x 9 ,v9c5t ,w+ 7#afea71gg ,se? ,w>d 7#afec71gh ,john ,wallis 7#afee71gi 9 8,r4 ,b410 a s*oolma/] 9 ,suffolk1#hj ,samuel ,fo/] 7#afei71ha ,jonas ,moore 7#affj71hb & ,isaac ,b>r[ 7#afeg74hc ,9 ! latt] "p ( ! sev5te5? c5tury ,oughtr$'s notation1 ,a4,b33,c4,d1 became ! preval5t1 ?\gh n univ]sal1 notation 9 ,great ,brita94 ,a trem5d\s impetus to _! adoption 0 giv5 by ,se? ,w>d1 ,isaac ,b>r[1 & p>ticul>ly by ,john ,wallis1 :o 0 ris+ to int]national em95ce z a ma!matician4 ,9 ,france we h notic$ ,oughtr$'s notation = proportion 9 ,franciscus ,dulaur5s 7#affg71hd ,j4 ,pre/et 7#afge71he ,r4 ,p4 ,b]n>d ,lamy 7#afhd71hf ,ozanam 7#afia71hg ,de l',hospital 7#afif71hh ,r4 ,p4 ,petro ,nicolas 7#afig74hi ,9 ! ,ne!rl&s we h notic$ x 9 ,r4 ,p4 ,b]n>d ,lamy 7#afhj71ij & 9 an anonym\s "w ( #afij4ia ,9 ,g]man & ,italian works ( ! sev5te5? c5tury we h n se5 ,oughtr$'s notation = proportion4 ,9 ,engl& a modifi$ notation soon sprang up 9 :i* ratio 0 indicat$ by two dots in/ead ( a s+le dot1 ?us ,a3,b33,c3,d4 ,! reason = ! *ange lies probably 9 ! incl9ation to use ! s+le dot to designate decimal fractions4 ,w4 ,w4 ,beman po9t$ out t ?is modifi$ symbolism 737 = ratio is f\nd z e>ly z #afeg 9 ! end ( ! trigonometric & log>i?mic tables t 7 b\nd ) ,oughtr$'s ,trigonometria4#ib ,x is n probable1 h[ev]1 t ?is notation 0 us$ by ,oughtr$ himself4 ,! ,trigonometria prop] has ,oughtr$'s ,a4,b33,c4,d ?r\gh\t4 ,moreov]1 9 ! ,engli% edition ( ?is trigonometry1 :i* appe>$ ! same ye>1 #afeg1 b subsequ5t to ! ,lat9 edition1 ! passages :i* conta9$ ! colon z ! symbol = ratio1 :5 n omitt$1 are reca/1 & ! regul> ,oughtr$ian notation is introduc$4 ,9 ,oughtr$'s po/hum\s "w1 ,opuscula ma!matica hact5us in$ita1 #afgg1 ! colon appe>s q (t5 b is mo/ likely due to ! editor ( ! book4 ,we h notic$ t ! notation ,a3,b33,c3,d ant$ates ! ye> #afeg4 ,v9c5t ,w+1 ! a/ronom]1 publi%$ 9 #afea 9 ,london ! ,h>monicon coele/e1 9 :i* is f\nd n only ,oughtr$'s notation ,a4,b33,c4,d b also ! modifi$ =m ( x giv5 above4 ,! two are us$ int]*angeably4 ,8 lat] works1 ! ,logi/ica a/ronomica 7#afef71 ,doctr9a sph]ica 7#afee71 & ,doctr9a !orica1 publi%$ 9 "o volume 9 ,london1 all use ! symbols ,a3,b33,c3,d exclusively4 ,! au?or ( a book entitl$1 ,an ,idea ( ,ari?metick at fir/ design$ = ! use ( ! ,free ,s*oole at ,?url[ 9 ,suffolk 4 4 4 4 by ,r4 ,b41 ,s*oolma/] !re1 ,london1 #afee1 writes ,a3a33,c3c1 ?\gh "p ( ! "t he uses ,oughtr$'s unmodifi$ notation4 ,we c be/ indicate ! tr5d 9 ,engl& by indicat+ ! au?ors ( ! sev5te5? c5tury :om we h f\nd us+ ! notation ,a3,b33,c3,d & ! au?ors ( ! eighte5? c5tury :om we h f\nd us+ ,a4,b33,c4,d4 ,! =m] notation 0 ! less common dur+ ! sev5te5? b ! m common dur+ ! eighte5? c5tury4 ,we h obs]v$ ! symbols ,a3,b33,c3,d 7besides ! au?ors already nam$7 9 ,john ,coll9s 7#afei71ic ,james ,gregory 7#affc71id ,*ri/oph] ,wr5 7#affh-fi71ie ,william ,leyb\rn 7#afgc71if ,william ,s&]s 7#afhf71ig ,john ,hawk9s 7#afhd71ih ,joseph ,raphson 7#afig71ii ,e4 ,wells 7#afih71ajj & ,john ,w>d 7#afih74aja ,( ,engli% eighte5?-c5tury au?ors ! foll[+ /ill clung to ! notation ,a4,b33,c4,d3 ,john ,h>ris' translation ( ,f4 ,ignatius ,ga/on ,p>dies 7#agja71ajb ,george ,%elley 7#agjd71ajc ,sam ,cobb 7#agji71ajd ,j4 ,coll9s 9 ,comm]cium ,epi/olicum 7#agab71 ,john ,craig 7#agah71aje ,jo4 ,wilson 7#agbd74ajf ,! late/ use ( ,a4,b33,c4,d :i* has come to our notice is 9 ! translation ( ! ,analytical ,in/itutions ( ,m>ia ,g4 ,agnesi1 made by ,john ,colson sometime be=e #agfj1 b :i* 0 n publi%$ until #ahja4 ,dur+ ! sev5te5? c5tury ! notation ,a3,b33,c3,d acquir$ almo/ complete asc5dancy 9 ,engl&4 ,9 ,france ,oughtr$'s unmodifi$ notation ,a4,b33,c4,d1 hav+ be5 adopt$ lat]1 0 also disc>d$ lat] ?an 9 ,engl&4 ,an approximate idea ( ! situation appe>s f ! foll[+ data4 ,! notation ,a4,b33,c4,d 0 us$ by ,m4 ,c>r 7#agjj71ajg ,m4 ,guisne 7#agje71ajh ,m4 de ,font5elle 7#agbg71aji ,m4 ,v>ignon 7#agbe71aaj ,m4 ,robill>d 7#agec71aaa ,m4 ,seba/i5 le ,cl]c 7#agfd71aab ,clairaut 7#agca71aac ,m4 ,l',hospital 7#agha74aad ,9 ,italy ,oughtr$'s modifi$ notation a1 b33c1 d 0 us$ by ,m>ia ,g4 ,agnesi 9 h] ,in/ituzioni analiti*e1 ,milano1 #agdh4 ,! notation a3b33c3d f\nd entrance ! latt] "p ( ! eighte5? c5tury4 ,9 ,g]many ! symbolism a3bc3d1 sugge/$ by ,leibniz1 f\nd wid] acceptance4#aae ,x is evid5t f ! data pres5t$ t ,oughtr$ propos$ 8 notation = ratio & proportion at a "t :5 ! ne$ ( a specific notation began to be g5]ally felt1 t 8 symbol = ratio a4b 0 tempor>ily adopt$ 9 ,engl& & ,france b gave way 9 ! eighte5? c5tury to ! symbol a3b1 t ,oughtr$'s symbol = proportion 33 f\nd almo/ univ]sal adoption 9 ,engl& & ,france & 0 widely us$ 9 ,italy1 ! ,ne!rl&s1 ! ,unit$ ,/ates1 & to "s ext5t 9 ,g]many2 x has surviv$ to ! pres5t "t b is n[ be+ gradually displac$ by ! sign ( equality 4 ,oughtr$'s notation to express aggregation ( t]ms has receiv$ little att5tion f hi/orians b is nev]!less int]e/+4 ,8 books1 z well z ^? ( ,john ,wallis1 are full ( p>5!ses b !y are n us$ z symbols ( aggregation 9 algebra2 !y are simply m>ks ( punctuation = p>5!tical clauses4 ,we h se5 t ,oughtr$ writes 7ab7 & 7ab7 ?us1 ,q3ab31 3ab31 or ,q3ab1 3ab1 us+ on r>] occasions a s+le dot 9 place ( ! colon4 ,?is notation did n orig9ate ) ,oughtr$1 b1 9 slightly modifi$ =m1 occurs 9 writ+s f ! ,ne!rl&s4 ,9 #afjc ,c4 ,dibvadii 9 geometriam ,evclidis demon/ratio num]alis1 ,leyd51 conta9s _m expressions ( ?is sort1 #acfbjdh1 signify+ 7#acfbjdh74 ,! dot is us$ to indicate t ! root ( ! b9omial 7n ( #acf alone7 is call$ =4 ,?is notation is us$ ext5sively 9 ,ludolphi ,cevl5 de circulo1 ,leyd51 #afai1 & 9 ,willebrordi ,snellii ,de circuli dim5sione1 ,leyd51 #afba4 ,9 place ( ! s+le dot ,oughtr$ us$ ! colon 7371 probably to avoid confusion ) 8 notation = ratio4 ,to avoid fur!r possibility ( unc]ta9ty he usually plac$ ! colon bo? be=e & aft] ! algebraic expression "u aggregation4 ,?is notation 0 adopt$ by ,john ,wallis & ,isaac ,b>r[4 ,x is f\nd 9 ! writ+s ( ,desc>tes4 ,toge!r ) ,vieta's horizontal b>1 plac$ ov] two or m t]ms1 x con/itut$ ! means us$ almo/ univ]sally = d5ot+ aggregation ( t]ms 9 algebra4 ,be=e ,oughtr$ ! use ( p>5!ses _h be5 sugge/$ by ,clavius#aaf & ,gir>d4#aag ,! latt] wrote1 = in/ance1 7#bc74 ,:ile p>5!ses nev] became popul> 9 algebra be=e ! "t ( ,leibniz & ! ,b]n\llis !y 7 by no means lo/ sight (4 ,we are able to po9t to ! foll[+ au?ors :o made use ( !m3 ,i4 ,err>d de ,b>-le-,duc 7#afai71aah ,jacobo de ,billy 7#afdc71aai "o ( ^: books conta9+ ?is notation 0 translat$ into ,engli%1 & also ! po/hum\s works ( ,samuel ,fo/]4#abj ,j4 ,w4 ,l4 ,glai%] po9ts out t p>5!ses 7 us$ by ,norwood 9 8 ,trigonometrie 7#afca71 p4 #cj4aba ,! symbol = ! ari?metical diff]5ce betwe5 two numb]s1 1 is usually attribut$ to ,john ,wallis1 b x occurs 9 ,oughtr$'s ,clavis ma!maticae ( #afeb1 9 ! tract on ,elem5ti decimi ,euclidis decl>atio1 at an e>li] date ?an 9 any ( ,wallis' books4 ,z ,wallis assi/$ 9 putt+ ?is edition ?r\gh ! press x is possible1 ?\gh n probable1 t ! symbol 0 ins]t$ by him4 ,7 ! symbol ,wallis'1 ,oughtr$ w\ld d\btless h ref]r$ to its orig9 9 ! preface4 ,dur+ ! eighte5? c5tury ! symbol f\nd its way into =eign texts ev5 9 f>-(f ,italy4#abb ,x is "o ( ?ree symbols presumably inv5t$ by ,oughtr$ & :i* are /ill us$ at ! pres5t "t4 ,! o!rs are & 334 ,! curi\s & ill-*os5 symbols1 = 8great] ?an10 & = 8less ?an10 7 c]ta9 to succumb 9 _! /ruggle = exi/5ce aga9/ ,h>riot's admirably *os5 & 4 ,yet su* 0 ! reputation ( ,oughtr$ t 8 symbols 7 us$ 9 ,engl& q ext5sively dur+ ! sev5te5? & ! beg9n+ ( ! eighte5? c5tury4 ,consid]able confusion has exi/$ among algebrai/s & also among hi/orians z to :at ,oughtr$'s symbols really 74 ,p>ticul>ly is ?is true ( ! sign = 8less ?an0 :i* is frequ5tly writt5 4 ,oughtr$'s symbols1 or ^! symbols turn$ ab\t 9 "s way1 h be5 us$ by ,se? ,w>d1#abc ,john ,wallis1#abd ,isaac ,b>r[1#abe ,john ,k]sey1#abf ,e4 ,wells1#abg ,john ,hawk9s1#abh ,?o4 ,bak]1#abi ,ri*>d ,sault1#acj ,ri*>d ,rawl9son1#aca ,franciscus ,dulaur5s1#acb ,james ,milnes1#acc ,george ,*eyne1#acd ,john ,craig1#ace ,jo4 ,wilson1#acf & ,j4 ,coll9s4#acg ,g5]al acceptance has be5 accord$ to ,oughtr$'s symbol 4 ,! fir/ pr9t$ appe>ance ( ?is symbol = multiplication 9 #afah 9 ! =m ( ! lett] x h>dly expla9s its real orig94 ,! au?or ( ! 8,app5dix0 7be he ,oughtr$ or someone else7 may n h us$ ! lett] x at all1 b may h writt5 ! cross 1 call$ ! ,/4 ,&rew's cross1 :ile ! pr9t]1 9 ! abs5ce ( any type accurately repres5t+ t cross1 may h sub/itut$ ! lett] x 9 its place4 ,! hypo!sis t ! symbol ( multiplication owes its orig9 to ! old habit ( us+ direct$ b>s to indicate t two numb]s are to be comb9$1 z = in/ance 9 ! multiplication ( #bc & #cd1 ?us1 #b #c _/ x _/ #c #d ------- #g #h #b has be5 advanc$ by two writ]s1 ,c4 ,le ,paige#ach & ,gravela>4#aci ,bosmans is m incl9$ to ! belief t ,oughtr$ adopt$ ! symbol some:at arbitr>ily1 mu* z he did ! num]\s symbols 9 8 ,elem5ti decimi ,euclidis decl>atio4#adj ,le ,paige's & ,gravela>'s !ory f9ds "s support 9 ! fact t ! cross 1 )\t ! two additional v]tical l9es %[n above1 occurs 9 a comm5t>y publi%$ by ,oswald ,s*re%5su*s#ada 9 #aeea1 :]e ! sign is writt5 betwe5 two factors plac$ "o above ! o!r4 ,,*apt] ,v ,,oughtr$',s ,,ideas ,,on ,,! ,,tea*+ ,,( ,,ma!matics ,,g5]al ,,/atem5t ,n[h]e has ,oughtr$ giv5 a full & sy/ematic exposition ( 8 views on ma!matical tea*+4 ,nev]!less1 he _h v pron\nc$ & cle>-cut ideas on ! subject4 ,t a man :o 0 n a tea*] by pr(ession %\ld h mature views on tea*+ is mo/ int]e/+4 ,we ga!r 8 ideas f ! quality ( ! books he publi%$1 f 8 prefaces1 & f passages 9 8 controv]sial writ+ aga9/ ,delama94 ,z we proce$ to give quotations unfold+ ,oughtr$'s views1 we %all obs]ve t ?ree po9ts receive special emphasis3 7#a7 an appeal to ! eye ?r\gh suitable symbolism2 7#b7 emphasis ^u rigor\s ?9k+2 7#c7 ! po/ponem5t ( ! use ( ma!matical in/rum5ts until aft] ! logical f\ndations ( a subject h be5 ?or\ghly ma/]$4 ,! importance ( ^! t5ets is imm5sely re9=c$ by ! conditions ( ! h\r4 ,?is voice f ! pa/ speaks wisdom to speciali/s ( today4 ,rec5t me?ods ( det]m9+ educational values & ! mod]n cult ( utilit>ianism h l$ "s exp]ts to extraord9>y conclusions4 ,laboratory me?ods ( te/+1 by ! n>r[ness ( _! range1 (t5 mislead4 ,?us f> !y h be5 inf]ior to ! ^w ( a man ( exp]i5ce1 insight1 & conviction4 ,,ma!matics1 8,a ,,sci5ce ,,( ,,! ,,eye0 ,oughtr$ 0 a great admir] ( ! ,greek ma!maticians--,euclid1 ,ar*im$es1 ,apollonius ( ,p]ga1 ,diophantus4 ,b 9 read+ _! works he exp]i5c$ ke5ly :at _m mod]n read]s h felt1 namely1 t ! almo/ total abs5ce ( ma!matical symbols r5d]s _! writ+s unnecess>ily difficult to read4 ,/atem5ts t c be compress$ into a few well-*os5 symbols :i* ! eye is able to survey z a :ole are express$ 9 long-drawn-out s5t5ces4 ,a /rik+ illu/ration ( ! importance ( symbolism is af=d$ by ! hi/ory ( ! =mula ixlog7cos xi s9 x74 ,x 0 giv5 9 ,rog] ,cotes' ,h>monia m5sur>um1 #agbb1 n 9 symbols1 b express$ 9 rhetorical =m1 de/itute ( special aids to ! eye4 ,! result 0 t ! !orem rema9$ 9 ! book undetect$ = #ahe ye>s & 0 mean:ile r$iscov]$ by o!rs4 ,ow+ to ! prom95ce ( ,cotes z a ma!matician x is v improbable t su* a ?+ c\ld h happ5$ _h ! !orem be5 ?ru/ into view by ! aid ( ma!matical symbols4 ,9 /udy+ ! anci5t au?ors ,oughtr$ is report$ to h writt5 d[n on ! m>g9 ( ! pr9t$ page "s ( ! !orems & _! pro(s1 express$ 9 ! symbolic language ( algebra4 ,9 ! preface ( 8 ,clavis ( #afca & ( #afdg he says3 ,:]e=e1 t ,i might m cle>ly behold ! ?+s !mselves1 ,i uncas+ ! ,propositions & ,demon/rations out ( _! cov]t ( words1 design$ !m 9 notes & species appe>+ to ! v eye4 ,aft] t by comp>+ ! div]s affections ( ,!orems1 inequality1 proportion1 aff9ity1 & dep5d5ce1 ,i try$ to educe new out ( !m4 ,x 0 ?is motive :i* l$ him to introduce ! _m abbreviations 9 algebra & trigonometry to :i* ref]5ce has be5 made 9 previ\s pages4 ,! p$agogical exp]i5ce ( rec5t c5turies has indors$ ,oughtr$'s view1 provid$ ( c\rse t ! pupil is c>efully taught ! exact mean+ ( ! symbols4 ,!re h be5 & !re /ill are ^? :o oppose ! int5sive use ( symbolism4 ,9 our day ! new symbolism = all ma!matics1 sugge/$ by ! s*ool ( ,peano 9 ,italy1 c h>dly be said to be receiv$ ) en?usiasm4 ,9 ,oughtr$'s day symbolism 0 n yet ! fa%ion4 ,to be conv9c$ ( ?is fact "o ne$ only op5 a book ( ,edmund ,gunt]1 ) :om ,oughtr$ came 9 contact 9 8 y\?1 or consult ! ,pr9cipia ( ,sir ,isaac ,newton1 :o fl\ri%$ aft] ,oughtr$4 ,! ma!matical works ( ,gunt] & ,newton1 p>ticul>ly ! =m]1 are surpris+ly de/itute ( ma!matical symbols4 ,! philosoph] ,hobbes1 9 a controv]sy ) ,john ,wallis1 criticiz$ ! latt] = t 8,scab ( ,symbols10 :]eupon ,wallis repli$3 ,i wond] h[ y dur/ t\* ,m4 ,oughtr$ = fe> ( cat*+ ! ,scab4 ,=1 d\btlesse1 8 book is z mu* cov]$ ov] ) ! ,scab ( ,symbols1 z any ( m9e4 4 4 4 4 ,z = my ,treatise ( ,conick ,sections1 y say1 x is cov]$ ov] ) ! ,scab ( ,symbols1 t y _h n ! pati5ce to exam9e :e!r x is well or ill demon/rat$4#adb ,oughtr$ ma9ta9$ 8 view ( ! importance ( symbols on _m diff]5t occasions4 ,?us1 9 8 ,circles ( ,proportion1 #afcb1 p4 #bj3 ,?is mann] ( sett+ d[ne ,!oremes1 :e!r !y be ,proportions1 or ,equations1 by ,symboles or notes ( words1 is mo/ excell5t1 artificiall1 & doctr9all4 ,:]e=e ,i e>ne/ly exhort e "o1 t desire? ?\gh b to looke into ^! noble ,sci5ces ,ma!maticall1 to accu/ome !mselves unto x3 & inde$e x is easie1 be+ mo/ agreeable to reason1 yea ev5 to s5ce4 ,& out ( ?is work+ may _m s+ul> consect>ies be drawne3 :i* )\t ?is w\ld1 x may be1 = ev] lye hid4 ,,rigor\s ,,?9k+ ,,& ,,! ,,use ,,( ,,in/rum5ts ,! au?or's elevat$ concept ( ma!matical /udy z conducive to rigor\s ?9k+ %9es ?r\gh ! foll[+ extract f 8 preface to ! #afdg ,clavis3 4 4 4 4 ,:i* ,treatise be+ n writt5 9 ! usuall syn!tical mann]1 nor ) v]b\s expressions1 b 9 ! inv5tive way ( ,analitice1 & ) symboles or notes ( ?+s in/ead ( words1 seem$ unto _m v h>d2 ?\gh inde$ x 0 b _! owne diffid5ce1 be+ sc>$ by ! newnesse ( ! deliv]y2 & n any difficulty 9 ! ?+ x selfe4 ,= ?is speci\s & symbolicall mann]1 nei!r racke? ! memory ) multiplicity ( words1 nor *>ge? ! phantasie ) comp>+ & lay+ ?+s toge!r2 b pla9ly pres5te? to ! eye ! :ole c\rse & processe ( e op]ation & argum5tation4 ,n[ my scope & int5t 9 ! fir/ ,edition ( t my ,key 01 & 9 ?is ,new ,fil+1 or r =g+ ( x1 is1 to rea* out to ! +5i\s lov]s ( ^! ,sci5ces1 z x 7 ,ariadnes ?read1 to guide !m ?r\gh ! intricate ,labyr9? ( ^! /udies1 & to direct !m = ! m easie & full und]/&+ ( ! be/ & anti5te/ ,au?ors4 4 4 4 4 ,t !y may n only le>n _! propositions1 :i* is ! highe/ po9t ( ,art t mo/ ,/ud5ts aime at2 b also may p]ceive ) :at sol]ti\snesse1 by :at eng9es ( aequations1 ,int]pretations1 ,comp>ations1 ,r$uctions1 & ,disquisitions1 ^? anti5t ,wor?ies h beautifi$1 enl>g$1 & fir/ f\nd out ?is mo/ excell5t ,sci5ce4 4 4 4 4 ,la/ly1 by fram+ l que/ions problematically1 & 9 a way ( ,analysis1 z if !y 7 already done1 resolv+ !m into _! pr9ciples1 ,i s\ght out reasons & means :]eby !y might be effect$4 ,& by ?is c\rse ( practice1 n )\t long "t1 & mu* indu/ry1 ,i f\nd out ?is way = ! helpe & facilitation ( ,art4 ,/ill great] emphasis ^u rigor\s ?9k+ 9 ma!matics is laid 9 ! preface to ! ,circles ( ,proportion & 9 "s p>ts ( 8 ,apologeticall ,epi/le aga9/ ,delama94 ,9 t preface ,william ,=/] quotes ! reply ( ,oughtr$ to ! "q h[ he 7,oughtr$7 _h = s _m ye>s conceal$ 8 inv5tion ( ! slide rule f himself 7,=/]7 :om he _h taught s _m o!r ?+s4 ,! reply 03 ,t ! true way ( ,art is n by ,in/rum5ts1 b by ,demon/ration3 & t x is a prepo/]\s c\rse ( vulg> ,tea*]s1 to beg9 ) ,in/rum5ts1 & n ) ! ,sci5ces1 & s 9-/ead ( ,arti/s1 to make _! ,s*ol]s only do]s ( tricks1 & z x 7 ,iugl]s3 to ! despite ( ,art1 losse ( previ\s "t1 & betray+ ( will+ & indu/ri\s wits1 vnto ignorance1 & idl5esse4 ,t ! vse ( ,in/rum5ts is inde$ excell5t1 if a man be an ,arti/3 b contemptible1 be+ set & oppos$ to ,art4 ,& la/ly1 t he meant to comm5d to me1 ! skill ( ,in/rum5ts1 b fir/ he w\ld haue me well in/ruct$ 9 ! ,sci5ces40 ,delama9 took a diff]5t view1 argu+ t in/rum5ts might v well be plac$ 9 ! h&s ( pupils f ! />t4 ,at ! "t ( ?is controv]sy ,delama9 support$ himself by tea*+ ma!matics 9 ,london & he adv]tis$ 8 ability to give in/ruction 9 ma!matics1 includ+ ! use ( in/rum5ts4 ,delama9 br\ght ! *>ge aga9/ ,oughtr$ ( unju/ly call+ 8_m ( ! ,briti% ,nobility & ,g5try do]s ( trickes & jugl]s40 ,to ?is ,oughtr$ replies3 ,z ,i did to ,delama9 & to "s o!rs1 s ,i did to ,william ,=/]3 ,i freely gave him my helpe & in/ruction 9 ^! faculties3 only ?is 0 ! diff]5ce1 ,i _h ! v fir/ m\ld+ 7z ,i may say7 ( ?is latt]3 ,b ,delama9 0 already corrupt$ ) dor+ ^u ,in/rum5ts1 & q lo/ f ev] be+ made an ,arti/3 ,i suff]$ n ,william ,=/] = "s "t s mu* z speake ( any ,in/rum5t1 except only ! ,globe x selfe2 & to explicate1 & worke ! que/ions ( ! ,spha]e1 by ! way ( ! ,analemma3 :i* also himselfe did describe = ! pres5t occasion4 ,& ?is my re/ra9t f su* pleas+ avocations1 & hold+ him to ! /rictnesse ( p]cept1 br\ght =? ?is fruit1 t 9 %ort "t1 ev5 by 8 owne skill1 he c\ld n onely use any ,in/rum5t he %\ld see1 b also 0 able to del9eate ! l1 & devise o!rs4#adc ,z repres5t+ ,delama9's views1 we make ! foll[+ selection f 8 ,grammelogia 7,london1 ab\t #afcc71 ! "p ne> ! end ( ! book & be>+ ! title1 8,9 ! behalfe ( vulg> ,tea*]s & o!rs10 :]e ,delama9 ref]s to ,oughtr$'s *>ge t ! s*ol>s ( 8vulg>0 tea*]s are 8do]s ( tricks1 z x 7 iugl]s40 ,delama9 says3 4 4 4 4 ,:i* words are nei!r cautel\s1 nor subt]fugi\s1 b are z d[ne "r 9 _! pla9nesse1 z !y are t\*+1 & p]niti\s1 by two mu* d]ogat+ f _m1 & glanc+ ^u _m noble p]sonages1 ) too grosse1 if n too base an attribute1 9 te>m+ !m do]s ( tricks1 z x 7 to iuggle3 because !y p]haps make use ( a necessitie 9 ! furni%+ ( !mselves ) su* k by ,practicall ,in/rum5tall op]ation1 :5 _! m weighty negotiations w n p]mit !m = ,!oreticall figurative demon/ration2 ^? t are guilty ( ! asp]tion1 & are t\*$ !re) may answ] = !mselves1 & /udie to be m ,!oreticall1 ?an ,practicall3 = ! ,!ory1 is z ! ,"m t produce? ! daught]1 ! v s9ewes & life ( ,practise1 ! excell5cie & highe/ degree ( true ,ma!maticall ,k3 b = ^? t w\ld make b a /ep z x 7 into t k9d ( ,le>n+1 ^: onely desire is exp$ition1 & facilitie1 bo? :i* by ! g5]all cons5t ( all are be/ effect$ ) ,in/rum5t1 r !n ) t$i\s regul> demon/rations1 x 0 ill to *ecke !m s grosly1 n onely 9 :at !y h ,practis$1 b abridg+ !m also ( _! lib]ties ) :at !y may ,practise1 :i* asp]tion may n easily be slight$ (f by any glosse or ,apologie1 )\t an ,+5u\s confession1 or "s m5tall res]vation3 ,to :i* vilification1 h[soev]1 9 ! behalfe ( my selfe1 & o!rs1 ,i answ]2 ,t ,in/rum5tall op]ation is n only ! ,comp5diat+1 & facilitat+ ( ,art1 b ev5 ! glory ( x1 :ole demon/ration bo? ( ! mak+1 & op]ation is soly 9 ! sci5ce1 & to an ,arti/ or disputant prop] to be kn[ne1 & s to all1 :o w\ld truly "k ! cause ( ! ,ma!maticall op]ations 9 _! orig9all2 ,b1 = none to "k ! use ( a ,ma!maticall ,in/rum5t1 except he kn[es ! cause ( its op]ation1 is some:at too /rict1 :i* w\ld keepe _m f affect+ ! ,art1 :i* ( !mselves are ready en\gh e :]e1 to conceive m h>%ly ( ! difficultie1 & impossibilitie ( attayn+ any skill !re91 !n x des]ves1 because !y see no?+ b obscure propositions1 & p]plex & intricate demon/rations be=e _! eyes1 ^: unsav\ry t>tnes1 to an unexp]i5c$ palate l bitt] pills is sweetn$ ov]1 & made pleasant ) an ,in/rum5tall comp5di\s facilitie1 & made to goe d[ne ! m readily1 & yet to reta9e ! same v]tue1 & work+2 ,& me ?9kes 9 ?is queasy age1 all helpes may bee us$ to procure a /omacke1 all bates & invitations to ! decl9+ /udie ( s noble a ,sci5ce1 r !n by rigid ,me?od & g5]all ,lawes to sc>re m5 away4 ,all are n ( l disposition1 nei!r all 7z 0 sayd be=e7 propose ! same end1 "s resolve to wade1 o!rs to put a f+] 9 onely1 or wet a h&3 n[ ?us to tye !m to an obscure & ,!oricall =me ( tea*+1 is to crop _! hope1 ev5 9 ! v bud4 4 4 4 4 ,! beg9n+ ( a mans k ev5 9 ! use ( an ,in/rum5t1 is fir/ f\nd$ on doctr9al precepts1 & ^! precepts may be conceiv$ all along 9 its use3 & are s f>re f be+ exclud$1 t !y doe necess>ily concomitate & are conta9$ !re93 ! practicke be+ bett] und]/ood by ! doctr9all "p1 & ?is lat] expla9$ by ! ,in/rum5tall1 mak+ precepts obvi\s unto s5se1 & ! ,!ory go+ along ) ! ,in/rum5t1 bett] in=m+ & inlightn+ ! und]/&+1 etc4 vis vnita =tior1 s z if t 9 ,phylosophy bee true1 ,nihil e/ 9 intellectu quod non prius fuit 9 s5su4 ,! diff]5ce betwe5 ,oughtr$ & ,delama9 z to ! use ( ma!matical in/rum5ts raises important que/ions4 ,%\ld ! slide rule be plac$ 9 ! h&s ( a boy be=e1 or aft]1 he has ma/]$ ! !ory ( log>i?ms8 ,%\ld log>i?mic tables be )held f him until ! !oretical f\ndation is laid 9 ! m9d ( ! pupil8 ,is x a good ?+ to let a boy use a survey+ in/rum5t unless he fir/ le>ns trigonometry8 ,is x advisable to p]mit a boy to famili>ize himself ) ! runn+ ( a dynamo be=e he has ma/]$ ! und]ly+ pr9ciples ( electricity8 ,does ! use ( in/rum5ts ord9>ily disc\rage a boy f ma/]y ( ! !ory8 ,or does su* manipulation con/itute a natural & pleas+ approa* to ! ab/ract8 ,on ?is p>ticul> po9t1 :o %[$ ! pr(\nd] psy*ological insight1 ,oughtr$ or ,delama98 ,9 ,july1 #aiad1 !re 0 held 9 ,ed9burgh a celebration ( ! ?ree-hundr$? anniv]s>y ( ! inv5tion ( log>i?ms4 ,on t occasion !re 0 collect$ at ,ed9burgh univ]sity "o ( ! l>ge/ exhibits ev] se5 ( mod]n in/rum5ts ( calculation4 ,! op9ion 0 express$ by an exp]i5c$ tea*] t 8weapons z ^? exhibit$ !re are = m5 & n = boys1 & su* dang] z !re may be 9 !m is ( ! same "* z any =m ( too e>ly specialization40 ,x is some:at ( a p>adox t ,oughtr$1 :o 9 8 /ud5t days & dur+ 8 active ye>s felt himself impell$ to inv5t sun-dials1 planisph]es1 & v>i\s types ( slide rules--in/rum5ts :i* repres5t ! mo/ orig9al contributions :i* he h&$ d[n to po/]ity--%\ld disc\rage ! use ( su* in/rum5ts 9 tea*+ ma!matics to beg9n]s4 ,t )\t ! aid ( in/rum5ts he himself %\ld h succe$$ s well 9 attract+ & inspir+ "y m5 con/itutes ! /ronge/ evid5ce ( 8 transc5d5t tea*+ ability4 ,x may be argu$ t 8 p$agogic dogma1 o!rwise s excell5t1 "h goes contr>y to ! c\rse he himself foll[$ in/9ctively 9 8 self-education along ma!matical l9es4 ,we read t ,sir ,isaac ,newton1 z a *ild1 con/ruct$ sun-dials1 w9dmills1 kites1 pap] lant]ns1 & a wood5 clock4 ,%\ld ^! activities h be5 suppress$8 ,ord9>y *ildr5 are simply ,isaac ,newtons on a small] intellectual scale4 ,%\ld _! activities along ^! l9es be enc\rag$ or *eck$8 ,on ! o!r h&1 x may be argu$ t ! p>adox allud$ to above admits ( explanation1 l all p>adoxes1 & t !re is no inconsi/5cy betwe5 ,oughtr$'s p$agogic views & 8 own c\rse ( developm5t4 ,if he inv5t$ sun-dials1 he mu/ h _h a compreh5sion ( ! cosmic motions involv$2 if he solv$ sph]ical triangles graphically by ! aid ( ! planisph]e1 he mu/ h und]/ood ! geometry ( ! sph]e1 s f> z x relates to su* triangles2 if he inv5t$ slide rules1 he _h be=eh& a ?or\gh grasp ( log>i?ms4 ,! "q at issue does n involve s mu* ! inv5tion ( in/rum5ts1 z ! use by ! pupil ( in/rum5ts already con/ruct$1 be=e he fully und]/&s ! !ory :i* is involv$4 ,nor does ,sir ,isaac ,newton's activity z a *ild e/abli% ,delama9's cont5tion4 ,( c\rse1 a *ild %\ld n be disc\rag$ f manual activity along ! l9e ( produc+ int]e/+ toys 9 imitation ( /ructures & ma*9es t he sees1 b to introduce him to ! realm ( ab/ract ?\ght by ! aid ( in/rum5ts is a diff]5t proposition1 fraught ) dang]4 ,a boy may le>n to use a slide rule me*anically &1 because ( 8 ability to obta9 practical results1 feel ju/ifi$ 9 =ego+ ! ma/]y ( und]ly+ !ory2 or he may consid] ! ability ( manipulat+ a survey+ in/rum5t q suffici5t1 ev5 ?\gh he be ignorant ( geometry & trigonometry2 or he may le>n h[ to op]ate a dynamo & an electric swit*bo>d & be altoge!r satisfi$1 ?\gh hav+ no grasp ( electrical sci5ce4 ,?us in/rum5ts draw a y\? aside f ! pa? lead+ to real intellectual atta9m5ts & real effici5cy2 !y allure him into lanes :i* are (t5 bl9d alleys4 ,su* 7 ! views ( ,oughtr$4 ,:o 0 "r1 ,oughtr$ or ,delama98 ,x may be claim$ t !re is a middle gr\nd :i* m ne>ly repres5ts ! ideal proc$ure 9 tea*+4 ,%all ! slide rule be plac$ 9 ! /ud5t's h&s at ! "t :5 he is engag$ 9 ! ma/]y ( pr9ciples8 ,%all !re be an alt]nate /udy ( ! !ory ( log>i?ms & ( ! slide rule--on ! idea ( "o h& wa%+ ! o!r--until a ma/]y ( bo? ! !ory & ! use ( ! in/rum5t has be5 atta9$8 ,does ?is me?od n produce ! be/ & mo/ la/+ results8 ,is n ?is ,delama9's actual cont5tion8 ,we leave x to ! read] to settle ^! matt]s f 8 own obs]vation1 k1 & exp]i5ce4 ,,newton',s ,,comm5ts ,,on ,,oughtr$ ,oughtr$ is an au?or :o has be5 f\nd to be ( increas+ int]e/ to mod]n hi/orians ( ma!matics4 ,b no mod]n writ] has1 to our k1 po9t$ out 8 importance 9 ! hi/ory ( ! tea*+ ( ma!matics4 ,yet 8 importance z a tea*] did receive recognition 9 ! sev5te5? c5tury by no less di/+ui%$ a sci5ti/ ?an ,sir ,isaac ,newton4 ,on ,may #be1 #afid1 ,sir ,isaac ,newton wrote a long lett] 9 reply to a reque/ = 8 recomm5dation on a propos$ new c\rse ( /udy 9 ma!matics at ,*ri/'s ,hospital4 ,t[>d ! close ( 8 lett]1 ,newton says3 ,& n[ ,i h told y my op9ion 9 ^! ?+s1 ,i w give y ,mr4 ,oughtr$'s1 a ,man ^: judgm5t 7if any man's7 may be safely rely$ ^u4 ,= he 9 8 book ( ! circles ( proposition1 9 ! end ( :at he writes ab\t ,navigation 7page #ahd7 has ?is exhortation to ,seam54 8,& if10 sai? he1 8! ,ma/]s ( ,%ips & ,pilots w take ! pa9s 9 ! ,j\rnals ( _! ,voyages dilig5tly & fai?fully to set d[n 9 sev]all columns1 n onely ! ,rumb !y goe on & ! measure ( ! ,%ips way 9 degrees1 & ! obs]vation ( ,latitude & v>iation ( _! compass2 b alsoe _! conjectures & reason ( _! correction !y make ( ! ab]rations !y %all f9d1 & ! qualities & condition ( _! %ip1 & ! div]sities & seasons ( ! w9ds1 & ! secret motions or agitations ( ! ,seas1 :5 !y beg91 & h[ long !y cont9ue1 h[ f>r !y ext5d & ) :at inequality2 & :at else !y %all obs]ve at ,sea wor?y consid]ation1 & w be pleas$ freely to communicate ! same ) ,arti/s1 su* z are inde$ skilfull 9 ! ,ma!maticks & lov]s & enquir]s ( ! tru?3 ,i d\bt n b t !re %all be 9 conv5i5t "t1 br\ght to light _m necess>y precepts :i* may t5d to ye p]fect+ ( ,navigation1 & ! help & safety ( su* ^: ,vocations doe in=ce !m to commit _! lives & e/ates 9 ! va/ ,ocean to ! provid5ce ( ,god40 ,?us f>r t v good & judici\s man ,mr4 ,oughtr$4 ,i w add1 t if in/ead ( s5d+ ! ,obs]vations ( ,seam5 to able ,ma!maticians at ,l&1 ! ,l& w\ld s5d able ,ma!maticians to ,sea1 x w\ld signify mu* m to ! improvemt ( ,navigation & safety ( ,m5s lives & e/ates on t elem5t4#add ,may ,oughtr$ prove z in/ructive to ! mod]n read] z he did to ,newton6 ,footnotes #a;,aubrey's ,brief ,lives1 ed4 ,a4 ,cl>k1 ,vol4 ,,ii1 ,ox=d1 #ahih1 p4 #ajf4 #b8,to ! ,engli% ,g5trie1 & all o!rs /udi\s ( ! ,ma!maticks1 :i* %all bee ,read]s h]e(4 ,! j ,apologie ( ,wil3 ,ovghtr$1 aga9/ ! slaund]\s insimulations ( ,ri*>d ,delama91 9 a ,pamphlet call$ ,grammelogia1 or ! ,ma!maticall ,r+1 or ,mirifica log>i?morum projectio circul>is0 #afcc81 p4 #h4 ,h]eaft] we %all ref] to ?is pamphlet z ! ,apologeticall ,epi/le1 ?is "n appe>+ on ! page-head+s4 #c;,companion to ! ,briti% ,almanac ( #ahcg1 p4 #bh1 9 an article by ,augu/us ,de ,morgan on 8,notices ( ,engli% ,ma!matical & ,a/ronomical ,writ]s betwe5 ! ,norman ,conque/ & ! ,ye> #afjj40 #d,new & ,g5]al ,biographical ,diction>y 7,john ,ni*ols71 ,london1 #aghd1 art4 8,oughtr$40 #e,rev4 ,ow5 ,mann+1 ,hi/ory ( ,antiquities 9 ,surrey1 ,vol4 ,,ii1 p4 #acb4 #f,skeleton ,collegii ,regalis ,cantab43 ,or ,a ,catalogue ( ,all ! ,provo/s1 ,fell[s & ,s*ol>s1 ( ! ,k+'s ,college 4 4 4 4 s9ce ! ,f\ndation ,!re(1 ,vol4 ,,ii1 8,william ,oughtr$40 #g;,aubrey1 op4 cit41 ,vol4 ,,ii1 p4 #ajg4 #h,rigaud1 ,correspond5ce ( ,sci5tific ,m5 ( ! ,sev5te5? ,c5tury1 ,ox=d1 ,vol4 ,i1 #ahda1 p4 #e4 #i;,aubrey1 op4 cit41 ,vol4 ,,ii1 p4 #aaj4 #aj;,ibid41 p4 #aaa4 #aa,op4 cit41 ,vol4 ,,ii1 p4 #acb4 #ab,mr4 ,william ,lilly's ,hi/ory ( ,8 ,life & ,times1 ,f ! ,ye> #afjb to #afha1 ,london1 #agae1 p4 #eh4 #ac,rigaud1 op4 cit41 ,vol4 ,i1 p4 #fj4 #ad;,aubrey1 op4 cit41 ,vol4 ,,ii1 p4 #ajg4 #ae,rigaud1 op4 cit41 ,vol4 ,i1 p4 #af4 #af,ow5 ,mann+1 op4 cit41 p4 #acb4 #ag,new & ,g5]al ,biographical ,diction>y 7,john ,ni*ols71 ,london1 #aghd1 art4 8,oughtr$40 #ah,op4 cit41 ,vol4 ,,ii1 p4 #aaj4 #ai,rev4 ,ow5 ,mann+1 ,! ,hi/ory & ,antiquities ( ,surrey1 ,vol4 ,,ii1 ,london1 #ahji1 p4 #acb4 #bj,op4 cit41 ,vol4 ,,ii1 #ahih1 p4 #aaa4 #ba;,budget ( ,p>adoxes1 ,london1 #ahgb1 p4 #dea2 #b;d ed41 ,*icago & ,london1 #aiae1 ,vol4 ,,ii1 p4 #cjc4 #bb,! full title ( ! ,clavis ( #afca is z foll[s3 ,ari?meticae 9 num]is et speciebvs in/itvtio3 ,qvae tvm logi/icae1 tvm analyticae1 atqve adeo totivs ma!maticae1 qvasi clavis e/4--,ad nobilissimvm spectatissimumque inv5em ,dn4 ,gvilelmvm ,h[>d1 ,ord9is qui dicitur1 ,balnei ,equitem1 honoratissimi ,dn4 ,?omae1 ,comitis ,arvndeliae ,svrriae1 ,comitis ,m>es*alli ,angliae1 c filium4--,lond9i1 ,apud ,?omam ,h>p]vm4 ,m4,,dc4,,xxxi4 ,9 all !re appe>$ five ,lat9 editions1 ! second 9 #afdh at ,london1 ! ?ird 9 #afeb at ,ox=d1 ! f\r? 9 #affg at ,ox=d1 ! fif? 9 #afic & #afih at ,ox=d4 ,!re 7 two indep5d5t ,engli% editions3 ! fir/ 9 #afdg at ,london1 translat$ 9 great] "p by ,rob]t ,wood ( ,l9coln ,college1 ,ox=d1 z is /at$ 9 ! preface to ! #afeb ,lat9 edition2 ! second 9 #afid & #agjb is a new translation1 ! preface be+ writt5 & ! book recomm5d$ by ! a/ronom] ,edmund ,halley4 ,! #afid & #agjb impressions labor$ "u ! defect ( _m s5se-di/urb+ errors due to c>eless read+ ( ! pro(s4 ,all ! editions ( ! ,clavis1 aft] ! fir/ edition1 _h "o or m ( ! foll[+ tracts add$ on3 ,eq4,de ,aequationum affect>vm resolvtione 9 num]is4 ,eu4,elem5ti decimi ,euclidis decl>atio4 ,s4,de ,solidis regul>ibus1 tractatus4 ,an4,de ,anatocismo1 sive usura composita4 ,fa4,regula falsae positionis4 ,ar4,!orematum 9 libris ,ar*im$is de ,spha]a cyl9dro decl>atio4 ,ho4,horologia sciot]ica 9 plano1 geometric del9e&i modus4 ,! abbreviat$ titles giv5 "h are1 ( c\rse1 our own4 ,! li/s ( tracts add$ to ! ,clavis ma!maticae ( #afca 9 its lat] editions1 giv5 9 ! ord] 9 :i* ! tracts appe> 9 ea* edition1 are z foll[s3 ,clavis ( #afdg1 ,eq41 ,an41 ,fa41 ,ho42 ,clavis ( #afdh1 ,eq41 ,an41 ,fa41 ,eu41 ,s42 ,clavis ( #afeb1 ,eq41 ,eu41 ,s41 ,an41 ,fa41 ,ar41 ,ho42 ,clavis ( #affg1 ,eq41 ,eu41 ,s41 ,an41 ,fa41 ,ar41 ,ho42 ,clavis ( #afic & #afih1 ,eq41 ,eu41 ,s41 ,an41 ,fa41 ,ar41 ,ho42 ,clavis ( #afid & #agjb1 ,eq4 ,! title-page ( ! ,clavis 0 consid]ably modifi$ aft] ! fir/ edition4 ,?us1 ! #afeb ,lat9 edition has ?is title-page3 ,guilelmi ,oughtr$ ,aeton5sis1 quondam ,collegii ,regalis 9 ,cantabrigia ,socii1 ,clavis ma!maticae d5vo limata1 sive potius fabricata4 ,cum aliis quibusdam ejusdem comm5tationibus1 quae 9 sequ5ti pag9a rec5s5tur4 ,editio t]tia auctior em5datior4 ,oxoniae1 ,excudebat ,leon4 ,li*field1 ,v5eunt apud ,?o4 ,rob9son4 #afeb4 #bc,rigaud1 op4 cit41 ,vol4 ,,ii1 p4 #dgf4 #bd,see1 = in/ance1 ! ,clavis ma!maticae ( #afeb1 :]e he expresses himself ?us 7p4 #d73 8,speciosa haec ,ari?metica arti ,analyticae 7p] quam ex sumptione quaesiti1 tanquam noti1 inve/igatur quaesitum7 multo accommodatior e/1 quam illa num]osa40 #be,oughtr$1 ,! ,key ( ! ,ma!maticks1 ,london1 #afdg1 p4 #d4 #bf;,clavis #afid1 p4 #ai1 & ! ,clavis ( #afca1 p4 #h4 #bg,see = in/ance1 ,oughtr$'s ,elem5ti decimi ,euclidis decl>atio1 #afeb1 p4 #a1 :]e he uses ,a & ,e1 & also a & e4 #bh,see ,*ri/ophori ,clavii ,bamb]g5sis ,op]um ma!maticorum1 tomus secundus1 ,moguntiae1 ,m4,,dc4,,xi1 algebra1 p4 #ci4 #bi;,*ri/ophori ,clavii op]um ma!maticorum ,tomus ,secundus1 ,moguntiae1 ,m4,,dc4,,xi1 ,epitome ari?meticae1 p4 #cf4 #cj,see ,f4 ,cajori1 8,! ,cross z a ,symbol ( ,multiplication10 9 ,nature1 ,vol4 ,,xciv 7#aiad71 p4 #cfc4 #ca,see ,elem5ti decimi ,euclidis decl>atio1 #afeb1 p4 #b4 #cb,see ,johannis ,wallisii ,op]um ma!maticorum p>s prima1 ,oxonii1 #afeg1 p4 #bdg4 #cc;,clavis ( #afca1 *ap4 xix1 sec4 #e1 p4 #ej4 #cd,we h notic$ ! repres5tation ( kn[n quantities by consonants & ! unkn[n by v[els 9 ,w+ate's ,ari?metick made easie1 edit$ by ,john ,k]sey1 ,london1 #afej1 algebra1 p4 #chb2 & 9 ! second "p1 section #ai1 ( ,jonas ,moore's ,ari?metick 9 two p>ts1 ,london1 #affj1 ,moore sugge/s z an alt]native ! use ( z1 y1 x1 etc41 = ! unkn[ns4 ,! practice ( repres5t+ unkn[ns by v[els did n spread widely 9 ,engl&4 #ce,philosophical ,transactions1 ,vol4 ,,xix1 ,no4 #bca1 ,london1 p4 #feb4 #cf;,ibid41 ,vol4 ,,xix1 p4 #ef4 #cg,!re are two title-pages to ! edition ( #afcb4 ,! fir/ title-page is z foll[s3 ,! ,circles ( ,proportion & ,! ,horizontall ,in/rum5t4 ,bo? inv5t$1 & ! vses ( bo? ,writt5 9 ,lat9e by ,mr4 ,w4 ,o4 ,translat$ into ,engli%3 & set =? = ! publique b5efit by ,william ,=/]4 ,london4 ,pr9t$ = ,elias ,all5 mak] ( ^! & all o!r ma!matical ,in/rum5ts1 & are to be sold at 8 %op ov] aga9/ ,/4 ,clem5ts *ur* ) out ,temple-b>r4 #afcb4 ,t4 ,cecill ,sculp4 ,9 #afcc !re 0 add$ ! foll[+1 ) a sep>ate title-page3 ,an addition vnto ! ,vse ( ! ,in/rvm5t call$ ! ,circles ( ,proportion4 4 4 4 4 ,london1 #afcc1 ?is be+ foll[$ by ,oughtr$'s ,to ! ,engli% ,g5trie etc4 ,9 ! ,briti% ,museum !re is a copy ( ano!r impression ( ! ,circles ( ,proportion1 dat$ #afci1 ) ! ,addition vnto ! ,vse ( ! ,in/rum5t etc41 be>+ ! orig9al date1 #afcc1 & ) ! epi/le1 ,to ! ,engli% ,g5trie1 etc41 ins]t$ imm$iately aft] ,=/]'s d$ication1 in/ead ( at ! end ( ! volume4 #ch,! complete title ( ! ,engli% edition is z foll[s3 ,trigonometrie1 or1 ,! mann] ( calculat+ ! ,sides & ,angles ( ,triangles1 by ! ,ma!matical ,canon1 demon/rat$4 ,by ,william ,oughtr$ ,eton5s4 ,& publi%$ by ,ri*>d ,/okes ,fell[ ( ,k+s ,coll$ge 9 ,cambridge1 & ,ar?ur ,haughton ,g5tleman4 ,london1 ,pr9t$ by ,r4 & ,w4 ,leyb\rn1 = ,?omas ,johnson at ! ,gold5 ,key 9 ,/4 ,pauls ,*ur*-y>d4 ,m4,,dc4,,lvii4 #ci;,j]4 ,colli]1 ,! ,great ,hi/orical1 ,geographical1 ,g5ealogical & ,poetical ,diction>y1 ,vol4 ,,ii1 ,london1 #agja1 art4 8,oughtr$40 #dj,rigaud op4 cit41 ,vol4 ,i1 p4 #hb4 #da;,a4 ,de ,morgan1 ,budget ( ,p>adoxes1 ,london1 #ahgb1 p4 #dea2 #b;d ed41 ,*icago1 #aiae1 ,vol4 ,,ii1 p4 #cjc4 #db;,e4 ,gunt]1 ,description & ,use ( ! ,sector1 ! ,crosse-/affe & o!r ,in/rum5ts1 ,london1 #afbd1 second book1 p4 #ca4 #dc;,f4 ,cajori1 8,on ! ,hi/ory ( a ,notation 9 ,trigonometry10 ,nature1 ,vol4 ,,xciv1 #aiae1 pp4 #fdb1 #fdc4 #dd;,a4 von ,braunmhl1 ,ges*i*te d] ,trigonometrie1 #b4 ,teil1 ,leipzig1 #aijc1 pp4 #db1 #ia4 #de;,h4 ,hankel1 ,ges*i*te d] ,ma!matik 9 ,alt]?um und ,mittelalt]1 ,leipzig1 #ahgd1 pp4 #cfi1 #cgj4 #df,m4 ,cantor1 ,vorlesung5 b] ,ges*i*te d] ,ma!matik1 ,,ii1 #aijj1 pp4 #fdj1 #fda4 #dg,?is matt] has be5 discuss$ 9 a pap] by ,f4 ,cajori1 8,a ,hi/ory ( ! ,ari?metical ,me?ods ( ,approximation1 etc41 ,colorado ,college ,publication1 ,g5]al ,s]ies ,no4 #ea1 #aiaj1 pp4 #ahb-hd4 ,lat] ?is subject 0 aga9 treat$ by ,g4 ,ene/rm 9 ,biblio!ca ma!matica1 #c4 ,folge1 ,vol4 ,,xi1 #aiaa1 pp4 #bcd1 #bce4 #dh,see ,f4 ,cajori1 op4 cit41 p4 #aic4 #di,see ,william ,oughtr$'s ,key ( ! ,ma!maticks1 ,london1 #afid1 pp4 #agc-ge1 tract1 8,( ! ,resolution ( ! ,affect$ ,equations10 or any edition ( ! ,clavis aft] ! fir/4 #ej;,a4 ,de ,morgan1 op4 cit41 p4 #dea2 #b;d ed41 ,vol4 ,,ii1 p4 #cjc4 #ea,see ,f4 ,cajori1 ,hi/ory ( ! ,log>i?mic ,slide ,rule1 ,new ,york1 #aiji1 pp4 #g-ad1 ,add5da1 p4 ii4 #eb,rigaud1 op4 cit41 ,vol4 ,i1 p4 #ab4 #ec,! ,new ,artificial ,gaug+ ,l9e or ,rod3 toge!r ) rules conc]n+ ! use !re(3 ,inv5t$ & writt5 by ,william ,oughtr$1 ,london1 #afcc4 #ed,w4 ,oughtr$1 ,apologeticall ,epi/le1 p4 #ac4 #ee,qu>t]ly ,j\rnal ( ,pure & ,appli$ ,ma!matics1 ,vol4 ,,xlvi1 7#aiae71 p4 #afi4 ,9 ?is article ,glai%] republi%es ! 8,app5dix0 9 full4 #ef;,aubrey1 op4 cit41 ,vol4 ,,ii1 #ahih1 p4 #ajh4 #eg,wood's ,a!nae ,oxoni5ses 7ed4 ,p4 ,bliss71 ,vol4 ,,iv1 #ahbj1 p4 #bdg4 #eh,wood1 op4 cit41 ,vol4 ,,ii1 p4 #dde4 #ei,rigaud1 op4 cit41 ,vol4 ,i1 pp4 #cc1 #ce4 #fj,rigaud1 op4 cit41 ,vol4 ,i1 pp4 #af1 #bf4 #fa,rigaud1 op4 cit41 ,vol4 ,i1 p4 #ff4 #fb;,ibid41 ,vol4 ,i1 p4 #i4 #fc,rigaud1 op4 cit41 ,vol4 ,,ii1 p4 #dge4 #fd;,ibid41 ,vol4 ,,ii1 p4 #dga4 #fe;,j4 ,w4 ,l4 ,glai%]1 8,on ,e>ly ,log>i?mic ,tables1 & ,_! ,calculators10 ,philosophical ,magaz9e1 #d? ,s]41 ,vol4 ,,xlv 7#ahgc71 pp4 #cgh1 #cgi4 #ff,rigaud1 op4 cit41 ,vol4 ,i1 p4 #fe4 #fg,rigaud1 op4 cit41 ,vol4 ,i1 p4 #hg4 #fh,k+'s ,life ( ,john ,locke1 ,vol4 ,i1 ,london1 #ahcj1 p4 #bbg4 #fi;,ex]citationum ,ma!matic>um ,decas prima1 ,naples1 #afbg1 & probably ,cataldus' ,trans=matio ,geometrica1 ,bonon41 #afab4 #gj,rigaud1 op4 cit41 ,vol4 ,,ii1 pp4 #dgg-hj4 #ga,miscellanies3 or ,ma!matical ,lucubrations1 ( ,mr4 ,samuel ,fo/]1 ,sometimes publike ,pr(essor ( ,a/ronomie 9 ,gre%am ,coll$ge 9 ,london1 by ,john ,twysd51 ,london1 #afei4 #gb,! ,works ( ! ,hon\rable ,rob]t ,boyle 9 five volumes1 to :i* is prefix$ ! ,life ( ! ,au?or1 ,vol4 ,i1 ,london1 #agdd1 p4 #bd4 #gc,! lett] is pr9t$ 9 ,john ,wallis' ,de algebra tractatus1 #afic1 p4 #bjf4 #gd,see ,la ,correspondance de ,desc>tes1 publi%$ by ,*>les ,adam & ,paul ,tann]y1 ,vol4 ,,ii1 ,p>is1 #ahih1 pp4 #def & #deg4 #ge;,h4 ,bosmans1 ,s4,j41 8,la premire dition de la ,clavis ,ma!matica d',oughtr$4 ,son influ5ce sur la ,gomtrie de ,desc>tes10 ,annales de la socit sci5tifique de ,bruxelles1 #ce? ye>1 #aiaj-aa1 ,"p ,,ii1 pp4 #bd-gh4 #gf;,ibid41 p4 #gh4 #gg,v9c5t ,w+1 ,h>monicon coele/e1 ,london1 #afea1 p4 #e4 #gh,se? ,w>d1 ,9 ,ismaelis ,bullialdi a/ronomiae philolaicae fundam5ta inquisitio brevis1 ,ox=d1 #afec1 p4 #g4 #gi;,john ,wallis1 ,el5*us geometriae ,hobbianae1 ,ox=d1 #afee1 p4 #dh4 #hj;,an ,idea ( ,ari?metick1 at fir/ design$ = ! use ( ! ,free ,s*oole at ,?url[ 9 ,suffolk4 4 4 4 4 ,by ,r4 ,b41 ,s*oolma/] !re1 ,london1 #afee1 p4 #f4 #ha,! ,miscellanies3 or ,ma!matical ,lucubrations1 ( ,mr4 ,samuel ,fo/] 4 4 4 4 by ,john ,twysd51 ,london1 #afei1 p4 #a4 #hb,moor's ,ari?metick 9 two ,books1 ,london1 #affj1 p4 #hi4 #hc;,isaac ,b>r[1 ,euclidis data1 ,cambridge1 #afeg1 p4 #b4 #hd;,francisci ,dulaur5s ,specima ma!matica1 ,p>is1 #affg1 p4 #a4 #he;,elm5s des ma?matiques1 ,p>is1 #afge1 ,preface sign$ 8,j4 ,p40 #hf,n\veaux lm5s de gomtrie1 ,p>is1 #afib 7p]mission to pr9t #afhd74 #hg,ozanam1 ,dictionnaire ma?matique1 ,p>is1 #afia1 p4 #ab4 #hh;,analyse des inf9im5t petits1 ,p>is1 #afif1 p4 #aa4 #hi,petro ,nicolas1 ,de con*oidibus et cissoidibus ex]citationes geometricae1 ,t\l\se1 #afig1 p4 #ag4 #ij,r4 ,p4 ,b]n>d ,lamy1 ,elm5s des ma?matiques1 ,am/]dam1 #afib 7p]mission to pr9t #afhj74 #ia,n\veaux lm5s de gomtrie1 #b;d ed41 ,! ,hague1 #afij1 p4 #cjd4 #ib,w4 ,w4 ,beman 9 ,l'int]mdiaire des ma?matici5s1 ,p>is1 ,vol4 ,,ix1 #aijb1 p4 #bbi1 "q #bdbd4 #ic;,john ,coll9s1 ,! ,m>9]'s ,pla9 ,scale ,new ,pla9'd1 ,london1 #afei1 p4 #be4 #id;,james ,gregory1 ,optica promota1 ,london1 #affc1 pp4 #ai1 #dh4 #ie,philosophical ,transactions1 ,vol4 ,,iii1 ,london1 p4 #hfh4 #if,william ,leyb\rn1 ,! ,l9e ( ,proportion1 ,london1 #afgc1 p4 #ad4 #ig;,elem5ta geometriae 4 4 4 4 a ,gulielmo ,s&]s1 ,glasg[1 #afhf1 p4 #c4 #ih;,cock]'s ,decimal ,ari?metick1 4 4 4 4 p]us$ by ,john ,hawk9s1 ,london1 #afie 7preface dat$ #afhd71 p4 #da4 #ii;,joseph ,raphson1 ,analysis ,aequationum univ]salis1 ,london1 #afig1 p4 #bf4 #ajj;,e4 ,wells1 ,elem5ta ari?meticae num]osae et speciosae1 ,ox=d1 #afih1 p4 #ajg4 #aja;,john ,w>d1 ,a ,comp5dium ( ,algebra1 #b;d ed41 ,london1 #afih1 p4 #fb4 #ajb,pla9 ,elem5ts ( ,geometry & ,pla9 ,trigonometry1 ,london1 #agja1 p4 #fc4 #ajc;,george ,%elley1 ,w+ate's ,ari?metick1 ,london1 #agjd1 p4 #cdc4 #ajd;,a ,synopsis ( ,algebra1 ,be+ a po/hum\s "w ( ,john ,alex&] ( ,b]n1 ,swiss]l&4 4 4 4 4 ,done f ! ,lat9 by ,sam4 ,cobb1 ,london1 #agji1 p4 #af4 #aje;,john ,craig1 ,de ,calculo flu5tium1 ,london1 #agah1 p4 #ce4 ,! notation ,a3,b33,c3,d is giv5 also4 #ajf,trigonometry1 #b;d ed41 ,ed9burgh1 #agbd1 p4 #aa4 #ajg,m?ode p\r la msure des surfaces1 la dim5sion des solides 4 4 4 4 p> ,m4 ,c>r de l'acadmie r4 des sci5ces1 #agjj1 p4 #ei4 #ajh;,application de l'algbre gomtrie 4 4 4 4 ,p>is1 #agje4 #aji;,elm5s de la gomtrie de l'inf9i1 by ,m4 de ,font5elle1 ,p>is1 #agbg1 p4 #aaj4 #aaj;,eclaircissem5s sur l'analyse des inf9im5t petits1 by ,m4 ,v>ignon1 ,p>is1 #agbe1 p4 #hg4 #aaa;,application de la gomtrie ord9aire et des calculs diffr5tiel et intgral1 by ,m4 ,robill>d1 ,p>is1 #agec4 #aab,trait de gomtrie ?orique et pratique1 new ed41 ,p>is1 #agfd1 p4 #ae4 #aac,re*]*es sur les c\rbes d\ble c\rbure1 ,p>is1 #agca1 p4 #ac4 #aad;,analyse des inf9im5t petits1 by ! ,m>quis de ,l',hospital4 ,new ed4 by ,m4 ,le ,fvre1 ,p>is1 #agha1 p4 #da4 ,9 ?is volume passages 9 f9e pr9t1 probably suppli$ by ! editor1 conta9 ! notation a3b33c3d2 ! p>ts 9 l>ge type give ,oughtr$'s orig9al notation4 #aae,! t5d5cy dur+ ! eighte5? c5tury is %[n 9 "p by ! foll[+ data3 ,jacobi ,b]n\lli ,op]a1 ,tomus primus1 ,g5eva1 #agdd1 gives ,b4,a33,d4,c on p4 #cfh1 ! pap] hav+ be5 fir/ publi%$ 9 #afhh2 on p4 #dai is giv5 ,,ge3,,ag,,la3,,ml1 ! pap] hav+ be5 fir/ publi%$ 9 #afhi4 ,b]nh>di ,nieuw5tiit1 ,consid]ationes circa analyseos ad quantitates inf9it p>vas applicatae pr9cipia1 ,am/]dam1 #afid1 p4 #bj1 & ,analysis inf9itorum1 ,am/]dam1 #afie1 on p4 #bgf1 h x3c33s3r4 ,paul ,halck5's ,deliciae ma!maticae1 ,hamburg1 #agai1 gives a3b33c3d4 ,johannis ,bapti/ae ,c>accioli1 ,geometria algebraica univ]sa1 ,rome1 #agei1 p4 #gi1 has a4b33c4d4 ,delle corde ouv]to fibre ela/i*e s*$iasmi fisico-matematici del conte ,giordano ,riccati1 ,bologna1 #agfg1 p4 #fe1 gives ,p3b33r3ds4 8,produzioni ma!mati*e0 del ,conte ,giulio ,c>lo de ,fagnano1 ,vol4 ,i1 ,pes>io1 #agej1 p4 #aic1 has a4b33c4d4 ,l4 ,mas*]oni1 ,gomtrie du compas1 translat$ by ,a4 ,m4 ,c>ette1 ,p>is1 #agih1 p4 #ahh1 gives 7#c73b337b73,lp4 ,danielis ,mel&ri & ,paulli ,frisi1 ,de !oria lunae comm5t>ii1 ,p>ma1 #agfi1 p4 #ac1 has a3b33c3d4 ,vic5tio ,riccato & ,hi]onymo ,salad9o1 ,in/itutiones analyticae1 ,vol4 ,i1 ,bologna1 #agfe1 p4 #dg1 gives x3a33m3nm4 ,r4 ,g4 ,boscovi*1 ,op]a p]t95tia ad opticam et a/ronomiam1 ,bassani1 #aghe1 p4 #dji1 uses a3b33c3d4 ,jacob ,b]n\lli1 ,ars ,conject&i1 ,basel1 #agac1 has n-r4n-#a33;c4d4 ,pavl9i ,*elvicii1 ,in/itutiones analyticae1 editio po/ t]tiam ,romanam prima 9 ,g]mania1 ,vi5na1 #agfa1 p4 #b1 a4b33c4d4 ,*ri/iani ,wolfii1 ,elem5ta ma!seos univ]sae1 ,vol4 ,,iii1 ,g5eva1 #agce1 p4 #fc1 has ,,ab3,,ae#a3q4 ,johann ,b]n\lli1 ,op]a omnia1 ,vol4 ,i1 ,lausanne & ,g5eva1 #agdb1 p4 #dc1 has a3bc3d4 ,d4 ,c4 ,walmesley1 ,analyse des mesures des rapports et des angles1 ,p>is1 #agdi1 uses ext5sively a4b33c4d1 lat] a3b33c3d4 ,g4 ,w4 ,krafft1 ,in/itutiones geometriae sublimoris1 ,tb+51 #agec1 p4 #aid1 has a3bc3d4 ,j4 ,h4 ,lamb]t1 ,photometria1 #agfj1 p4 #ajd1 has ,c3 ,,bc3,,mh4 ,meccanica sublime del ,dott4 ,dom5ico ,b>taloni1 ,naples1 #agfe1 has a3b33c3d4 ,occasionally ratio is n designat$ by a4b1 nor by a3b1 b by a1 b1 z = in/ance 9 ,a4 de ,moivre's ,doctr9e ( ,*ance1 ,london1 #agef1 p4 #cd1 :]e he writes a1 b33#a1 q4 ,a fur!r v>iation 9 ! designation ( ratio is f\nd 9 ,james ,atk9son's ,epitome ( ! ,art ( ,navigation1 ,london1 #agah1 p4 #bd1 namely1 #c44b33gb44dh4 ,curi\s notations are giv5 9 ,ri*4 ,balam's ,algebra1 ,london1 #afec4 #aaf;,*r4 ,clavii ,op]um ma!maticorum tomus secundus1 ,may5ce1 #afaa1 ,algebra1 p4 #ci4 #aag;,inv5tion n\velle en l'algbre1 by ,alb]t ,gir>d1 ,am/]dam1 #afbi1 p4 #ag4 #aah,la gomtrie et pratique gnrale d'icelle1 p> ,i4 ,err>d de ,b>-le-,duc1 ,+nieur ord9aire de sa ,maje/1 #c;d ed41 revis$ by ,d4 ,h4 ,p4 ,e4 ,m41 ,p>is1 #afai1 p4 #baf4 #aai,novae geometriae clavis algebra1 au?ore ,p4 ,jacobo de ,billy1 ,p>is1 #afdc1 p4 #aeg2 also an ,abridgem5t ( ! ,precepts ( ,algebra4 ,writt5 9 ,fr5* by ,james de ,billy1 ,london1 #afei1 p4 #cdf4 #abj,miscellanies3 or ,ma!matical ,lucubrations1 ( ,mr4 ,samuel ,fo/]1 ,sometime publike ,pr(essor ( ,a/ronomie 9 ,gre%am ,coll$ge 9 ,london1 ,london1 #afei1 p4 #g4 #aba,qu>t]ly ,j\r4 ( ,pure & ,appli$ ,ma?41 ,vol4 ,,xlvi 7,london1 #aiae71 p4 #aia4 #abb,pietro ,cossali1 ,orig9e1 trasporto 9 ,italia primi progressi 9 essa dell' algebra1 ,vol4 ,i1 ,p>m5se1 #agig1 p4 #eb4 #abc;,9 ,is4 ,bullialdi a/ronomiae philolaicae fundam5ta inquisitio brevis1 ,auctore ,se?o ,w>do1 ,ox=d1 #afec1 p4 #a4 #abd;,john ,wallis1 ,algebra1 ,london1 #afhe1 p4 #cba1 & 9 "s ( 8 o!r works4 ,he makes great] use ( ,h>riot's symbols4 #abe;,euclidis data1 #afeg1 p4 #a2 also ,euclidis elem5torum libris ,,xv1 ,london1 #afei1 p4 #a4 #abf;,john ,k]sey1 ,algebra1 ,london1 #afgc1 p4 #cba4 #abg;,e4 ,wells1 ,elem5ta ari?meticae num]osae et speciosae1 ,ox=d1 #afih1 p4 #adb4 #abh;,cock]'s ,decimal ,ari?metick1 p]us$ by ,john ,hawk9s1 ,london1 #afie 7preface dat$ #afhd71 p4 #bgh4 #abi,?4 ,bak]1 ,! ,geometrical ,key1 ,london1 #afhd1 p4 #ae4 #acj,ri*>d ,sault1 ,a ,new ,treatise ( ,algebra1 ,london 7no date74 #aca,ri*>d ,rawl9son 9 a pamphlet )\t date1 issu$ sometime betwe5 #afee & #affh1 conta9+ trigonometric =mulas4 ,!re is a copy 9 ! ,briti% ,museum4 #acb;,f4 ,dulaur5s1 ,specima ma!matica1 ,p>is1 #affg1 p4 #a4 #acc;,j4 ,milnes1 ,sectionum conic>um elem5ta1 ,ox=d1 #agjb1 p4 #db4 #acd;,*eyne1 ,philosophical ,pr9ciples ( ,natural ,religion1 ,london1 #agje1 p4 #ee4 #ace;,j4 ,craig1 ,de calculo flu5tium1 ,london1 #agah1 p4 #hf4 #acf;,jo4 ,wilson1 ,trigonometry1 #b;d ed41 ,ed9burgh1 #agbd1 p4 v4 #acg;,comm]cium ,epi/olicum1 #agab1 p4 #bj4 #ach;,c4 ,le ,paige1 8,sur l'orig9e de c]ta9s signes d'opration10 ,annales de la socit sci5tifique de ,bruxelles1 #af? ye>1 #ahia-ib1 ,"p ,,ii1 pp4 #gi-hb4 #aci;,gravela>1 8,ov] d5 oorsprong van ons maalteek5 7710 ,wiskundig ,tijds*rift1 #f? ye>4 ,we h n _h access to ?is article4 #adj;,h4 ,bosmans1 op4 cit41 p4 #dj4 #ada;,claudii ,ptolemaei 4 4 4 4 annotationes1 ,ble1 #aeea4 ,?is ref]5ce is tak5 f ! ,encyclopdie des sci5ces ma?matiques1 ,tome ,i1 ,vol4 ,i1 ,fasc4 #a1 p4 #dj4 #adb;,due ,correction = ,mr4 ,hobbes4 ,or ,s*oole ,discipl9e1 = n say+ 8 ,lessons "r4 ,9 answ] to 8 ,six ,lessons1 direct$ to ! ,pr(essors ( ,ma!maticks4 ,by ! ,pr(essor ( ,geometry4 ,ox=d1 #afef1 pp4 #g1 #dg1 #ej4 #adc,oughtr$1 ,apologeticall ,epi/le1 p4 #bg4 #add;,j4 ,edle/on1 ,correspond5ce ( ,sir ,isaac ,newton & ,pr(essor ,cotes1 ,london1 #ahej1 pp4 #bgi-ib4 ,,index ,adam1 ,*>les1 #ga ,agnesi1 ,m>ia ,g41 #gg ,alex&]1 ,j41 #gf ,all51 ,e41 #ce ,analysis1 #ai1 #bj ,apollonius ( ,p]ga1 #bj1 #he ,ar*im$es1 #ah1 #bj1 #he ,ari/otle1 #fi ,a%mole1 ,e41 #ac ,atk9son1 ,j41 #gi ,atwood1 #ef ,aubrey1 #c1 #g1 #h1 #ab-af1 #eh1 #ei ,au/91 #eh ,bak]1 ,t41 #hb ,balam1 ,r41 #gi ,b>-le-,duc1 de1 #hj ,b>r[1 ,s41 #a1 #cb1 #gc1 #gd1 #hj1 #ha ,b>taloni1 ,d41 #gi ,beman1 ,w4 ,w41 #gd1 #ge ,b]n\lli1 ,jakob1 #gh-hj ,b]n\lli1 ,john1 #gi1 #hj ,bill+sley's ,euclid1 #ae ,billion1 #bj ,billy1 ,jacobo de1 #hj ,b9omial =mula1 #be1 #bi ,bliss1 ,p41 #fj ,boscovi*1 ,r4 ,g41 #gh ,bosmans1 ,h41 #gb1 #hc ,boyle1 ,r41 #a1 #fi ,braunmhl1 von1 #ci ,bre>ly1 ,w41 #ei ,briggs1 #f1 #cf1 #ee ,brookes1 ,*ri/oph]1 #g1 #ec1 #ei ,cajori1 ,f41 #bg1 #ci1 #dj1 #dg ,cantor1 ,m41 #dj1 #da ,c>accioli1 ,j4 ,b41 #gh ,c>dan1 #ga ,c>r1 #gg ,c>rete1 ,n4 ,m41 #gh ,c>yll1 ,c41 #g ,cataldi1 #fg ,cavali]i1 #fe1 #ff ,cav5di%1 ,*>les1 #ag1 #fb1 #ff ,*>les ,i1 #i1 #fj ,*elvicius1 ,p41 #gi ,*eyne1 ,g41 #hb ,circles ( ,proportion1 #ce1 #cg1 #dh1 #di1 #ea1 #ei1 #hg1 #hh ,clairaut1 #gg ,cl>k1 ,a41 #c ,cl>k1 ,g41 #fc ,cl>ke1 ,f4 ,l41 #c ,clavis ma!maticae1 #a1 #e1 #aj1 #ad1 #ag-ce1 #de1 #df1 #ea1 #eg-fc1 #fh-gc1 #ha1 #he1 #hg ,clavius1 #bf1 #hj ,cl]c1 le1 #gg ,cobb1 ,s41 #gf ,cock]1 #gf1 #hb ,coll9s1 ,john1 #ae1 #ai1 #fc1 #fd1 #fg1 #fh1 #gf1 #hb ,colson1 ,j41 #gg ,con*oid1 #ab ,conic sections1 #aa1 #ec ,cossali1 ,p41 #ha ,cotes1 ,r41 #a1 #he ,craig1 ,j41 #gf1 #hb ,cross1 symbol ( multiplication1 #bg1 #ch1 #ee1 #ef1 #hb1 #hc ,cubic equations1 #bh1 #cd1 #db1 #de ,decimal fractions1 notation (1 #ba ,degree1 c5tesimal division1 #ci ,delama91 ,r41 #d1 #i1 #aj1 #aa1 #dg1 #dh1 #ea1 #fj1 #hd1 #hh1 #hi1 #ia1 #ic1 #id ,de ,moivre1 #cb1 #gi ,de ,morgan1 ,a41 #e1 #af1 #cg1 #df1 #dg1 #ed ,desc>tes1 ,r41 #a1 #be1 #dg1 #eg1 #fh-gb1 #hj ,dibuadius1 #gi ,diff]5ce1 symbol =1 #bg1 #ha ,diophantus1 #fc1 #he ,division1 abbreviat$1 #ba1 #bc1 #bd ,dulaur5s1 ,f41 #gd1 #hb ,e>l ( ,arundel1 #aj1 #ac1 #ae1 #ag ,edle/on1 ,j41 #ie ,ene/rm1 ,g41 #dj ,equations1 solution (1 #ah1 #bh1 #bi1 #ca1 #cd1 #ci-de1 #hg ,err>d de ,b>-le-,duc1 #hj ,eton ,college1 #c1 #d ,euclid1 #a1 #ae1 #ah1 #bj1 #be1 #bg1 #bh1 #gi1 #ha1 #hc1 #he ,eul]1 ,l41 #cg1 #ci ,ew>t1 #ei ,expon5ts1 #be1 #bh1 #bi ,fagnano1 de1 #gh ,fl[]1 #ef ,font5elle1 de1 #gg ,=/]1 ,w41 #ce1 #dh1 #ei1 #hh ,fo/]1 ,s41 #bg1 #fg1 #fi1 #gc1 #hj1 #hi ,frisi1 ,p41 #gh ,gascoigne1 #ei1 #fa ,gauss1 ,c4 ,f41 #dh ,geysius1 #fg ,ghetaldi1 #gj1 #ga ,gibson1 #fg ,gir>d1 ,a41 #cb1 #hj ,glai%]1 ,j4 ,w4 ,l41 #ed-ef1 #fd1 #hj ,glorioso1 #fg1 #fh ,grammelogia1 #d1 #dg1 #hi ,gravela>1 #hc ,great] ?an1 symbol =1 #ha ,greatrex1 ,r41 #ae ,gregory1 ,d41 #cb ,gregory1 ,j41 #bg1 #gf ,gre%am ,college1 #a1 #f1 #bg1 #ei1 #fa1 #hj ,guisne1 #gg ,gunt]1 ,e41 #cg1 #dg1 #hf ,gunt]'s scale1 #cg ,halck51 ,p41 #gh ,hales1 ,j41 #g ,halley1 ,e41 #a1 #ah1 #fi ,hankel1 ,h41 #dj ,h>p]1 ,t41 #ah ,h>riot1 ,t41 #de1 #dg1 #eg1 #eh1 #fi-ga1 #ha ,h>ris1 ,j41 #gf ,h>tlib1 #fi ,haughton1 ,a41 #ce1 #ei ,hawk9s1 ,j41 #gf1 #hb ,he>n1 #ef ,helmholtz1 #dh ,h5ry1 ,j41 #dh ,h5ry van ,ett51 #eb1 #ec ,h5%aw1 ,t41 #h1 #eh1 #fa ,hobbes1 #gc1 #hf ,holl>1 #ad ,holsatus1 #ac ,hooganhuys51 #fd ,hooke1 ,rb41 #a ,horn]'s me?od1 #de ,horology1 #ah1 #ej ,horrox1 ,j41 #d ,hospital1 de l'1 #gd1 #gg ,h[>d1 ,?4 ,see ,e>l ( ,arundel4 ,h[>d1 ,w41 #ag1 #ah1 #ei ,hut*9son1 ,a41 #f ,invisible college1 #a ,j\le1 #dh ,kepl]1 ,j41 #f ,k]sey1 ,j41 #cb1 #gc1 #hb ,keylway1 ,r41 #fe ,k+1 #fg ,k+s ,college1 ,cambridge1 #c1 #ce ,krafft1 ,g4 ,w41 #gi ,lamb]t1 ,j4 ,h41 #gi ,lamy1 ,r4 ,p4 ,b41 #gd ,laud1 ,ar*bi%op1 #fe ,leake1 ,w41 #ec ,le ,cl]c1 #gg ,lee*1 ,w41 #ei ,le ,fvre1 #gg ,leibniz1 #dg1 #gh1 #hj ,leonelli1 #ef ,le ,paige1 de1 #hc ,less ?an1 symbol =1 #ha ,leure*on1 #eb ,leyb\rn1 #ce1 #fd1 #gf ,li*field1 ,mrs41 #ai ,lilly1 ,w41 #h1 #i ,locke1 ,j41 #fg ,log>i?ms1 #f1 #ba1 #bg1 #bh1 #ch1 #ci1 #db1 #df1 #ed-ef1 #fe1 #ib1 #ic2 natural1 #ee2 radix me?od ( comput+1 #ee1 #ef ,l[]1 ,w41 #eh ,ludolph ,ceul51 #gi ,mann+1 #ef ,mann+1 ,o41 #g1 #h1 #ac-ae ,mas*]oni1 ,l41 #gh ,may]1 ,r41 #dg ,mel&ri1 ,d41 #gh ,m]cator1 ,n41 #ac ,m]s5ne1 #fc ,milb\rn1 ,w41 #de ,million1 #bj ,milnes1 ,j41 #hb ,moivre1 de1 #cb1 #gi ,moore1 ,jonas1 #cb1 #ed1 #eh1 #gc ,morel&1 ,s41 #gj ,morse1 ,r41 #dh ,multiplication1 abbreviat$1 #ba1 #bb1 #bd2 symbol =1 #bg1 #hb1 #hc ,mydorge1 #ed ,napi]1 ,j41 #f1 #g1 #ba1 #bg1 #ch1 #ci1 #eb1 #ed1 #eg1 #ei ,napi]'s analogies1 #ci ,newton1 ,sir ,isaac1 #a1 #be1 #bi1 #dj1 #da1 #de1 #dg1 #ei1 #fe1 #hf1 #ib-ie ,ni*ols1 ,j41 #f1 #ad ,nicolas1 ,r4 ,p4 ,p41 #gd ,nieuw5tiit1 ,b41 #gh ,norwood1 ,r41 #cg1 #ch1 #hj ,opuscula ma!matica hact5us in$ita1 #af1 #ba1 #ge ,or*>d1 #ef ,oughtr$us explicatus1 #fd ,ozanam1 #gd 1 symbol =1 #cb ,paige1 ,c4 de1 #hc ,p>dies1 #gf ,p>5!ses1 #bf1 #gi1 #hj ,p>tridge1 ,s41 #dg ,peano1 #hf ,p]fect numb]1 #da ,pitiscus1 #ae ,planisph]e1 #ec1 #ib1 #ic ,pre/et1 ,j41 #gd ,price1 #aa ,proportion1 notation =1 #bf1 #bg1 #gc-gi ,pro!roe1 #eh ,ptolemy1 #hc ,quadratic equation1 #bi1 #ca1 #cd ,radix me?od1 #ee1 #ef ,rahn1 #bg ,raphson1 ,j41 #dj1 #da1 #gf ,ratio1 notation (1 #ba1 #gc-hj ,rawl9son1 ,r41 #ci1 #hb ,regula falsa1 #ah ,regul> solids1 #ah ,riccati1 ,g41 #gh ,riccati1 ,v41 #gh ,rigaud1 #g1 #ab1 #ac1 #ai1 #dh1 #fa-ff1 #fh ,robill>d1 #gg ,rob9son1 ,w41 #ac1 #dh1 #ei1 #fb1 #fc ,rooke1 ,l41 #ei1 #fa ,salad9i1 ,h41 #gh ,s&]s1 ,w41 #gf ,sault1 ,r41 #hb ,sc>bor\gh1 ,*>les1 #af1 #ed1 #eh1 #fj ,s*oot51 ,van1 #a ,s*re%5su*s1 ,o41 #hc ,scrat* me?od1 #bc ,%akespe>e1 #eb ,%elley1 ,g41 #gf ,%ipley1 ,a4 ,e41 #a ,%uttlewor?1 #ei ,slide rule1 #i1 #df-di1 #ej1 #fj1 #hh1 #ic ,sme?wyck1 #eh ,smi?1 ,j41 #ej ,snellius1 ,w41 #gi ,solids1 regul>1 #ah ,speidell1 ,john1 #ch1 #ee ,sph]ical triangles1 #ec1 #ed1 #ic ,/okes1 ,r41 #ce1 #cf1 #eh ,sudell1 #ei ,sun dials1 #e1 #i1 #ej1 #ea1 #eb1 #fj1 #ib ,tann]y1 ,p41 #ga ,todhunt]1 #fj ,torporley1 #eh ,triangles1 sph]ical1 #ec1 #ed1 #ic ,trigonometria1 #ba1 #cf1 #ee1 #ge ,trigonometric functions1 symbols =1 #cf1 #cg1 #ee1 #ef ,trigonometrie1 #ba1 #ce1 #ci ,trisection ( angles1 #bh ,twysd51 #ei1 #fh1 #fi1 #gc ,v>ignon1 #gg ,vieta1 #a1 #b1 #be1 #cb1 #cc1 #ce1 #ci-da1 #de1 #fc1 #fg1 #gj1 #ga ,vlack1 #fe ,von ,braunmhl1 #ci ,wadham ,college1 #e1 #ec ,wallis1 ,john1 #a1 #ai1 #bg1 #cc1 #de1 #eg-ei1 #fc1 #fd1 #ff-gd1 #gi-ha1 #hf ,walmesley1 ,d4 ,c41 #gi ,w>d1 ,bi%op1 #ac ,w>d1 ,john1 #gf ,w>d1 ,se?1 #ee1 #eh1 #fj1 #fh1 #gc1 #gd1 #ha ,wat*-mak+1 #ah1 #ej ,web]1 ,w4 ,e41 #dh ,w$dle1 #ef ,wells1 ,e41 #gf1 #hb ,:>ton1 #fj ,:itlock1 ,b41 #h1 #i ,wilson1 ,j41 #gg1 #hb ,w+1 ,v41 #gc1 #ge ,w+ate1 ,e41 #cb1 #dg1 #gc ,wolf1 ,*ri/ian1 #gi ,wood1 ,a41 #fj1 #fa ,wood1 ,r41 #ah1 #ei ,wr51 ,*ri/oph]1 #e1 #eh1 #ei1 #gf ,wright1 ,e41 #f1 #bg1 #ch1 #ed ,wright1 ,s41 #ed ,transcrib]'s ,notes ,a h&ful ( typos1 mo/ly misplac$ punctuation1 7 sil5tly correct$4 ,,html & ,,utf text v]sions make heavy use ( ma!matical symbols3 p>ticul>ly sup]scripts1 subscripts1 & comb9+ *>act]s4 ,"s view]s may require us] assi/ance to f9d fonts conta9+ ^! *>act]s4 ,! text v]sions miss mu* ( ! =matt+1 especially 9 ma!matical =mulas3 --,sev]al ari?metic examples mu/ be view$ 9 a monospac$ font 7:i* recognizes comb9+ *>act]s7 to be legible4 --,=mulas "u ! horizontal l9e ( a squ>e root symbol are p>5!siz$4 --,subscripts are prec$$ by 804 --,sup]scripts are prec$$ by 804 --,italics1 us$ prim>ily 9 =mulas & bibliographical entries1 are n indicat$ 9 ! text4 --,italics 9 ! index are delimit$ by 804 --,und]l9es are n indicat$ 79 p>ticul>1 9 ! fractional "p ( a decimal numb] 9 ,oughtr$'s notation74 --,! idiosyncratic 8great] ?an0 & 8less ?an0 symbols are indicat$ z symbol 9 ! ,,ascii v]sion4 --,ov]dots1 und]dots1 & sla%m>ks ar\nd digits 79 ! long division example7 are n indicat$ 9 ! ,,ascii v]sion4 --,greek lett]s are spell$ out )9 curly brackets 9 ! ,,ascii v]sion4