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Show ARITHMETICORVM, 103 , a.in b.ac triplo eius, quod ex qmclmto iplius b.in a. Sad per pri{col Per pg 1; mam {ccfidi Euclidis,quadmtum iplius mcum co quod cx a. in b». funt b.gq1ia 3 _].a.cfi L":- ctit ante-31mm p:o:olinmm in 1 mituvliml-n 1 l). E? nomnldbi ficuhi, (I‘ll cognitllhgponrnnlt:, (cilia: cf‘. fibrin: in pro-gov limul {11um 33.3 In; limul gqualia {Lint ci quad ex :1 l). in :1. Et pot tandem , quod fit «tion‘: Cit‘wmm num :torungtnn': w Igitur T‘iPhiH‘3'fi ell ci, quod ex Produclo totius a b. dc min b-. hoc Eml‘olido mum ,tunc mm g, q:1‘unk.:runt rationals; qumrimtcs : quantum coIn in cubi fun: cu‘uinvlmfli , Pit pmccdcntcn: quandaqnidcm q-uod ex quadrato iplius l). in a. a'qunlia flint Ci , quod ex produ- uai‘c & triplum illius, a'qualc triplo huius. Ergo cubus tou'us a bim‘qualis cut his , lc1licctcub01pfius a.cubo iplius b. 8: triple folidi, cums latcm fun: a b. a. l). (&od cm: dcmonl'cmnduim ' ot‘ollvium 1.1;"C lmius,ip- (i? m iénituglincs 1 l). cunt :1 l inixcon com‘nsnlhraibilcs. Vnd: i" "iPlOI‘W' 6h) i‘plius a b. 8; :1. in b. lioc ell: folido crium latci‘um a l). a. 34: b. moi}. Sillii'luii- swab, 1049 ex quadrato ipiius min b: vni Cum co.quod ht ex a bin hatqualc o totius a l). in bxqmle tol-‘rdummhxfi (Alli), 1,34 lotch ;1 b. a. b. Atquc, oquod rs);l).produdl in a. hoe cfl , folido trium latcguano {uiiifulido 31).; b. cl": ci, quod ex quadrat iplius rum :1. b l). Igitur , quod cx quadraro iplius a. in b. vm‘l cum co, Qiare & LIBRI PRIMI, PARS n. di. ab. 3. b. P R OP 0 8 II 1 0 Quf'dt'll Ippolimm. 232° producfitur ex qtndmtis numaroi‘um cf. in Proportion: cuisica exil‘tmtium, mulclp-licatis viCilliai in ipfos nunu‘os c F. (hum-.obrcm clung k. tun: lint ratiomles , comm tripli fcilicct 11 Ha. rionllcs crunc:c:1m'1<1: c f. pct hvpotlisiim lint rationales, quio. cu'fi cogniti,crit aggrgztum ex 6 F11 1. ho: cl , iplL- m. cu‘ous ma cl? reperirc culmm rclié} e , qui ell F. Sit iraqi :: n. qui fit ex 3 b. ton in :1. led nut-3m lit ex n. in: b.1it o. cuius. triplum lit merit- 7; T4. 3-; 7 men fimilcs a .d' tolcs- cum-1 vr in 00muo Elcmtntorum Ollcnlum- (flue par gxntcprqmillhm. m. aeqmlis aggregate 1pforum- e F. 8: r. d c f 576 : 155 g 13,324 .___ l1 '------"814 n .__.__. ""45 0 ""35,. hot. all x!.. l‘ ell, liabcnt ndmulccm [811011611] , qunm calms numcrus ad cu- _____. Imqu; ex n.1'v1vromm a b.fiat p 8: ex m. in a flat q. Vnd'cgper'pri- _________ _m.1m {Ecumli Euclid. p. rqmliscrimggrcgato Iplai‘um oq.Au- 0&au1m oCltaui Elcmcntorum , ipfis a d. inr'erfimr duo numcri mcdij proportiomlcs, qui {mil} C. Sit imquciplms I). qua~ inmuo abiplo m. & lupcrcrit f. cu rcgatum cum '1‘. fzzi‘zgg imwo _ W 5‘ :1 b. {ubbus {ciliccr iplius b.quxfitus, quzpofiipfius 3. Atom drarus ipfefiSc ex b.in f. fi'lt l1.qui cubus erit iplius l). Ollcndam igiturfluocl g. xqualis all ipfi l). hoc modo. Ratio ipfius 6. ad ip~ {um F. per vndccimam oé‘tmi , cll‘licut ratio ipfius a. 1d ipfilm by q , qui cotmétion-xm rclinqu‘mr. Hic rurfinn nota‘, quod fi cu'si c :1} 1. m rmqug cubi licut m mince rad gniti lupponunrur, iClllCL‘E m. 8c c. filti‘m magnipfr; lmiusj mg tdcci qmttz numir‘; : tunc per corollarium z. c. lcs. Vndc tudmcs a l7.tot;1&ci1. cruntad inuiccm' commcnlumlui z.:,.f. um',_cll.crcubosnu~ m.8 1tfic necalli: Cl}, Culwos ipfu‘um r qumaguitudin 54.1" €3.- (it: :3. ad f. wrcmcr vicclimamfepmni, qui firex d. in c. 1105 all, ipl}: g.2&qualis all 61 , qui fit ex l). in Elloc cit ipli l1. Calms nutcm fuit h. iplius b.- ergo Sc g cubus idem crir.Qu'0d efiproPofimin.. PRO-PO'SITIO 2.43. ‘Tropofitis‘duabm quantitatibus who tannin; cogniti:,eax com'un‘ t gere : (73' minorcm a‘ maiori fizbrmbero . Sunro- propolira: rim-r ~---‘-: guitudincs a. l).- quamm quadmm a b. & quarum cu bi of. volo« M _~ -__7 7__ €15 coniungcrc per Cubos , hoc ell, comparirc cubum. totius a l). mnaifhocé u. x-cuniM-M- mnqufivmusmagnimdinis. Duco a.in (L85 proucniat g.Cui9 tri- 13 plum 11th. Item duco l). in c. 34 proucniat k. cuius triplum fit 1.. ;6 __ 8[ bum numerumlSitquc iplius a. quadratus humerus c. 3: ex sin d'. fiat g. Aio , qnod g, cubus numerus ell. Nam per dccimom» duplicam : quoniam fcilicct c f. l‘unt ipforum a l). quadruific ratio 1). ad 6.. all rationis 41. ad l). duplicgm. Igitux, licut 1). ad do m ___._._..-. r {uhtmhcrc morgmtufl:(10113,. cum; cams c. pique per cuooslloc Sifuerint duo nnmcrz in proportions moor/4m numeromm, qui fie: b m [le ab. nun-3m; ntiomlis: quire tom qumtims :L b. crit who cognira , 8c vnius nominis , ficut‘ corollarium 14.9 concludit. o ciuS»m.vol per_ culmmne a b.‘ cognim 1 «.1: ton nmgriituz‘li 1 , Crmtri 1 ' . ' ox vno comm inqtmo'ratflrcliqui,cubm erit. Sunto duo {olidi pua :1 2+ 3 M0); aggrcgatum‘ipfotfi efli l. fitm.Q1_i,per z 15 prasccdenrcm, exit cub‘3 rotiqs a l). qu‘i qgaarcbmun Vndc radix cubica ipfius rm. 1:" K CHI 5+ iplum r.. {CEO igitur' ipfilm 61. ab iplo p 85 lap-trout o. cuiusrr _.»P 1.014;"; hoc cf: :3, r, Vt mcros , 8: perine‘lc iplfis p q. ell} ruiomlcs: vnd: lcqmtu cubus , numcnis rum Cllt‘r‘TCntll lbilicc-t 0.. lit ratiomlisxiuliquc. ad inuicem, (1-. calms. Qpil ficr)ll:nd1 porcll.CL‘1:n m.& If. lint uu acimam otlatmnwéb cut cubi nuxnci‘i : inrsrcrunt iplio, pcrdr ailtcm lplius m. (1111-: 81! f. r s qui'lin , duo: all} Proportionales c. numcrus n.qui m.m ex q‘uc x.l'1:[ ifa.rus c.qu.u. iplius draws L86 fiat numcrus uin numco n; filit cuLus magnit" iii; n.E1;xm.1n n. me. [in numcrus P' qui Exit culus magnitudinis p. Itemqicx‘ , quod plumme- itut Dicmg magnitudinis q. q. qni fiiit cu‘ us (1 numcrus all cubus llpfius f. ms ell culms iaixeius r. Arquc 111641 , 8660- cub) numeri N.lm,(1\1m m canumcri fin! ml muiCcm, ficm nutrierus, prxoedmtcm, min mm qmdmti lint t. 8: x. 1.1m pin: mum x. Producxtur, Lubus‘o cx qui ms nums qnlxm t. in " i :31 c. numcms. (in I W. >-W"""""" '4 2‘; "‘ "‘WW 5! m 7-.1 ‘ |
