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Show 134. . A RITH MET'I'CO R"VM LIB‘RI SECVN'DI‘, PA'RS n. "135' mcnfmabflcm . Exempli gratis. , rationalis quantitas fi;. multiplicetquantitatezn b. porcntin tanu‘xm l‘atiomlcm , Pnoposx'rxo 51". 8; Faciar c. 'Axo,qubd c Potentitl mmt‘xm rzlrionalis Cfl,& ipOm, Sum dam m qmntZt-t/tm inxziccm commcnflzrabéléum 1‘1 'b.multiplicmm Commcnfilm'oilis. Sitcnim ipfius a. qua- dratum A (‘5; ipfius hquadmmm 08:. ex d.in mfiat {Ermine per mm". vnderimg huiusfiquadratun} ipfius C. Cutm'luc ex diflinitionii‘usguantiratum a b. ipf: (Hit numcrus qua. (INJd nat‘zfmlt danszcem flmt quazir‘ati numc‘ri: (y Cit/)ifldiflm- (cm, (7': mt mlr'z' mtmcri: {fr ferzmzla quzzcirsm ,fimt [22's (fwd/at} ,z/mzcri : Vt I} fin: :1 b. quantitn {1's inuicgm commcnlhmbiv Its , qu ‘w'fi qmdratzx Hut C d. cnbi :u'xc c F. li‘cunda mt»; 1m. dmtus: ipii'antcm e. numcrus non quadratus : mm comm Produfl'um fiper corolHEcundm nom' Eudmpn crit numerus quadratus. Igfim‘ c. qua: radlx clhpi‘zus {.pcr({1fl§n.crit Pore-min Ianmm mtiomlis. Cu m quc pg di‘flm. m ulniphcu tionis,c;produ6‘tfi 3dJamalriflicategmht [1cz‘1ra‘ nmitipliCans ad pofimm : firc'lnc a. polka: ccmuuntumbilis , quiz rationalis:inm,pcr pmxcdrntcm, i191} c. ipfi b.CommcnfiIm bilis eritz: ficut proponitur. Similitcr :1 urgmfi lucu'bo mn- tilm rationalis fupponarur, oih'ndctur &' i‘uih c. who ran- tum rationalis,&' iyfi b. commcnfus'ubélis‘ : 6:13 [mquadmto fecundo mml‘nm rationahs pommr, 8c xpih c. qmdmto {ccundo mntum rarionalis , 84' ipfi b. ,connncnihmbilis dc< monfh‘abitur. Sicur propanirur. PROPOSITIO dr.1mgh.r\io,qur\dc (Lam n t ficutqmdr.1tinumeriadmuiccm: C? c F. iicut'cu'fi numcri: & g h {icvlt his quadrati numeri. N ‘m,pcr .1, :5" Imius,;1 [xqunnrimtus crunt ad inuiccm, firm ntmcrns no: numerum; {cd mm in quitiUtibnsquiul in nu nwris quu'h'am (hurin dul‘r'm: cubi in triph : {ccunda qua 7mm in oniadruph ratiunc mdicfn lgitur C (Lfimr Jppora tionalwqu1dmris taliu‘u numerornm. E: c [proportiona- L-s cu‘ms x 11m 11 zmmcro:‘um:& g h. proportionalcs bisqm-draris miium- numcrurum. Et hoc all Propolitum. PROPOSIIIO 553m 0714an (mg quantitaes¢mrum quadfizmfimt'aa'imfirem (17-: rut qum'mri mmfie '2; 1'0! ({I¢.;ru7n mbifimt adimflccmfiz'ut cxn'n' 5c‘. ‘mmxeri .'1Wquanrmfi'mnin qruzdmr‘z fimtadinuémmflwt bis 552 produc'lumfiwrét commenfiwal‘ilc 7r.w;'tip;'z'(atae qmnrimti, tmzc Wizflz‘ipliczm's cf! rariomlz'y. V( 11 a. nauha'plicans b. £1---- -----' Ciar Lipfi b. cammcnfnmbiltm :ni0,quéd :1. mriomlis cf‘tzNzlm perdiflin.multiplicatiomsm‘i[.,1icutc.nd b.1ic 3, ad pofitam. (fink/THC per hypo. C. {imammcnilwrzflnlis iyfi [mm per antcpm'miflhm 3.10m man {u min-His feline, quart fcrdiffin.a.rationalis: (10.0ch propofitum. PRO»I‘OSITIO ' 51‘. 0772715: quantitas diuéfa‘prr qrmntitatcm [5/72 comma/imbilem,mbib€t in quoticnteqwmémtcm r¢zrzbn.1/(v7n.,. Sznr a b. 'quanrimres commenfurabiks interfe , 8; diuuiutur 1). pct ipfam a. & proucniat c. Aio , quéd c. quantitas rationalis cflz. Nam , pcr dian. diuifionisxdtficma.diuidcns;1d.v0'fitam,ficb.'diuilh ad 'c. proucnicnrcm.ErpcrmuIntim,f1£ut and b. fic pofita ad c. Scd ‘a. per hypotcummrnf‘uml'iilis cg: 'qitzm'mtimmzré, {/11 fr]? cr‘mmerrfitmlxi/cx. Excmpll gmtinfint dim qunnriLm-s :1 b. qmrum quadmra C d.& quarfi tubi e f. & qutrum I'ccumh qmdmta g h. Aio, quédfi c d: filsrinradinuicwn, (L‘ut qLudmti n u :ncri : Val 11 c f. Fucrinr :rdinuiccm, fitnrcu‘f mum-n; vc! F. g h fixerinmdinniccm, ,._------~ flcut bis qnuimfi mnncri : Tunc in omni~ mli C;1fi1‘,i.D{E€ a b. qmnzitrrrvs grim: :I'dtnntccn'l :0 mucnlhmbilss. Nam [i c' (I. fim ink-rib, ficut qu :«A‘mti numcri 3 chm talibus nu- merifi inrnfit Vnus un-.d::m fl'J‘JIJL'US propoz‘rionzllis , inter" crir ipfis c dzvm m :ah 1. qu mrim< proportiomlis, qur fit k. crun-fluc c kd. qxuntimtcs n'ai'nus triblls numeris propor‘ 16. 2+. 36.54.31. tiomlrs 2 mm 1n:qu.:x7111t;1fint in duph muonc mdimun: crit ficu: c..1d k. 1};th :1. ad 5. Scd Q. «Hi. ficnt mmlcrus‘ ad numn'um : i;‘irur :1. 30; b. ticut mlmcms ad numcrumz q'flfll‘c‘ pHrflcun-jhm yarn-m 4fhums,:1lmimniccmfom- ipfi b. ergo per 485prscmifihm . (S: pofim CmemfuI‘al‘ll- mtnfumlvjks: quad (H propoiimzn. Si nutcm cf. lmt in» tcr {‘6 iicut'cuhi nvnwcrit tun: , quit [.1Ii'ous numeris inter-v 'hs ipfi c.Ergo c.rationalis:quod cl}; Propofitum . Hoc idem ‘CX Prxccdcnti oficndi potcfi. . . 11.5 c f. dux mcdw L1L14n:.(.1-.;S pr portionalcs, qure {intv . P n «0‘ {uni duo mum-[i mcdij g‘l‘uportionnlcs , intcrcrunt ipEc 4. 1m. |