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Show ISO ARITHMETICORVM in d.fi1te. quod pen-S" crit binomium.V€rL\1m pct prinfiahi fcxnficut had (Mic cad 3?: b.commen (urabilis yen-mig- htcr. zpfi d. 1g!!ur,p€l‘4 8a & c.commen{umlfii!is potentizzhL rcr 1pfi c. Sfr'. cubmommm :ergo , per 67ihuius, c 12.no- mmm eat: quod fuir oflcndcndun‘. Similircr flu: a b. fin: bmomm, hue bimdiaiin prima, flue ex rri'mzs garmribus rchqms cflc fivpponantur, fempcr c. binomiumdcmonfimbxrur. ‘ I . V L' LIBRISECVNDI, PARS II. rationalnn (lam czltcm b d. ficut rcliziua proportionalium & comm:nfiu‘al‘iiimn nominum , crunt b d. intcr f: commcni'urcbili; : fed per "vimam {ext}, ficut bad d. [1: C. ad C. Igitur per quadragcfinum 0 (Shaun huius, c. commenfi1m~ bilia ipfi e. Cumu'luc c. {it 1‘.1i'i0ndli5,2fit 8: c. rationalisfih cut dcmonlmndmn filit. PROPOSITIO 151 fin: 3: 65m :uihmbilia, 3: ex (iuC'l'u a in 11.50.: c.Ai0,q uéd C. rationale cft. Punaturipli binomio rsqmlin. nomim Imbens d. rcfiduumz Sc ex :1. in d. 2:71: C. quéd pct Prmccdcnrcm cgir ' 75". PnoPosr'rxo DIM quantitatcs rcfiinalcs eézsfdcm generis inuiccm pormtia 76‘. ummcnfumbi/E: , imcrfe mu/répiéarm , rtfzdmam prodmmm. Excmpli gratin, n. 8: b. rc-fidua ntcfliah': fi-cundainniccm potentialiter commenfln‘nl‘vilia : & L-Y. :1. in b. flat 5. Aim, q; c refiduum cfi.0fienditu 1‘ luff. 0m Dino Her I prceccdcnszhoc; exccpro, quc‘Jd p10 583cimnda aft 6: P,qui1y>cqv.1:e dc rcfiL dunlibus agit. A‘ PROPOSITIO 74.1. 0mm binomfzmz in Tg'iduzm ccrundcm 31072311993 multipli- catz:7;2,prod:zcit qmmimmnrflriom cw .. EPco iw'nmr .. 11 cuins 11mins mcm'mum a b.minus veil) b (1140'; izafi 6 5.336112Iis cfla b d. eritc'lumd rcfi 'me coxurdcm 2011.13an , hoc CF: cxceffias corimdcm munfnorur... Imauc ofl‘mdcndum eff, qubd G C a. binomium nmhx'pIimnu ill: a dyroducctur qmntims rmiomiis. Cum Lnim a: c. fitagoreqatum aunnti- mtum (I'Lzarum a b. b c. nrquc a L}. fir difi‘gczfiia eorulndcm, conflatqne per quEnmm fecundi Elcmcnrcrum , quéd 6X APQLI agzgl‘cgati mdicum in diflh‘cntiam comm Producamt d!fl:;rcmia quadrntorum : 1am iHud2 qubd fui: r: a c.in iD~ {am :1 d.eritcxccllhs,quofl. ipfius a b. cxccdir quadratuin lpfius b c. Yerilm, per diflin. binomij Imjufmodi qmdrata ranonalia iunr; :gi ur mlls cxccflhs mtiomlis cfl. :1an 1'9.ti-onalc elf, qucd fit cx ac. in a d. quod fuit‘ demonfimndum. ' PnoponrIo 75". 07?!sz binomim'in Refiduum proportionalium é?" commmJfi4r'abzt2um nominzmz multiplf wrungproa'mf: quant'z farm: rarim 1mm? . Sun‘m duo l‘inomia (Screflduum .1. 8c '0. 0110mm ncmma mams majori, (36 minus mincri Proporltionaha Si Tfnomium multiplirans aliquam 71¢mt2tatam¢roim3/:th quanfimrem mtionflm,:mnfiplfmm [panting rqfidmm 03, mm: nomimz proportionaléa , {f commcnfsmlziléafimt binomii nomirzibas . Binomium :1. Vmulr‘iplicct b. quandmtcm , 8C Producat c.rarionalcm.Aio,qubd b.Rcfidu um,cfl: cuius nominaproportionalia fun: CY commcnlhmbilia ipfius .1. binomi} nomimims. Ponnntur cnim d. Reflduum corundcm nominum , {it e commcnfumbilium , 8x: proportionalium cum nomimbus a. binomij. 8: ex min d. fiat c. criujuc pct Precedcutcmwcl ante prrmilll 1:1 i171}. 6.R:1ti.omlis.Sed pct: Prim-am Ikxti, {icut (1:111 afic cad icommcnhu‘nbiiis:cfl: au rem c. ipfi 6. quiz. film rationales. Ergo PCI‘ quadmgcfimam 03.}1u1n‘. huius, b.commcnfiu'abilis ipli d. Yuit autcm d. rcfiduum : igitur per 64": & b.1'cfiduum 86 commenfitmIndium ncmimim ipfi d.5cd nominn ipfius d.commcnfi1ra- bilia nominibusipfius a. binomij , & proportiomlin: itaq; & ipfms b.1‘cfidui crL‘mt cil‘dcm Commcnfumbilia. 5: Propon tionalia : quod fuit dcmonflmndum. Pnopost‘rlo 77'- " Si Rcfiduum multiplimzs aliquaw quamitatcmficcrit (1mm mmm (1?,- (u- Iitatem mfiozmlem , mn/tiplicam quantitas biizq noiu: nomiiw proportlcnnlmfmzr, (y cognmcnflwbzlm refiduz ,& eodem pr?minibm. ch in cadem omnino dcicripiionc atur b1celTu demouf‘tmmr: Hoe exec-pro , quéd '{bi poncb nomium , ponatut :cfiduum, 8: £- contmrio. Pf I, P"°‘. .1 |
