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Show as. fiRITKMF"¢yQHVfi b uertcturquantitarmn radonmd‘htzodux». .. o 1'2t13,1c<%.qa fic o‘dcnditur. antims mtiomlxs mmumplicans 1.121 mtita, té rationalcm bhcu c. Dico run‘c,qu€)d c.qu;mtims rations. lis efldmmq; ex min {c filt d.& tun: per primi fecundi Ele- mcntomad quantitatcs redaflti erir, ficut a. 1d b. tic d. ad c. {ed .1. ipli b. commcnfilmbilis cf}: par ilypothzfimzcrgo 8: d. ipfi C.C3mmcnfilmbilis ed,pcr Ioi dccimi. Carnal]; d. ratiog nodis {it (quid qugtdmtum CH: ipfius a.)iam per diifiufic am: tionalis admin )d ed propofitfi. Similiter procedure poterinms,rcliqu.15 dccimi Elmncnnpropolitioncs demonfimn(10., thuod nom eiufdcm libri dc quadratis of‘tcndit , p6: criam ld cubos 8: 21d fecundl qumdmm quantitamm rchr< rifle-,A commcnfilmbililms inuicem quantitaribus PL'Odll-x 6h quadl‘ata, fimtad inuiccm ficut quadrati numcri : 8c; produfti cubi,ficut cubi numerizc‘k produéh fecunda qul- dfflta,fiCL1I{CCLlndi numcriqmdmti. Contri,& quantitatcs {anyquarfi quadmm {untad inuicem, {icut mnncri quadra- 1 ti , quim, qun‘um cubi fimtad inuiccm, 11:th numcri Cue. z . 3 4 . 6. 9 S. x 2.. I8. 17 26.2.4.3 6., 54., 8 I bi: qukmfi; gun-um, {CCLUICLI qundmm fun: ad inuicem, ficut {ccundi quadrui; that Sindinuicem omuino com [11ch filtabilcS. wad [mud diflicilius oficndirur, quizm noun ipfa. quoxd qmdmm. Hoc, {cilicet filppofito 8c anté dcmonfh‘aw to, qubd ficu: inter duos quad-gates numeros flimPCL‘ intelx iacct vnusnumcrus mudius proportionalis: im intcr cu» bosinteriacenr duo mcdij proporci011;1lcs:& inrcr facundosr quadratos trcs medij proportionales.Ab incommenfumbi- libus veroinuiccm, quantimtibus fl1&.1qu1drara110n fun: adimuiccmficut quadrati numcri; ueq; cubi, [i'cut cubi nu« meri : ncc [bcundl quadrant ficut fecundi quldmti numeri. Contri, & quantimms, mm quaruln quadmm non that ad inuicc111,ficm qu.1dm.ti numeri, quim qulrum cubi n5 fun: inuicem, ficur cubi numeri,qu‘zmjx c qunrum {ccund .1 qua‘ dram non fimr inuiccmgficut (ccfidi quldflli m1 mpri; {unt intus fcmcémcnfumbiles. qua dun: proportioncs {squantur cx przmims ideftruc'tion: contmmor um . ng fit , vr LIBRIPRIMb-FARSIL PRonosn'Lo‘ 2‘. 89 - Omnis q/mmimt'm ddditéo ,v fitbtmfio , muz'tz'plémtio , [€24 diuifio, 7/61 Ndiwnz eff/41.150, fit per 605 maze/05, i {[;£2]),‘.4S ip- f5 qmntimtc'x figmjv' may . Ho: cf‘t , nrlmcrorum . per quos dug vcl quothbct quintimtcs (111331103 [111311196 figni‘ ficantur , aggrcg‘umn cft numcrus fignificms radium gum- titatum aggrcguum. Er numcrormmper quos dux quantitat-cs inqunL-s {ignificmtur cxceflhs, cl} numcrus {ignificis ipflufi quantimrfi cxccdhmlrem nulnzrorunnper quos d m; qumtimtcs figmficantur, pl‘OdudxlSfifl numcms, fignificans can? qumtimtfi produfilmu. Alhuc diudb nunuro in numcrfx, proueuit {cu elimtur mum-ms {ignificans qumtimtcm proucnicntcm cx diuilionc qumtimcis Illius m'd in quantitatéllt1i°.DcInfi 01$ radix quadrati, vcl cubi numeri cfl: nu- meLjus fignificans quantitntéqux radix; cfl: qu mtimtis qu1< dram: vci cubicze pct ipihm quldmtfi v31 Cu'ofi fignificux. ‘ Pnoposn'zo, 53., .Q/mntitates, quamm denomimtorcsfimt mpmlegfimt adm- ufcem ,fiwt numeratores . Sinrduaa quantitates ab. c (l. quarum dcnomimtorcs b d. pomnrur :Equnlcs : nume- mtorcs autem fint a c. Aio,qu€)d quantitas a bad quantita- tcm c d.cfl:)(icut a. nd c.NJ.1n ratio quantitatis a bad quanLitatemlc d. componitur ex rationc ipfius a b. ad pofitam, 8C6); rations pofit-E ad ipfimm c d. Numeriafit 14d numcrfi C. ratio compouimr ex mtionc numcri 3. ad numerum b.& ex rations numcri b.vcl d. (fimr enim equalcs per hyppotc- fim) ad numerum c. Scd Per difli.tcr1nin0rfi,quanrims a. 17. ad po[ita111,c&iiCL1E numcrus mad numerfi b. quadtims .113: Pofimad quitimré c d. ficut numsrus dad numero c.1‘g1tur per équi proportioné exit quantitas a b. ad quantlmtc c d. flcut numerus 3. ad numcrfi c. nod crat dcmonflmndum. PROPOSITIO 4‘- ,(Luanritates-, quamm numeratorc; fun: wquales , fimt ad Sumo, {1. inuicem ficut denomimtores, ardine commumm. cut in; prcemiflh, qumtimtcs a b. c d. in. quibuo ponanrur quot linelrum itratiomlium {pccicsvtmchnmr indccimo od xqualcs ipfi numcgtorcs :1 c. A10 runc, q; qua'nnmo :1 b. Elemsntorfi,cotidéciufdé noznmis, 8c carundé propricratfi quitimté c d. CR lxcut numerus d. ad numcrd b. F13: 6mm ex 21. in d. numcrus c.& ex b.in c.fiat flex [xvcgo m d. proneniat g. Ctitc'luc‘, per primi fc;x§i,,ficutn. ad b. Inc ‘c. 11d gA-Itrin {pccici inucn‘iitur1nvterquantimtcs in gcncrc fil‘JlPEBS. [[3, inqui,vt in 0mm quantitatc vnius generis exifl'auc 055 talc; tati'onalium fpccies..~{{ct hanc igirut propofitioncm qmni}: geometrica {Peculatio‘rccfigirur ad numeram'am praxim. ' - ' P a o' p 0‘ Prime. ptopohtionc huigof'ccddng :‘ quatcficut ln'dlfl'mmo- nibus Patuit,quititas c gmuahs cut lPfi ab. Item erllirtéirnu)1 |
