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Show I60 ARITHMETICORVM quadramm d. Erunrijuc cd. potentialirer commcnfurabilcs, qmndoquidcm carum qlmdmrgiunt fecunda (111:1er ta ipfarum n hper hy};.commtnfumbma. Sed ubmomium fecundum eff, per quix1q'ttagctxnn;1,1110&.1mm harum : ergo 6: per {exagefimam Icpnmnm lnnummm em. Qimrcxpfius d. radix ipfa 13. per quinquagcnmam 16p tmmmwri-t ah}- qua {ex bimembrium. quod era: dcm(mill-andum.Snmlirer {i a, ponarur binomium,vcl hing-dial»: {ccundumflcl aliqug ex tribus rcllquis : {cmpcr d. bummmm sire argucrur, 8;: crinde b.vn:1 ch genemm, in quibus bmomium numera. tur. Eodem (yllogifmo vtrris prq rcfiduahbus , dum [0C0 quinquagefimx gangs Cltctur {gage-{1.11121 puma, &‘loco quinquagcfimmicpnmzc vocctur lexagchmaflux dc rclxdms‘ loquicur, flcut in antcprxnnura. 1mm SECVNDI, PARSII. I61 qmmit H Pornmirzlitcr in infinimm irratiomlis, Coni‘m‘ 13;: £11 , quanums :1. sins quadratum b.ciu(l{cm qua. mmtxvfm‘ 1L 1:1.dum guns (11111113111111 tcmum d. & (16:111(cys m 11 Hum. (Luandolgxtur quamlms a.bimcmbris I). , ~ 1 I ~. ‘ w" , ‘ I ‘ I c", mm 1 1;~-;at11:1.(1111153 111114111 oflmmm b.cr1tbmo mxum, . .R» "v\1.-v,.. ' .' ' ‘ ' 1 rqm (f' u 115L1-.tx_1qzxjx 111111 1nfin1tum quadratufcmpcr b1n0< 1171.: }1::m-1.($131111)Irrauozmlm Em, conflat propofitum. lemg; 1:11; qunnnms :1. rchdunlis fupyonimr, tunc PC]: 1rx:1g::i1n1z puma I). crir rchduum. Indc eutem c.& (1.86 {cqucntm hmpcr quadmm L‘clu‘lua prima, & permdc irrationalm, quglnadmoduxn dcnwnl'tmndum proponirur. PROPOSJTIO 95‘, Tinnmiram13%}‘0711'1114212 noiszI/m inter [2' magnitudine, fcd (325.177.! prSmo,fccmz.Ja,@‘ Mimi dcz'nccps 2'72 infinity?" q;¢.zdmto in- Omnfs irrationalis quantitas fine ale numero fit bimembrium‘ ‘fiue refidzmliummonfoldm magnitudine ac patmtiairmtéonali: cfl,hoc cfl, quo ad primnm quadrarum; fa! e‘tigmmw ad fecun- L‘cmmcnfiti‘abélu fuzzL . Sit .1. quoduls bmomium. [Lautcm quodlibct L'L‘IHLILIm. Ai0,qubd a. bit fimplicitcr, S: potentialitcr in mfinimm incmnmcnfilmbilin 111m. Nam ii hipfi a.commu1tingbflis cill‘tfil‘lm :1. firbinomhm1,cflbt & b. bi- dum , qua ad trrrmm , (y quo adfequentia mmfmm't qtma'ralnzr nomjum per ilxngclimam qunrmm huius : quod c1} cuntm hyp. Non fun: igimr :1 b.commcnfiuahilcsfiéd incommen- Nam, quo ad binomium primum, fecundum, quarmm, 86 17_1r;1bi‘;c_<.Dcindc {unto ipforum n Imprinm quidcm quadra- quintum,in quibus vna portionum rationalk, rclxlua irras m c dibcunda c513; dcinccps {equentim Emmi; pct quinm tionnlis d} ,.pntct propolitum : Cfim em'm pin-res {mt inter: {eincommenfin‘abilcs , crit pct quadmgcfimmn l‘qon'mnm qmgcfimAm oftaunm & fixagcfimam primam huius,c.bi~ 110111111111, (1. 311mm 1'cfldmn11prj111i ordinis. Er fimilirer e. binomium , CV f. rcfidnum eiufdcm ordinis , qum fimrin- uicrm, hoc c1}, mm c d. qufim c f. &‘ dcinccps, incommen{urabiltst quoninm {cificct binomium Rcfiduo mwmmcn tori, (36 perindc rotumirrmomlc : (‘5: quoniam sxcd‘ins incommcnfum'biiis partibus, criz (‘36 uxcclihs exiam irmnona- lis. Q10 fit, vt tam binomium , quim rcfiduuum primum, fccundu-m , quartum , & qumtum irrational: fir. Scd pro binomio ratio, 86. (are, {uoqucrc-fduo, ac p112 castcn's bimcmbri um , nut 17:5:th um gcnerihus fic proccda-m. Sit a. bimedialc primum, aio , qubd a. irranomlc cl} magnitudi- nc. Exponatur cnim-cins quadra tum E). (111011: per quinqua- gefi111a1110€tauam huxus, erit binomium fecundum: fed binomium fecundmn dudum irrational'e fuit. 15km mpot‘cntin. irrationalis cPc : quarc 84' magnizudinc pw poihcmumé corollarium quinquagr'fimm tcrtig lmius. Er fimilitcrfisciam dc cxrcris generibus mm bimcmsmhribus , quém rca fidualibus : loco tamen quinquagcflmm 061mm addurfta 61"..Q39d autcm omnis tam bimembn's quém rcfidualis quantum {urnbilcdnzhun rumnfhm of}. Iginn‘potcntiwipz'brum ab. primg, {L'CundxC\'1'Lqucntcs incom:ncnfumbilcs ad inui< ccm , flcut proponitur. L. huius ,ram congerics , quém exccfllzs incommcnifi11-11111: PROPOSITIO 96". L. 9+". A -L...L_»- "-52..." P'nopasxrxo 'Rimcmlvris (711.17er 11: vi)" rg'id/mlfs non folks; intm‘fimagn}. fwd. ifccz' {Tim/2 porrizrigifzvr 272 i;7_fi1zfr1mz 511(‘072272;Ciqfizmbil'z‘: fimr. Sit .1. qugcunquc bimcmbrii, [1. \L: quichbut Refi- durzlf .J‘xéo,<‘;;1€:d.1[minccmm(1111111131135adinuiccm (um: {L'C‘CS L‘nfm 130' {cxngcfinmm (111.11'13111 I1 Magelfi‘m ciuflz'm gmcris Z quad aft contra hypothufm.1,)cindcfimipihmm :1 11.q11g_1h';t;11,»:1'11121 C d. fecunda c F. & drinccps: annulus Perquunplug/«511114111 oé‘t‘uum, 8C (61153061111111 primxm C. Gg binomium, "WW-i. my!" man 1. m; F‘W "M . - |