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Show 14.8 ARITHMETICORVM V{ E‘SRfiOLLARIVM' ngcnjam c um c ,quéd awrcgazum x (1mm man bus inuiccm comm mfufilbkjiilmgcl } $33.3???" u-bus commenfumbilc 56 ciufdcm gcncrls cum diam: P t. PROPOSITIO 67‘. PROPOSITIO @772an qzmntita; patemialiter wfimmfura-éilir alicm" ex ' mtron.1lzbm,:fl ciltfdemgmcri: qzmntims. Sit exam Ii rd fr- quanfims Lbimediale {Ecfidlnn:fit{j; iofi a.porenti§‘i§;n ‘ab ___ mcn‘umbilis ipfu b.Aio,qu€>d b. cfi-m‘iam bimcd x'fi;{ C0. dunnS'finto mm qtmdr? r1 ipaius 4.1-1:' 5.110 "'4" ‘ - LCUH‘ " fidfiriruficmer 58" huius,c.bmomiLIlm tcrtiL;:111\:1~} :3‘Jl;:nlth" 1 ‘bf‘lis‘ autwn ER pct hyp. ipfi C. infa d. I'T'ilurvw;6 '5 inc? "6.41111: mium tertium CPLSi'd ipfilljs dil‘ltffix 1"‘1'5154'3 Frills P" :7" f, > 7645116iiécundumcrir. (mod fillit dct111c‘>x;;'iy'§:: du\m. h 1.11\‘("1:‘in cmtcris irraticmliL-us, tam bimem briab' quamr rcndua lbus ~onfl'aL‘ir Propofitum. PROP 05 11-10 ' 68*. Own}: qwntim potcnz‘ia rarian‘zfix mulz‘z'alicam 412‘ mm: m- p'nzrmmlzlm proa'uiit cinfiirm qrmr}; qta'arfirirtzt: mJ Elem 'r'h Emma. quantitas pozcmég rfifiom'tis multim ‘icc-t bl. bimmml; [ccum'EU'mCx‘ producat C.Aio,qubd 001‘": bimcdieflc {gcgndunL Naifigpcr diffim‘mlripiicutinnis, [LEE]: cfl 1 m'ulqpl‘xcuns ad pofxram zutiomlcmfik urlrcéufium ad‘l.‘ mu! upl'xcnmm. Seal 9.. potentiaiitct' comlfimfilrabilis 61% (.3fitzz mucnah pct l1yp.igitur per 485 huius .& cipfi b. otcfiti alh rcpr com m cnfiu'abilis CPLCumCl, bfzr bimcdialc {gcun dum 23:»? pfmccdgarcmfék chimediale fecundum. quod rm; cnucnqum. J. on :1 iter in 0 ' ' ' " I nis irrationalib us conf‘mt "£23153:leTCIIS Vifq uuc OAdl‘ Pnox'osa'rlo I. IBRI SECVNDY, P ARS II; I49 cft ipfi uper 487‘ huius. Scd bbimedialc primum. Igirur vc c.bimcdmlc primum pct 66'ip1‘rcnnflhm. quod filitoflzcndendum. Er codem {yllogifmo per Iingula irrationalium gcncm repcnto, conf'mt propofiumn. 70‘» "Dim: qumztitatc: bimcmbrex eiufdem generis imu'cem com; mcizjumbilcs, per orciincm fcx irratiomliwz fumpm , inter fc mtdtipliattaz,produczmtfingttlas birmr-nif flmcics. CH?" 58" pro pofirio dc quadratoJmc dc Produfl‘o irratiomlium conclu dit. Sunto , cxempli gratin, a b.11ngulx quantitates bimedizdia fecunda , inuiccm commcnfin'abilin. ngrum punL‘lum fit C.nio,qubd C. cftbinomium tertium. Sircnim ipfi :Bqualis quantiras d. 8% ex :1. in dfiat e. Eritq; c.qu.1dratum ipfius a.& pctindc binomium tertifi pct 58‘ huius.Et quoninm, per primam {cxtificut 1). ad d.fic c.3de.&ip§1b.ipfi d.pcr hypxommcnfixrabilis cfl. idcirco,p:r 48"]1L11LIS, & C. ipfi acommcnfumbilis exit: Srsd cabinomium tcrtiumzergo, PCI‘ 645 & c. binomium tcrtium CH. quod fuit Eicmonflmn- dum. (Luéd fi .1 [upommur binomin com111eniurab11ia,m'it abinomifi prim .'..Si aurcm a b. bimedialia ptinm Communfilrabilia: hinc abinomjum fumndum. Si maiorcs,binmnifi quartum. Si potentcs rationals 11C lxlcdialcil‘inomifl quilb tum : fi pOi'CntCS duo medialia, binomium lcxtum €116 dcmonflzmbimr: flcut pL‘OPOGIiO COHCIUdiE' PROPOSI "no 71'. Dim qzmztimtcs rqfldzmlvx eiufdcm gmeri: Zrmlcem common fa mulnflzmfiuuzbz'lex,p[r ordineinfez qtnerimzflzmpm, inter no dc propofi 61fv (Eod m;PV0dz¢c14ntfingul.zs rgflduéf/wcics. childlr. quadrnto, hazc pr‘tfcns dc prqduéto rcfidlfimhum»con Giralta. 8: 4.3" 58"& Ber cl} Iraquefiauprxccdcns ORGY"? proccfru <5: dc« mecns propofitio per 61" 48" 8C 64," codcm 69'. ratpimfu qtmygtasvzrratz'qnxlis diuifa in quantitate m potentid F 207111ny , ,_ x'mbet m quotztnre quxnrimremfibi cognomincnu bimCd .xc'mPiaJE 10::1t}1, I quanu ' tas ' 3.por§r1at W 'm rauon ‘ alxs, ' duuda ' ' t b.' , Npumum '. 8: prg-nc-mat c. nio , g; c. 6% bimcdiale Elihu"). alm perd1f‘fin.d1mfionis,ficutcfl diuifor ad Pbfirat 10m. cm , fic CR 17. dlmfn ' ' , ad c. qnoncnte ' m . 86d :. poreptmh-ter commenfumbilis cfl: Fofirx rarionali pct ‘ypotmm . ergo 8: b. potmtialitcr commcnfilmb ilis :fi fcriptionc dcmonfimbir. Pnorosrrxo 72‘. potentizlitcr ‘wa quantfmfcs Mmembrcs duflicm generis mt bino- od_/m am,pr éplic mizlt fe inuiccm commcnfim bilegintsr ia {ccunda pobimcdial min . Exempli gratis. , {untq a. & b. bilin . , & UK a. in b. fiat c. aio, tentialiter inter {‘c commenium d. ipfi azzquaiis2 85 ex a. 6mm cfiPomtur gubd c.binomium 5 m d- |