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Show - 1‘3" 3 . aux-gmm-l ARITHMETICORVM prxccdcntis , fi illa difl'ctentia fucri: rcfiduum prima: (pa; cici : hzec differentia crit rcfiduum . Si illa,Rcfiduum zgfpecicihxc Refidufi medialc primfi. Si illa,Refidufi z.q fpecici, hmc Relidufi mcdialc fecfidfi. Si illa,Refiduum 4.9 fpccici:hmc irrationalisqum Minor. Si illa,Rcfiduum 5‘3, lléL‘C Cum rationali mcdialc pom-n5. Si illa,rclidunm 6"l ,hscc cum mediali mcdmlc- potcns. Er hoe cft,quod denionlhandLun proponebatur. COROLLARIVM. Vnde manifcl'cum cfls. qubd c0mpcrris per §75 prqccdcn; LIBRI SECVNDI; 15AM n." 145 . Binomia Fex (turf: radices {um teiidé im‘ules quamiiarcsfibimébnes. anum 7fv.r.4o ...... B-nomiumr Lg} 1.1 Sccundum 1' 1843.4.- .. lecdmlcprimumxns 6.:r.:. Tcnium [.2243 r.24..mee.liu.lc fecundum n.i‘:.fw.rr ;. @41me 6 p_r.8. "Maior x'.v.;.fy r 7 p.r.v. z.m.r 7. ngm r 31.!!4. ..Pmens xatiomlr Sc'mflii‘alc [.V. 13. fizfi r.v. 1'. 8.51.1. Sexrum I 2.4. p.r3..,. Patcns duo mudmliar V. (6.13.2. {3: v. r.6.ri4.:. .. Ex quibus‘perablciflizmcm mmonis incmbri 2i mains, ficnttam in Binomi~ ' Refidufl (emu... O\Igvmm radicemozidem Rtfiduales irmtionalcs f'cilicct, m1;s,quimincorum radiubusnotidem RefiduaJioc paflo. pumum 7.rn no ...R-:u'duum r 5 £1 m. Sccundum [.18 "'1.*.,RCS. medich pximum fl RJHHJ. Tcrtium m 7 61.:.:4,Rcfi.medialc fecundfi n. "flung. Quinum 6.ri1.r_3 ..,Minor L5. ;.fi x 7 rh r v. ;.fi1 r 7. ngumm z_.m.4...Cum rationali medial: pozcns. r.v. :- s.‘ 1. if: r.v.r.8.r'i1.z, Saturn x.2f.m.r.8...Cum medlali medialc porcns. r.v.r.b p z.fix.r.v.x.6.fii. :. Sic habescxcmpla prafiica eoxum , qua: dcmonfixaxa funr. temfex irrationalibustluuntimtibus prxdiélis, qucg lingulz cx binis mcmbris conihmtinxqualiimsz 1.1m eorundc'm mé Pnoposx'rro 61‘. brorum diffcrcnrim lingulx crunt Rclidualcs quuirimrcs prmdiéhrum bimcmbrium. Item {1 blinébribus fim lmgulis Omni: quantitas‘ rationalis' multiplimns 'Birro mium pcr‘ Re- quadrataattribuanrurg'qux binomia lunt)t:11ium binomia- fiduum, producit etiam Binomz'um 7121 Rcfia'um eiufdcm [pe- ciei,ac multiplicato commcnflzrzzbi/c).Rationalis quantims a. rum Rcfidua crunt fingula lingularum di&arum Rcfidua~ lium quadrata. multiplies: Binom‘i L} b c.& producat quitimtcm d c.21i‘0, q; d.c.Binomi-fi cfl: .I'pfi b chinomio c6111€fi1rabilc,&ciufli§ Q): Pnorosl‘r 10 61". cici.Vt fi,6xépli gmr‘ia,b c. fitbinomifi primfxufic d aerit bi Sex irraficm'mm quantftmmz >5; Cdm'im, [Ci/ice! Rfidui, Rcfidui ml‘dialis primi, 1-.3 ' 5;; medal/.55 fizmndi , M!220ri5,€um ration/112 medial: pom/fix , Cum, medaafi 2726:1241}? notcnti: , [Em gulamm per ordirxsm, "Inga .1 rilxtaa'mzta [mt 'anulze fcxflmcz'e: fRefidui. Sicnt pix-ccd-‘m {cquitur cx dcmd‘tmtls 5998: ;7Q Ira pracfl-ns prepofirio limilitcr ex i}s , qu; in 59‘ (Sc 58" o. ficnlh (um, c0qu15w-lt. COROLLAVRIVM. Hinc manifcllum cfi , qnbd Binomii , 8:. Rcfidui haben‘ tium .tqmlia nomina , radices inter l7: imbcnt etiam .tqtuo lim no-nvmt: Sc 3- conturfo, Blnomfum 8c Rcfiduum, quorfi mdiccs b.1531: xqznlii nomin;1,lbttiunfur ctiam inter 1} no mini xqunlil. ldcm'fluc dc: nomlnibus propotrionalibus di Ccniu 1n. Nam :equilims nominum in quadratisfacitzqub nomifi p‘KSint cm'm ipfius‘ b c.binemij mc'lxra b c.&' ex min 13.61: (Lt-x min 06:11 c.5ic cnim,per primam {ccfidgcrit d c. to:fi,qu~od fit ex. .1 in b c.1mquc Cam 1) c. 5: binomium primum,cz‘ir per diflin. hmaius m‘cmbrum‘ rationale atquc C. tcliquumpotc'tialiter tannin] rationals: Cu‘mq; axationa11$ in lingulas b C. quantimtcs £1Ciutli'ngulas d c. i5 per 495 hufuzipfn Li.L'i'lCI;1[l()l"1:7,ll$,&lpi:l c. porcnria tantflm rationalis:& torum d CJOCI b c.c0mmcnfiu‘nbilc. [mu lit iplius a quadratum Equod rationale er]tzziiquci'pflimun b aqua(il'ltl limg h. Mox f. multiglicnns igius g h. producat ipfas k Lerunrq; pct coroilwndecimx huius,1~;1. qgadmm lp‘flll‘fi d C.Cumq; per pri'imm {cxtifit licurg. ad 11.11cl'.ad l. trit cucrlim licnr gadl cxccllhm, quo cxctdit ipfiim h‘. fiCCU'fllEl kad txcclfimifiiuo exccdit iplhm LVHfim gad fuum ex cel{um ell liCul unansms qmdrams ad nu-mcrum quadratfi, p 515 huius:quoni;i pci'iiifi‘inirioné primi binomij, b. porno litarcm nmninum in radicibus : 8: r} contrario. Proportio cxccdit c. portiomm porcn-tialitcr , CACCH‘U‘, guius 1'3.le 6R: Vcrb proportionem , licur p :r procel'fiim dcmonfirationis 57‘ 5: 58‘: confhrc potcfiLNunc 3xpon1m hlc {ex (pccics bi‘ g 11. éz prrind‘: r; is cxcclfiis 17c hubs: ad g. l1§ut tunnel-u: nomlorum, 8: rotidum 3.1mm radiccs, qux fun: {ex irrati0< nalcs quantitatcs. commcnfiu‘abilis iplib.@iuxcc1fus cft d1fl:l‘_cnn.¢ i1)larum qmdmtus ad mun :rum quadmmm per 5L‘.lg1(urk.ad fin} cxccll‘u fc lubcbit lieu: nfis quadmcus ad nu 21cm qumlmu . E f Binom' mate. |