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Show INN tatcm corundcm, flue prororiionalinm, 8; commenfuxabllium nomi- nun, , pioducit quannmrrm yore". (in iationalcm, 8: quandoquc rationalrm . I f; mamas quzlibct bimcmhis li {cctr tur per refidualcm quaurimrcm pro portionalium, & commcnfurabilifi nominummroucnirt cx diuIfionc ta E rtmxa ipl‘m‘um (3!:Aiarriv-iyix1fij".§;li Radicum quorlzbcxHi 1- (ll! ah mm": ordimtarum; quol firm as rrrga. [0 mul xipllraro in duplum ("luau timzfi muga‘mnum iplb radlcnm aggregato,ccnflabiz uiplum aggrc. gar: omnium qualratorum cx dim; raducibus Gngulis fadouim 119 Radiccs quotliberm fucnt ab'vnitarc 154 ordinatc‘: \ quod fir c; aggrwaro pn. @ntirax quqlibcr rcfidualis {i fcccrur per bimcmbri quantitaxcm propor Meme: 5: fequcmis radiéunfi in pro li Binomium . tionalium, 8: c6mcnfu12bilii|ml10. mmu m,prouenctit cx diuifionc tali Refiduum . I 1;; Quintin; omnis medialis multipli cansaliquam irrationalcm dc mum: to {ex gcncrum , fiu: bimcmbrcm , flue rcfidualcm , producir omnino aliquid dc numero carundcm 158 (bulltlmt omnis medialis &iuidcr.s all quam cx irrationalibusfiue bimcm bxibus, fiuc rcfidualibus , prxfiatin quotient: aliquam dc numcro ca. :undcm ' 1y9 Quintin: om nis fecundo quadrato commcnfutabilis alicui irrationali , flu: dc numcro bimcmbrium , fiuc‘ rcli-dualium , cfi ctiam dc numerol carundcm . ibid. Quancims omnis irrationalis , {iuc dc dm‘lum ex cvfdcm , duplum (cmpcr cfl ad congairm cx cubu quadrato. 85 triigulo collateralibus pofircmz: E: pen-indcm (Excuplum pyramidls quadrant collateralis, hoc cfl,aggre gaci quadratorum ex radicibus oxdi. natis produdorum . no Radicc‘ fingularumrcfidui fpccicrum, qualcs fintmmnmarcs,&qux I4; Radices quando habcant zqualia nomma,&écomrario. 1:4 I Radicibus quotlibct ab vnimc propo- fizis , {i radix proximé [Equcns mul. tiplicctaggrcgarum cx quadrato P0 fltcszC ex dimidio ipfius pome- I Radix omnis numcrnria multiplicata in radiccm (cqucntcmmroiluiirldu- fol. a Radiccsuumerorum , qua: 2.8 Radiccs nilmcrariz fingulre duplicntx conl‘muunt gates numeros fingu plum rrianguln flbi collateralis . f Radix omnis duéla in imparcm colla:cralcm , producii licxagonum pxi- gum in agwrcgamm quadrarBium m um collateralcm . Radix omnis mcdia inter vnizatcm Sc imparcm in ordinc radxcum, multi- Plicata in ulem impan'm, quid Eln- ducac . apfmumra icum producitur differ Radix omnis fixcuplicata, Sc cum vni- 105 per unlincm . U4 Radicum vnitatc dillantium cx nggrc talc, Dalian S. nc , Cunt quandoquc potcns Ratim 164 nnlc,ac Mcdmlc,& dcmccps Solidn Rrguiniia quomodu formaur. fol C. Rarionis dam, [OKlCS quotics quis pro, 12; ponar,mulriplicatio . Ratiouis datr bilhrix, flue [l‘lféll‘lir , plurif‘arizmrcunque quifpiam pofiu SolidOI rim VEZLH'RJ‘llOquHC ex qui'uur, 49 confine dul‘xu . 5,5 Solidomm d: mmucs ‘ alifi , 1i Sphxm, cuius diametcl‘ r‘minn n4. lauerigzqualitcr parririq. circunlhilmt quiuquc [nlula regula Rationum duarum propofnaium con - Iia ~, mm pyrunmlis , qulm 03am: i 23 iunétio . Rationum duarum propofimmm alt:- m dri) & cubi 1.1L apozcuzin mmle [lOlL'llC ell: ipliquc illmisrro lungitudiuc incouumcufumblc: L acus lacus aurcm 8c lcofahcdii , minor -. verb dodccahedri. Rcfiduum {ex- ibul. rius ab altcm Gibnadho. 8_6 Recifumflux quan rims voccmr. o Revulariorum folidorum forman ol.c.& (sq. 168 . chulz dc figuris zquilatctis . ‘1 6? dc {olidibus regulanbus qucnrcm . lhurum mcmlnorum, ll‘iuam um 137 dcl'initionc, impatlibilu El}. Rationale tam porentis \ ac Mcdialc , qufim POIL‘nUS duo Mcdialia porrio fpofitamm, vltima in fucccdcmem imparcm ; cum fequcnti verb (6» Rc'nduu cllc uni-Hum .IllL‘rl'llll], quim 1 ibid. LI ordinatis radicibus faé‘torum . .1 mca , Regularia , flue folicla Geome 46 _ . quot 8L quz Radix omnis numeraria cum radicc przcedcnti , facix fibi collateralcm dc formemur . qux 169 tum. De litcra T. Tetrahedrum fi)l.c. fold. uod cl‘t cubus miflus . Termhcdrus ccmmlis vnde confida2.; tur . cf. Tcuahcdrus omnis centralis,potefi 8: com mcnfu. ccm proportionalia , propermbilia nomina , fortiunrur tionaliaimer (e 8: commcnfurabi‘ _ fc cubus cubas ccntmlxs tcrzij gene- 1;; ibid. xis . . 2. Tetms {olido cf‘t fimilis . Trianguli primi numcmmm lmcaOla. tium confiruflio. line Trianguli fecundi numerorum mumi Rcfidui fpcdcs , quarum quanu "4‘ . uadrata fint . c_ Re iduum , quz quantxtas nuncup 86 tur . .' 1 2.8 Refiduumfiuc Apotomc quid 12.9 Rcfiduum medial: primum quid.quan Refiduum multiplicans aliquam rauctitatcm, fi fcccrit quantitatqm. Bino nalcm ~, multiplicata quantilas ional mium cfi,cuius nomina Proport lia fum,& commenfurabilia Rcfidui feu Pyramis , Regula. re folidum, ex quibus coul‘truatur . Raoul: habent mm Re ulna , quorum radlccs lia nomina. 154- lionc licliduum pnmnm . Ratiomlis quantiras qux voccturi 118 ibid. Irratioualis veio_qux Razionalis potcnua tamum quantims , , ‘ _ Rcliduum medxalc {hundum quui .' ‘ ibidcm . 66 ngpxoducctur triplfi fummx qua. quo ad primum quadratum ; {ed criam quo ad fecundum, 8c fequcutiaiu infinitum quadram "So ,,, x noniuib‘is . Rufiiluum 1i lL-ccmx Fer liinomiuml pmportionalium, 3x mmmenlurabi‘ lium nominum , plUUCnlLL ex (lilll-l qux . dratorum ipfimm radicum propofirarum . 1u Radicu m ab vnitatc per oxdinem dimulriplicam, producit numerum, cuius dimidium ell aggregamm ip- faium omnium mdicum . n6 Adiccs numcrorum lincarium vn .__._.__.._.__ ,__. ._.. V_ tam cumque fcxcuylo prrccdvntis: lrinnguliconix1nflu,qumu formam 10 nun'icral'ia m confhmmct. Rationalis tamum quantum, quz 35‘ Rationdlzs magnitudlnc quantitas , qum Re ula ad lubendum cumulum razorum a quorcunquc ab mime numtro llt bimcmbxium , fiuc rcfi. dualium. non folum ma nitudinc,! ac porcmia irrationalis cl , hoc cft , Dclitcm R. DEX IN X arium formatio. fol.5.6. A s m or Triangulis in mbus continuau' curedine triangulorum congcncs me. morum,vnitatc CXCCdlt duplum l _ dij . rau ct Trianguli latus ad laws quad ~ CO Cm |