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Show 1'28‘ ARITHMETICORV‘M DIFFINITIONES. ‘ Commcnfurabilcs magnitudlncs dicunmr guas commu niS mcnfizra meritur. _ . Incommcnfurabilcs vcrb,-quarum impofllbilc efl: inucmin" communem menfiu‘am. Commenfurabiles potentia quantitatcs {unnquamm p0 tcntix,hoc ell quadrata,fi1nt commcnfurabilia. ' in commenfurabilcs vao-pormtimgumum quadmm in. commcnfurabilia. ‘ Comm c-nfilmbilcs inrl‘ccundn potentia quantitatcs fimt quarum fecundaqnadmta‘funr com mcnfumbilia. lncommenfurabilcs fimilitcr,qua111mincémcnfirrabilia. gCommcnfirtabiles cubo quanti_tatcs funt , quarum cubi Cdmmcnfurabilcs. ' lncommcnfurabilcs verb cubo, «quarum cubi incom-' menfurabiles. . . Qibus im {e lmbentibus , G proponatur quart-rims quipiam ;crunt lnfinitm quantimtrs illi ccmmcnfuml: 'lcs , & quantitnre,& potcmia,& porcntia fecunda,& cubo. Vocetur itaque propofim quanlims Rarionalis , vnclc 8: quadratum ipfius,& {ccrmdnm quadratfi,&' cultusfi: quar- cunque dignitates ab ea props ga n; rationalcs crunt. vEt quantitas Propofirm , liuc magnitudinc, flue potentia commcnfumbilcs,rationalis voccum Incommcnfiu‘abilis varéfirranonalis. @ibus im diffinitis firblungcm us fingulas irrationalium diflinitioncs : mm, cum antitas rationalis fit, qug Pofitg rationali'commcnfurabilis ell. Rationalis potenria tanrfim crir, cuius quadratum cluntax It rationale ef'c. Similrter & rationalis cubo tamirm, cu- im cubus tann‘rm rationalis ell. Mcdialis aurcm , cuius fecundum quadratum duntaxat ntionalc ell. Ex quibus diffinitionibus liquitur, vr quanti‘ ms rationalis fit ctiam & potentia, & culvo , & potcnria {ccunda rationalis: non aurem é contrario. Item vt quantitas po'ccntia mtionalis fit ctiam potentia {ccunda raticnalis, non aurem & contrario. Nunc diflinicm us quantitates irrationalcs bimembres. Binomrum confia‘t ex cluabus quantitatibus rarionalibns ac Potentia Lanu‘xm commcnfurabilibus. (Luarum cxcdlus A poromc LIBRISECVNDI,PAR9IL m9 Apotomewcl Rcfidum dicitur.Er necetlE elkvt carum quadram confidant rationalcmarum verb procluétum mcdialc. Bimedialc primum confint cx duzrhus qmntimtibus mcdiallbus potcnm tantilm comm en furabilibus _, & rationale comprchcmlcntibus 2 quarum quadrata conficiunt mcdialc . Harum cxccllhs . Reliduum medialc primum di~ cmlr. Bimcdialc fecundum conflar ex duabus qumrimtibus mcdialibus potentia tannin commcnflrrabrlrbus & media- lc comprchcndcnrilms I quarum quadmm conficiunt me: dials, quod ell mediali pra‘difio incommcnfirrabilc. Ha« rum cxccllhs Rcfiduum xncdialc fecund um dicitu 1‘. Maior confhr ex dmbus qmntitarilms porentin incom- mmfumbilibus : qlmrum quadram conflant rationale : Sc quod [11b ipfis mcdialc. Harfi verb cxcdllrs dicitur Minor. Potcns rationale ac medialc conlht ex duabus quantitatibus potentia incommunfin‘nhllibus,quarum quadram c6- fiant mudialc,& quod {11b iyfis rationale. Harum cxcclllns drcrtur cuzn rational: msdillc totum Potcns. Perms duo mzdialia Coru'hr cx duabus qrmntimribus p0 tenrm incomrrrcnfrrralwilxluxrs , quarum quadrata conllant medial: , CY quad l‘ul) ipfis medialc prmrliclo incommcnfib raffll: . Hll‘um cxcclllls dicitur cum medial: mcclialc to- tuzn porcns. In qulbus {ex dflinirionibus mediallcinrclligirl)" qnmiicas porcnzia mnu‘lm mtionalis. Nz‘unquc‘omnfs ‘u‘ca, llu-:omnc prolluc‘lum potentia tantum rarrona~ 1:3, (alum!) Euclidemcdialc vocari. Etlinea potcns ralcm aru'n , fold ab coda-m linen mcdialis dici. (End [amen non inrsrturlmbir propofitum nolh‘um. Nos eniln quan"fulfill Ln generc (in: ill: linca (it , {inc area , potcnm} mntirrn ntimhlun vocqmus , cufu; quadmmm rationale. litidlnm var"), cuius quulratum {ccundum tanu‘lm ratio- mle 2H. .Scdin diffini‘rionibus diéhrum {Exirrationalium feancmur Euclwlcm. Pmkrm [th11 binomlum, quim refiduum hgbcr (1'); {pc- CiCS llc rlilllnchs (Lunch nmior porno Binomi‘j ,‘lru rclldug/3f} potcntior b-g-uiol'c‘ln qumlraro qu‘lntltatlS'lllWl con).x'nt'nfilr.1l7ilis ipfum :ll primas , lecundx, vcl tern; (pccm. 043mm) vcrbmrior portio‘brcuiorcm porentralltcr ancedlt in qmdratoqlunzitatis hbi inslolmmcfilurlblllsi,lplum all: qmrrr , quimx, Vcl {cum {9 ccrcr. Dcmdc lr rnnor por‘ Ec nonum |