OCR Text |
Show 96 ARITHMETICORVM vcl fecundum quadratum mnn‘im cognhum offcrtur, mnl capien dum cfl fimiliter quadramm,vcl c11bvs,vcl{ccfidum quadratum quantitatis per fc cognim, & dcmdc quadratum in quadratumfiue cubus,in cubumfiuc fecundum quadra. tum in Iccundum quadrarfi multiplicandum cfi. & fic dc- inccps pro tcrtijs,aut quotiefcunq; quadratis.5ic (‘56 dcméRatio dudfi memorata proccdct, & propofitfi abfolucrur. COROLLARIVM. Vndc manifcfium cit , quéd ex duétu quadratorum , Gun cuborum, fiuc fecundorum quadratomm, an: fcqucn tium, fcmpcr producitur quadratum, fiuc cubus, flue qmdmtus fecundus ptodué'ti cx multiplicationt radicum , quarum quadram , {cu Cubi , {cu fecunda , vcl {equcntia quadrata. (Ea: omnia,ficut iam dcmonfiram fungita per Arithmeticam praxim , [am in quantitabus rationalibus , qufim po- tentia, flue cuboytanu‘lm rationaiibusfiue mcdialibusfiue duorum pluriumve nominum, filpputando comprobiruv, qucmadmodum in Arithmeticis quztflionibus Per cxompla tradidim us. PROPOSITIO 11‘. Dual)": quantitatibu: propofitfx, quamm quadrant tannin: val rubitantfingvcl fecunda quadrant tmztz‘mz cognira fupd- LIBR'I PKIMI, P'ARS'II. 9'7 Kim C c"? prouenict'b d.qu:1dratum,fcilicct ipfius b. quotient-is: q‘umnlz: m (kxticct cx diuifione produéh' in In ulriplicantcm, proucnii .t u!""}‘rliCatfl. . Item quoniam cx multiplicatione ipfarum gh. (juzr fun: {crunda quadramipfiuum 1 b. producimr k. fc‘cundum qmr‘mtum ipiius e. produéh ex ipfis a b. jam fimili- ter {1 pro ('siuiacmm quantitatc c. offlraunfccundum cius quad-rnu‘m Hit 3"" druidcntc aproponetur {Ecundum sins quadra- tum g. mncdiuidam ipfam k. in ipfim g. 6; proucnit h. fecun‘dum quadr'nutn iyfius b.quot1'emis. Nam 6x diuifionc produéfi in multiplicanrtm. profilit multiplicam . 7T ab. producimr n. cubus ipfius c. produé‘ti primarij : non alitcr, {1 pro qnantirat: c. pudenda dcmr cius culms n. 85 pro diuifio- né a.ponau1t‘cius cubus 1. mm: pattinrcubum ipfum n. in ipfum Exemplar. Vnim 1. & prouenicr m cu‘uus EFFUS [xquotientis.Namciucprodud‘um 1-l _‘ Rid. in multiplicantem «:iimfu'n ., c‘xlnlvct multiplicatam. Ncc {ccus z,_3 __5 facicndufim pro ‘rcrt‘qs, :u: C-qumnbus qmdmtis, quoufquc pro- 4"9 ~56 U chTcrit curioficas . (Em? 11 (HUNG: , an: diuidmdus nu'ncrus 8 v7.2.7V-216 Q PO- mnmnu unis its. olfcmntur, vr alter ‘lrcy .i-cnozu‘s fit _. alterius ,13»~_81-Jz96c1 z tenria Vcl ‘Cubus vol {1:deer quadratmn cognimm pi‘OP'imd- {civ: , tut: tunc par dignims "apicnfla cl} numcri pct {c cognm licct, vcl qundmmm in quadmmm ; vcl cu'wum in cubnan ,vcl fecundum quadm um, in {ccundum qtlfl};ttum , Vt] diggnmrtcm finitioncm , quando multiplicanturinuiccm dun: quanti‘ rates, produé‘tum ad multiplicamm cfi, ficut multiplicans ad pofimm: lam fl multiplicans nunc fit diuidens,ac produ quamuis in parcm d‘fgnimrem pnrriaris : hcutin mHIUPIICMmHC ha£18m m cfi. Sic mirm b: demonf‘rmtio dudum cxplicata l scum «bct , 35¢ quEEiho 5n cm. .COROLLARIVM. in qua"Ex quihus nmnitncf‘tum cfl, qubd ex dilliflOncquadrnti, dratumfinc cu‘n‘é in cubum, fiucfl-cundi guadmti 1n (ccundum {ccgndus rqimdratum , {Empcr yroumit quadratuslfcu Cubpsflc-u radxccm, quadrntm illius (motlcntisquod cx diuilu'm: mdms m a": diuifione ipfius c. in igfim :. Sit isgitur , cxcmpli gra- taro. Sumo cubos tam/2m datox, tongsriem ,aut (cu-(fl‘pm 'U-ih. rm, diuidcnda qtmnrims e. dmidens 121E211} mé'c ofil-mgmr firfl'olg ca:dun? quantiraics ab. quarum quadram c (I. Logmrg harum quadmm tanrfim , {Cilicst f: quadratum diuidr‘ndx c. arque C. quadratum diuidcntis a. diuidam ipfam flin ip~ hum; , mulnphrum congericm pronuncinrc. Pct vndcmnnm (mm C. 15 C-C Dcmmnquoniam uideqs ad pofimm . Itaquc diuifo produnflo in multiplicanI [cmjicmgcr cx diuifione proucnit multiplicans.ngd cum I. 1: im 11:,abioluc1nus problema,pcrdcfcriptionem pcnitus,ac p. 5 fuppofiriopem prmccdcnn‘s propofilionis. Sint igvitur, ficut 2 c d in prxmitlamropofitg qmnmatcs a b. quarfi qujdmm Cd. C ...__.-._. 6"" Eroduétum autcm c. & ipfhrum c d. produétum f. Often4. f 11 {um efi: crgo,quéd f. cfl qmdmtum ipfius e. qudd {cilicct f: .35; ---6 g: fit c-x dgflu c.in ngitur ex diuifioncipfiiius Ein ipfnm cpro l6 3 » ucnlct xpfa d. quod cfl: qundmmm imlus b. proucnientis 1296 b ex multiphcauonc cu.‘*~ou~.m 1m. qui {cilicet funt cubi 1pfarum pommmr ; alteram in alteram partiri . QLoniam , pcr dif- flum fit diuifinn, crir multiplicam, quoticns. Chundoquidcm, per diffindiuifn quantitas ad quotientem ef‘chcut di- a E quarum {um qundrataflel cubi, ve}(ccnnd.1 quadmmhur‘oucnlc- corolbat. ngd corollarium (Equitur innilitcr cx prgcadcpns mulPctlpfis , n.1fcebatur propgfitgonc ex lario,ficut propofitic‘) r. 5 .._‘_ 'tiplicationis it dmimonis dif'zmuoncs. PROPOSITIO '15" per Trapofimmm dam-um qwmfitatum ,pcr porcufia; mgnims,rmt proucnnc e.'}‘1n1us co a in b. Per nota ipfarum quadrata c «.1. 6: Cc dupmn . mum". , |