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Show ix} '- nmm 76 ARITHMBTICORVM Pnoposn'ro 6". Ipfe d. crir quadratus ipfius b. Er 1'pr f. quadratis ip. Gus c.1rcm c. partc alrera longior, fiuc {uppl'uncnruni in quadratoipfius b .C' Adhuc ipic g.cr1rcu‘*u?-ip1:us b.113fc aurcm l. cubus iphus c4 1pm quoquc 11 1;. :ncmuwropomo- LIBRI PRTMI a PARS '11. 7‘7 fb. cxlcritju; coi‘rclntiui. Confiarcx ‘ccmp ofirionc xqua- lium propornonunycx quibus pater conditio & proprieras huiufcc dcfcriptionis numerorfimon r5 ad neceffi taré demo firationum , (4 ad plc‘niorem {uppoiitionis intelligenti am . Pnoposrrro 10‘. ' nalcsfupplcmcnm in Cuba ii‘leus b c. Dcniguolgfl: miqua. Sicut 'vm'm: efl difl'ercntia duorum fcqumtium b c. numero- dra rus {ecundus ipfius meC cit qmdmrus iplius (UPI: nu. Arum; int ipfi duo b c. film differential Mum fcquentinm d 6/2 It bi rre: difi‘l'remize qzmtuor fizqumtium g1) kl. quuc bi "rem qquadrarus iccundus ipfius Liioc 1ft guacratus 1pfius E Ipfifruc n 0 p. mcdij proportionnlus ad intc'granoum, v} patcbigqundmtum {ccundum IF‘HIS b C. lroc oi}, qua‘dmtu demum quatuor differcntiaa quinquc m n o p q. poflrmum per cius quadrnti , quem conf‘rituunr Qumran d r. cum unplo ipfius L‘.H'.L‘C omnia confirm: C): tiiflrriirioxiiiviis igforun: gun. dra tofum,'cuborum,& flippiemc‘ntorum,icd qundrnm ‘31‘1- ordénem fumpn‘arf'arct hoc totum per tertiam prxmiflhrum , quotics opus cit, addué‘tam. Puoposrrro 11‘. Omnis impar pmcedcnti quadrato zippofit1¢s,rq02mitfequm- mum &£}:cundum, & cubus ipfius b c. dc n nitrabuntur. temquadratum. Pater : niin pro‘polita dcfcriptio ncnpforfi Pnopomrro 7‘. Poflvnimrcm duo numcri b c. funt termini proportio- nis filPt‘fpal‘tiCUifll‘iS. Taméuc tresnumrri dc E, {cqumtis ordinis, quém quatuor g h k l. pcnultirnizqi..amn1; grimguc m n o p q. poflrcmi, iunr COX][2:11LIC‘pl‘OPOIUODLL‘iCS‘ 1n diéta dudum proportions. qulonium tciiioct b, muluphcanifingulos b C. fucit flngulos d c.1dco Per Iccundam it‘rx'unufigru, Eritiicutb. ndc.1ic d. ad a. Ium quonisni c. muinpnrnns Iinuulos b cfacit (ingulos e fiaiso p c365, ficur 17. ad 6.1}cc. adkflluarc d 6 (fun: cétiuuc proportiomhs inpropornonc forum b c.51mihter & Per candcm , oficndunus, quod turn {4 i1 kl qufim ipii m n o p q. {nut in €9.de Eropornonmp b 1c. {cmpcr vnus eff impar, & reliquus par fibi coilnrcrnlis. @arc torus b c. impar crir.Sed per prrccdcntcm, b 6 fun! differentix ipforum d CF. igitur b c. impar adic€tus ipfi d. quadraro,c65ciripfiim Equadratfi fequentéqd cfi Jppofiui. PROP osxTxo I2". Numcri quadrati df. ex ipfl: b afiue rvni‘mtcfiue quorum]; numero diflercntz'lmswnd mm duplo ip/iu: e. medij propomomz lis,conflant quadmmm ex tom 11 Lfifffl. Hrc in 16".noni per numeros,& in 4} fitcundi Elcmentorum per linens demon- ftratur. Dcmonflrabitun‘k hic hoc modo. Ipfc b. in be. fingulos, per 5i prxmiHarum, flicitiplbs d c.fingulos.1tcm ipfe c. in b cfmgulos Facir ipfos e f: fingulosflgitunper primam pratmiflilrum,torus b C. in totum b c. fitcict aggrega- forum '0 c. continue proportionalcsflhod cit profomum. rum cx d c c Ehoc 6ft, quadmmm,quod ex b cmquabit con< PROPOSlTlO 8". Item ficutipfi a b d g in. fun: continui‘ proportionalcf: im & ipfi c c h n. ncc non ipli fk 0.Atqucipli1}).funtm gcricm ipforfi d f. duplk'luc ipfius C'Qf'd {uit dcméflridd. eadcm proportions continua proportionnlcs. Adhuc,hrut ipfi a cflq. {unt COHUHHC proportionales 3 im mm xpii b e k p. quim ipfi d h 0. (111311151; gn. funtin cadcm connnua proportions proportionnlch-Icec omnin Patent per pt; ccdcntem , 8: per permummm proportiomlimtcm. PROPOSITIO 9". _ In? a c ofunt in proportions continua ficur b 11. & cxton ad mquidifiantinm dcfcendcntes. Similircr m 13f. flint 1n proportione continua, fiC g6. & cmtcri condclccndcutcs. Dcmum ipfi q k d. {unr in proportionc continua, 1n qua o PROPOSITIO 15‘. Duo quadrati proximi cum media part6 altcm lb'gz'orc 6072210: 6?}, zanficmnt nmrzerum lacxagonum flqnidngu/me. ch efl- 3 1" primi liorum Arithmeticorum. COROLLARIVM. Hinc fegtur pulchcrrimfi corollarifi,vidcliccr,chngonfi quangulu cu parts altcra longiorc collaterah c6iuné‘tfi,con (Lima: qundmrum impari§ collateralis: Ni pcrantcprmnif- {lumroru d cf.(qc‘i perprrcmiflum ell hexagonfi qquiangulfi) cum ipfb c. (quicfi part6 alrcrn Iongior) conflat quadratum tozius b C.imp.1ris collaremlis.Q1_od {cquitur fupponcmio, V ipforum b c. difil‘rcntmm crib vniratcm. P R o p of 8 m 1:. n 0 :6 2.4 36 x 18 P S |
