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Show 124. ARITHMFTICOR‘." bis ipfamet fibi,fi t1'i1*‘i(‘3.'in.iiiipi ‘ tr: Lam ‘unf‘yn ' " ken-my; fiqundruplirandn, Iri‘l infg iiingz‘rurircruri : ireguedcirCLI'SJM (mm imclligimr multiyrcmi rn:io,vtl‘jsgruflm rervc ccnrinuciur m teaminisNiidcquar'iiuoium rum (in p11 : cubontm nip]: 3 {Ecundomm quadraromm quadrupiaad latcrum flue radicum rationem. COROLLARIVM. Igit‘rarionis dqunrx teriizinis vn91nrercrit i136di°pt0f0r tionaiiszTrifl:Undue 3 imdi'uplatmfircszitaqucduinccl‘s. PROI'OSITIO 42‘. Damm rationcm bifin‘ifi, fine trifiiria'mjiue quadrifvrii, fiue n-r IIEERSECVNDVS. ray Irbm {i iubeal‘ ipfis (6. & 5+. duos propot‘tionalcs inter; poncrezquoniam tales numcri flint ad inuicéficut 8.8: 27‘. cubi numeri,quibus inrcriacent duo medi} proportionalcs, {ciliccr l2.&18.i&1flid€0 8c pi‘opofiris totidémedij propor tionalcs interiacebfit (Eilicct 24.86 56.1m1miiiyfis 5. 8c 48. {res mcdios proportionnlcs accémodarc velimmé minus li-‘ ccbir: cum finrficut I. 8‘: 16. quadratifccundi quibus trL‘ ‘ 2.4.8.1nedij intsrihutmrfirq; interrppofitos medi) 6.12.24. Adhiicfihis numcris'g.& loz. lubctintercluderc quinquc Exempla Irmtiom/ium.» medias Proportiomlus poiiibile ei‘ittquidoquidé tales fun: in proportioncipfbrum [.é‘c 6.1..qui fimtqmdmti cubori'i, 2 plmifiriam , rummquc quiffidm goflulamrit , mqimfiter parriri. Sinr dam ralionis termini a c.1iolrortcat mtionem a. mi c. bifizz'iam p0.i'tiii,»inte1'ponarurcis media proportiomlis b. Si surcm dorm i'arionis termini finta (i. 8: opoi‘tcar ipihm quibus nemo nefcit quinq; numeros intereife proportiona- r. 6. trifhrizm cliuidcregtfic interponitur cis diam mcdix propornnhs b c. Si verb dang mrionis tcri iini fin: :1 0. & oportcr‘. d'ixiimis,nuinei'iproportionalesdéd quitimrcsirmrionalcs. Y-CU- "-Exempli caufa,prop0nantur duo numcri nulli dié‘tlrfi pro- f- Cu- 1 8 f- Gil-12 r. ‘50- I 3 Excmpla rariomfiunb. ipiiim qua tirifgriam partirinunc inrcrpomntui‘ 613 ms me- portionu‘m ad inuicem fermnrcswtpotc 2.86 5. 15 his nul- r-_C_l_1_-_27 larcnus medij proportionalcsquos diximusfintererunr; {ed r r. 16. ' - 4 b~---2. C -_‘-,._ dm-m-S C----- ----16 3. 4, 12.. 6 18. 9 16. 8 24. 12. 56. 18 5.1. 27 3. 6. i 1. . disc proportionalcs qmnrimtes b Cd. Cuius Problcnmtis yrs. ("rim c>.ccaitio,quamuisi nobis in Al‘ithmcticis qumfiio- . nibus fitabundc tradita , hic ramcn ab exemplis non nbflincbimus. Er in primis nomndum, qubd quando l‘i‘opciim: qunn timtcs {tint adin uiccm licut qua diam nu m m: tfic vna quantitas interiacet illis media proportionalis: quniido au- 4 tcm , lieu: cubi numeri , runc dum mcdim . (limmio verb 8 Iicur quadrnti qundmrorum, tum: tres mcdiit. Quando dc- 16 11‘,111T37flClI r quadrati CLIl‘oruimrfic quinquii mcdi. ‘ propor- tionales quantiiatcs propoiiris intcriacmt : 8c in omni tali Cain mics quanrimtcs continuepioyorrionalgs {um :v'iimii- Cé Céméfurabilcsgquippe qure in rcr {c in ratione r. umcrurfi: vndcfic rationcs ipib: tune iimr rationslchmc (‘I‘rrmr mime ros exprefli'c, xtq; idco propofira ratio runc [ccctui‘ in rationcs cogniras per mtmcics. Si Verb Pl‘CFciil‘m gunniimars {cCus, quz‘im ciiflum (fl, fldinliiCL111 ic- hubeanr : irisriolitm proyorrinnnlesintuit ‘atioimlcs ncn (mm. D; . I‘iif,' rm, fropomnrur milii duo numerj 8. 8e 13.L;11i't‘.l15i11ii.‘0f medium pi‘opcrtionalam inucnirc, quoniam trLs nunwri {c lzrlxitt adipuicrnglicur 4.8: 9. quncirnri 2112!"?11, (pl-bus iiircriaCct mrciius131(=}‘cltiz.nuiisin Ida: .9 pic} ('Iizis Vitus {:milirei‘ mediusmru‘crit Fl‘Ci‘rOlTiOl‘.' is 12,. Cuivirm 2d illum medium , fiuir Freyciirz ad quadra'cs dupli fimt. Item r6 [cs {iciiicct 2.4.8.16.5 z. Vndc 8: propofitis inrerci‘unt toti- r. L ' ' dé feilicct 6. [i.2...1..48.9 G. (had (1 propofiti numeri a‘ircr, _' )' g _ fidiéhi cf‘tndinuicem {c imbeantmon intereruntipfisfluos 1" CU- 5 - ' l qumdi irrationnlcs quantitates. Itnquc (i velim ipfis 2.86 5.1‘ r. 24" medii includcreproportionalé , agi per eorfi qimdmtos +. r r. 3 6. &9.quib" intcreir 6.quiqu;1dr:1tus erir mcdiie quneiirrcflurc r 1‘. 5+ 2, "1 24 r. 5 1' r. 54 iam potentia tantfi notcfcrt. Nam ficutsrcs ql111dl‘zltl4.6.9. 1- r. g L fun: continué proportionales , in 8: corum radices fcilicet r 1:] r cu 6 r.4.r.6.r.9.fi1nr continue proportionales. Si nutcm ijfriem riflir-cu. : _ _ 5 "‘2'- I"?! rim 9‘ numeris vclim dms medias pi‘oportionalcs inflercre, nflii- .' ' '9" mam eorum cubos 8. & 2.7. quorum medij duo fimt 12.:gm::::4g 8: 18.quicubi {unrduarum quas quxrimus mediarum: riflir-cu. : Nam radices cuborum proportionalium fimt & proPor- r'D'r'CU-ng tionales. Si Vc'l‘O , ijfixzn tics medias inrerponerciubea-r, r-[jir‘cuizq rZu .12.. rt] i6 ' ricii.iS.. IE! r.cu ."3 expomm corum fecundos quadmros , ficilicet 16. 8c 81. ' ' ' _..___.. quorum tres numcri mcdi} fimt‘, {Cilicet 24. 56. 54. qui {ccr'mdi quoque qludmri crunr quantitamm trium me. diarum‘, quas qucerimus : El: quoniam horum numerorum medius qua‘drazus numerus cf'c, iam media trium quan- titatum non {blum ficundo quadmrc fed‘ctiam primo ne‘-~ tefcit : critcjuc ipfa'r. 6. Si dcmum‘, i-pfis 2.5‘6 5.quinq; men (ii-is proportionalcs procurcmfiliciam ex ipiis quadratos-cu borum,fiuc cubos qundmtorfifiui fun: 64,86 7 2.9. Quibus» interponi pfir quinq; numeri portionaliter.C96.14.4.7.1? 52.4.486g fimilitcr crfit qua: mi cuborfi qumq; mcdmru, quas» " |
