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Show I70 ARITHMETICORVM Quantum Iateris ofkahcdri, dup lum cf} ad quadratu‘m femidiamctri. andmru m larcris cubi,fchuiterriuxn femidiamcrri. eff ad quadratum COROLLARIVM. Vndc manifi-flum eff,qu<‘)d Jam s Pvtamidls ad latus 0&3 hcdri potcnria {chuircrrium : ad latus cubi : dupIum, 8c larus ochhcdri ad lntus cubi fqu uialrcrum. %adratum lateris icoihhcdn' cl": rcfiduum quartum,cu. ins maior portiodupla efl ad qmdmtum femidiamem': minor var?) portio potentialircr l‘u hfdfiuiqunrm ad quadra, tum femidiamctri. Vndclams ipfum cri: irrationahs,qux < M r N o R. Lntus dodccahedri efl: Refiduum porrio cflporenrialirer fixpcrparricns-(cxtum', cuius maior dms tcrtias ad {6mirfiametrum ; minor vcré Porrio lubtripla ciufdcm femidiamctri. Ex quo calculo fequirur, Ingeniofimme Lea-or, vrficm quadramm larcris hexagoni , fine {cmidiamctri cum quadrato latcris dcca oni Coniunékum conflar quadratum la‘ tetis pentagoni; {igc & in {olidis in cadcm {plum :dcfcnl Pris, quadmtum latcris pyramidis , cum quadmto cubici late-H's {imul acceptum, conflicuirquadmtum {patriot diametri. Item ficut in Circulo , {cmulmmcrm , fiuc Iatcrc hexagom {ecundum LIBRI SECVNDI," 13AM II: 171‘ LATERA FIGVRARVM AEO‘YILA TERVM. Semidiamcrct circu1i~1. Rat‘i‘. a.ciL15--4. Latus A" ~----r.1 1.Ra.po. Dams-~11. Lam; [3""t. 8.Ra.po. [Lei us 8 Latus >§<"i z. Ra. [leius 4 Laws dccagoni-~r.v. 51.x. Rcs.5"‘ E].ci'-~ 6.fi. r.zo.Res pf thus Ovr.V.--lo.1fi.r.zo.Mmor D.ei'-1o.rfi.r.z o.Ref.+" Latus 8".--r.v-3.xfi.r.3 LMEnor. D.ci'--8.fi'1.r.32.Re£+f' Latus u." r.6.xfi.r.z. Res. 6". LATE R A SOLIDORVM REGVLARIVM. scmidlamcitcr fphgrac 2.Rat"‘ mains-‘4 Latus Pyramidis -- r. 10; Rmpo. [3.61115 Latus Oéhhcdri thus Cubi to; r. 8.R3.Po. E].cius--8 r. 5;. Ranpo. Gems-~54. exrrsm am , medmmqu: rationcm di~ L.Icofahcdri-r.v. 8.51m. 11;. Minor D.ci'8.IfLr.11;: Refq,‘i LDOdccahcder. 63351.1: 13'. RCCCS‘i omnia quamquam demonfirara fun: in Elcmcnns Geometricis , tamcn ex ipfo Calculo npcrtifliné notcicunr. @r . . Si linen éuorfi pcdx': {cccturfccun‘dfi extremi medlqn-qq; >mtionem,‘naior cius porrv'o fie: r. 5m I. Rcfu‘ium fcxhce't quintum. Minor wro.3.r§1.r.y.pnmtfm. {Rm x1 Lm'ca r431. mfa, mnor portio efl dccagoni latus : 1m in {ph ("m , later: cubi {imilitcr dluifo , m Lior portio crit doiccah :dri Jatus. Q2 um exempla hicfubij do, fimilitcrdmidamr, maior cius porrjo CT 1'. 6. ,- m. r. 1,- xcflduum fcxtum. Minor veer. 12. .m.r.6,-. PROPOSITIO 109‘. Si circuli pentagoni? .cquilatcrii cfrcffj'fribc'mti:_ diamcferfucrit [Enca irrationali: Minor (szcnfiflabzlzi mmfrz proprlc'; tum. lam: pcntaganicrit Relidugm qvmrtm.'51a1ftc [allay muggy {Arxnt pomrur Rationale ,- time dimmer erzt zrmtwnalzsl, qua; d‘fi- ior. 5i dcmum lam: pentagon: ponatur "4413;115:121 .e _ , |
