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Show ‘ La. i . "12"."; .._.-..A _ 114. EVCLIDIS ELEMENTORVM culo a. b atrianguium xquilarcrum a b c. fir infcriptum cuius cirtuii ccnrrum d. 85 diameter {it a d c: Aio qubd quadrarum iplius a b.1a-‘ teris triplum efh ad quadmmm ipiius :1 d.vci d c.1ismidiametcr. Conncékatui' cnim b c. qucd cf": latus hexagoni : & 5; idco :Equalis ipfi a d. Er hoc vterr: nrgumcn to. Nam quamor qmdmm ipfius :1 d. (inc b e. limul acceptafunr cequaiia quadraro ipfius a c. diame- tri. '\ 'PROPOSITION'E‘S.' II; ' Et {3 quadrilarcrum circulo infcriptum fit: tunc duo , qux produ. cuntur ex binis oppoliris latcrilms , parireracccpm rcéhnguia {unt xqualia ci,quod (11b diametris cius comprchcnditurfieélangulo,vt Pto- lemxus olrendir. Vnde,fi duorum arcuum datx fint chord: , dabitu: tam corum aggrcgati , quém difiérmzizr chords. . Hinc arcuum Per 'totum {emicu'culum chords: & {inus rcéti notcfccnr . Et omnis Chordimctriaquze mm ad planorum , quiun ad fplm‘ralium triangu- Std quadra mm a cycr pen ultimam pri mi, :equum CR quadrariq ipfirum a bi) climul filmptis . Igimr quzuiratu lizvciimul fumpra , :cqua lorum fcicntiain ncccflhria 6ft. Nunc i‘edcnmus ad iblida . P 'r R A M I o E M conflituc'rc, & dam (pliccra comprclicnderc: & dcmonflrarequéd ipfius {Phacrm dimeticns potentia iéfquialtcr 61} ad funrquatuor quadratis ipiiaa b c. 0&1ng dempro vtrinquc qundmro vno iplius b L‘.fi1PCIfi111E rria quadram b emqualia ab.& ipi'a a c.dupia ad ipfgm c [mum duéh c d. ipfi qmdrato iplius 9. b. Triplum cficrgo quadratum ipfius a b. ad quid 21mm ipiins '0 6.511: igiius .1 .51. quod firir demonficrandum. : pcrpcndiculari,crit per 17‘Jexri,quadratfi ipfius a c.dupl& ad quadratum ipfius C d.& per pcnulr. Vndcnmnifcflum cfkquéd Circuii diameter potcfl: trianguli tequi- lareri 8c hexagoni :rquilareri iiivi inkriprorum latera i i Item parcr,qu€>d a hiatus trianguli ad pcrpcndicularem a f: potenv tialitcr fefquircrtium cft.Er qubd d cdémidinmcter par {squalid {bearur primi , qmdrarfi ipfius 3. d. triplfi 2d quadratum 1L-------‘--\‘L ipfius cd. Ponamripfi a b.92quaiis k l.& ipfita C. in pun 610 F. --X- ‘Pro reliquammfiguramm iateribm additio. frem pro co triangulum Equilatcrum {g h. 85 ducantur fciemia cbordamm . larus ipfius PyramidisSir datze fphxra: diameter . Quadrati quoque laws in circulo def‘cripti potcn rialiter duplum CHE ad femidiamcrrum circuli conflar pa: {cxmm qmrti ‘ , Dcfcriprio autem Pcntagoni intra datum circulum fit per deci- mam & vndecimam ciufdem. ‘ Hexagoni verblatus xquum CHE: {cmidiametcr circuli, Conclufum' cfl: in quindccima eiufdem. 7_ Exhis diuifo per mqualia nrcu later-is quadratimorcf‘cir latus 0610‘ ‘4! N \ :cqualis k c. & cream. perpendiculari e f. in femi~ circulo k flfupcr ccntro afiat circulus {g h.& in rcét'} (k. gk. h k. Sic pyramis th k. Conflnbit intra {Phxraim quam dcfcribct {cmicirculus fkl. equilatera. Nam vnumquodqne trium latcrum k f. k g. k h. quadmtfi triplum crit ad quadmrum ipiius c {ficur quadramm tripliim eff ad quadrarum ipfius cd. 66 Per prxcedentcm vnumquodquc‘ trium laterum fg. g h. h f. quadratum triplum efl ad quadratum ipfxus c F. Igitur til-nth larcra pyramidis k fg h. inuiccm xqualiai drun- quoniam b a. fi'lquial'tera elf ad ipfhm goni‘ Arcu quoque hexagonici inrcris {imiliter (crib, coqnofcitilr a c.prbpterea per 8‘.&17".i‘exr1, quaditirfi ipii'uswa bfciquiaiterum cfl' Dodecngoni Ia rus.Namque chorda dimidiati arcus cf}: undid propor~ tionalis inter diametrum circuli, & cius Portionem , (111$ 5; chords. to- mlis arcus nbfcinditur . T ad quadmrum ipfius a digirur 8: qrmdrntum ipiuis k Lqiig cfl {phmrg Porré, ii ponarurcirculi diameter long,De vr‘l {altcm porcnria ra« tiomlis , lams Oirogoni in‘rm circulum dEfCripti , erit irrationalis Iinca,qu¢c minor dicirur. Laws vero dodccagoni lines. irrationalis,qux apotomé vocatur.Q1dod quidem ex ipfo caiculo confiarc potefl : ficut 8c dc larcribus Pen mgoni 8: Dccagoni in circuio rarionaiem diame'tru m habcntc defcrip rorum : 8: dc larcribus Icofahcdri 8: dodccahcdri Emcere poliémus . .It‘cm Pro cnlcuio chordarumiliud notandum,qu<‘)d dua: chordq femiarruium complen tegcontincnt anguium reé‘tfi : vnde vna carum dam, dabitur & reiiqua Perpenultimam primi . E: G 3~w,v,\w .u: my ~ diamctcr , {Eiqiiizilrei'iiin cf]: ad quadratum jpfius k f. quod cfi: larus Pymmidis , quod ef'c propoiimm. ' O€rahcdrum confirm-re , & data, {phmm comprehenderc : 8: oficnderc, (luéd ipfius fphxrse dimcxicns poremia latcris jpiius oé‘mhcdri dupius CPLSit :1b.d(1KB (1)112:rm diameter . qua: in punétf) CPL'Y mqualia fixerurfi; cxcr- / temr c d.perp€dicularxs.MOX / dcfcribatur quadratfi efg h. a 1 C c‘uius larus fir ipfi a dqqunlc. ‘ Er Produéris diametris c g. f 11. {c in puric'to IE. fecanribus,cducatur.l k tn.plano quadra r1 fig-rpm l dicuiaris. |