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Show 154 nvcrrms ELEMENTORVM 'PROP'OSITIONES. oéhhcd‘ri perpendicularis ieofahedri maior ethquérn pcrpeudiculgris e1)chd am 10r,qu 1dcoma cum minus (quoniam illius triangulum imr. prepon um ‘crand demonf flout cularis cubi, M A 1 v 5 CR icofahedri latus fphcerx , intra 'quam defcribirur', femid'amerm. Iutuerc dcfcriprioncm vltimrc prescedentis libelli:in 135 mains erir reé‘mnguio c g,fi1itaiitem rcé‘tangulum Im. squum trianulo h k 1. 86 ideo Vigecupl'nm ad rrinngulum d.- Er rcé‘tangul‘am cg. ofl'uplum ad c.qmdmtum . Igirur diéhun vigecuplmn maius diéko oé‘ruplongod era: dcmonflrandum. Imc‘) x 9.~trinngula huiufinodi cxccdum difli quzldrarioéiuplumwr doccripfa rarionum Compofitio. qua a h.& m b.fimr gquaics : (Scharum vrralibctm'aior , quém m .1. 8:: 1c 0 s A H E n R! {uperficics maior'efiquém cubi in cadcmiphazm halfumxr dc ideo maiorfluém k l.&idco amnior', quim h mlgltur m Eofiri fuperficiesl‘hmmcr prrccdcntem, viginti'triangula xquilatcm {up-2r femidinmcrro {111:1me céflirum mains fungi 0&0 quadram fag {emicirculo plufqu‘am 'tertiam parrcmmrgo mai-us c'fl: m b.qu§m larus Ilcxagoni in ipfo circ'ulo dcfcrip to . Quins latus icofahcdri maim éro {emidiametro {phmrmquod cfi-propofitudeem confiat in lincam , longior d. c quonii b. quéma m longu d. a vbi ionis. reperir a: ‘rxdié‘c _ .. qulun b c.& {imilitcr confiat Propofitum cadé (cmidiamerro dcfcriprafled p 24"" huiusdarus icofahcdri mains cfl fphccrcedn qua locarur, femidiamerro.A‘ fortiori‘ergo zo.triangula fupcr lams icofuhedri confliru'ca,maiora fimr,quz‘un 0&0 quadmra [1199 D v o quadrata,qux ex fpha-rc; diamcrro fimul {umpm xqualxafunt fupcrficici Cubi in fphmra Conirrufli. Per 18‘ cnim prremifli libelli, fcmidiamctro {phxzw defcriptaSed z o.rriangula huiufmodi céponfit totam icofahcdri {uperficiéfitofio quadram {cmidia met-ti fphxrahs, Per 2 5"" conflant roram cubi fupcrficié. Ergo & icofahcdri {upcrficies quadmrum , quod cfl: {plum diamcrro triplum , ctr quadrato cubiti maior crir, quéun cubi-fuperficics. ficur dcmonffrandum proponirur. lateri-s -. cumc'lue fcx quadram cubi pcrficiant 'cubicam fupcrficicm. I c o s A H- E D R v M mains CR cubo {ream in vna {plixm dcfcri- pro. Pater.Nam Pcrpendicularisf‘a ccnxro {Pfixrx adbafimicofahcdri pater propofitum . Hinc manifcfium cfi, qm‘>d 0&0 quadrata, qux} {phxrica femidiamaro, adxquant cubicam fiiperficiem . V r c r N r r triangula azquilat-era maius flint,qu:‘un 0&0 quadrant Vt (1 {int {upcr Iiucas a bxqualcs, fupsr cifdem dcfcripm larcribus. qundmrum c.& rriangulum dazquilarcrum: Aio, qubd zo.triangula. :cqualia fingula triangulo d. maius {Lint quiim S. quadrnra fingula xqualia quadrato c. Sit cnim e£oftupla ad lincam a. & fg. xqualis ipfi a . eriréuc rcétangulum c g.o&up1um ad aquadmtfi. A B Sit quoquc h k. vigccupla ad a ipfam b.& h Lquanta cif per‘ pcndicuhris in rriangulo d. e b S ‘ maior eff , per-2. 3"" huius , qufim perpendicularis ab codcm ccntro ad bafimcubi. Er , per prxccdcntem , iu \erficies icofahcdri maior cf?) quim curbi fuperficies, ugm ob reimh ed‘uétisr'xé ccnrrofphazrcc reé‘tisr ad angulos folidorum difiinguanrur ipfa {olida ih-pyramides : dcindc fiat pyramismui'us bafis fir omnibus icoihhedri‘fimul fumptis bafibus‘ zqua‘ds , cclfi‘rudo verb mqualis perpendiculnri :‘1 cenrro {phrer-z: adx Bafiurfolidi : qua: pyramis fir,A. Mox fiat aha. Pymmis,cuius.bafif fit mqualis tori cubi fupsrficici: celfirudo verb mqualisperpcndimlaw a.. ad bfl‘fim (ll‘bi': qurz Pymmis fir B..Iam per 6"" dtlodeciini.5 pyramis pymmi& quoniam Er .. crit :eqlmlis cubo b. icofixfiedro, Pyramiswcro A. & bafi &£1fligio {uperat B. pyramidem : erit pmculdubio maior' cadcm. @arc 8£icofahcdrumx cube mains erir. quod cI'c.EroEofituin.. f K m J .1 «z: Er erit triangulum h k 1. vigccuplum ad trianguium d. Serif; quoq; ficr a'qualia‘h k.in punéto m.erit rcéhngulum l m. quum rcflangulo k LPCr 41‘ . primiLritun fgad ipfam h1.POCt'nI§fllith fchuitertiz, per primam huius.Scd h mail ipfam c EPcr liypothcfim,ficut 5.ad 4. 8.: idco potcnrialircr ficut z 5.3d 1 6. Maior ergo efi ratio h mad ipfam c Equiun ratio ipfius fgad ipfim h l. Sitiraquc ficur hm. ad ipfam c fific fgmd ipi'am h n. Eritt'}; per 85 quinti h n.1ninor, quim h 1‘ Fiat brgo rcfianguium m n. quad , per 15"" fexri,crit :equum tefiangulc cg. proprcr rccxprocam latcrum rationcm . Quarc rcétangulum Im. mums _4\ A circqu dcfcripri le 3. circuIi' centre inpcntagoni latusin ipfo fquc & eius , qua: cx: perpendicular-is ducirur , dimidia ci‘t fim ui vrriu cuculq a b g.ccutro & latcris dccagoni in codem-circulo ddcripn. In gonirqure" cuius ccntrum c. {it c c..perpcndiculnris ad a b. Iatus penta decagomr latris d: b 'Iuc dlcriu lum {foducarur ad pcrifcriém in pund‘ io ipfiusbd. dimid 8: d c iphus io dimid eff lis exqua c unc aio,quéd 5 ' r 1 c+{3‘86 conniégatu 1911 c dagualis in ‘ Icfium conififiisfiumatur cnim |
