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Show "‘1 8 ARI‘THMETICORVM pROPOSITlO IO 15"} 5 4;. LIB'E R PRIM‘VS. V gut: per prxmill‘am pmtagonx mquiualent. Sic concludes, Dmnit colrzmm pmmgona confirmmr (x (ii/(abut? coll/4mm, colum mm-hexagomm tetragonicam azquiualere aggrcqatum, 10-2 5-3 5 feiliccr tpmrz'mta collaterali,trz'zmgula pmrcdmzn‘ t'j' eittrngido columns: quadratcc collateralis , dupli column-x tritrngula: 10.15-35 fircccc'dtm'z'. Exempli gmria,columrm perttngouzt qumm 17;. quartx, duplicjuc trianguli quarri . "135-3 5 aio, quod conficirur ex duabus columms , lc111cct quadrata "045:15 qninm 125.&:t1‘jungula quarra, {cxlxect 40. 8c ex trmngulo ------- l pcr - (llfi.COllllUDr. ' . e pentagon". ' . qu i n a 10.40 125~175quarto,lc111cet IO. Ram coaccruatur ex quinque pt‘ntngonis qumtisi. Talcsc'luc picn- mgoni ; per diffin. ex quinqucquaillaus qumtrs, to‘tulcmque tri‘nngulis quartis. Cuma'juc quinoue qualmn qumtr conficlrm t,pcr dillinrcolumm m qr: tom tam-,iru: cnl‘u m qmntum: nrque, cum quinque trgurguri quam' mquuulcant colum- tmm trinngulam quarrnm , CV trxmgulum gunrtunr; mm plnne lEquitur , Vt column: pentagon-a quanta, trqt‘uualmt culmm quimum , columnzuu triangulnm quu‘mu‘, cc man{julum qunrmm . Nequc aliutl firit‘demonllrm‘f;um. Sed origumcn ratio pro quiuto locofaé‘r;1,l1militc1‘acl nirutl quemnis nccommodnlfiturficut propolmo conclutlitjvotes aura-nu hlc, pro cubo, {ulfiftituerc 6.1, quilms per prxccocnteru regul-unlct culmsSic enim Columnn pentagona mqumalclut mangulam columnam collutcralem, dnplum columnrc tmngulca quartmfiuplumt'lue triangull quam. Pnovostrro 44. Omni: (alumna bt'mgom rzz‘mgmfim (onfiiruz'mr 0x collaterali (alumna pcntagom, c.1555} pmrczlrmi 60114772274 nib" j '4 and mmpmcrdmté triangulo. Excmpli grammcolunmn hexagon: 35-45 tetragonica quinrafcilicct 2 2 ;.conhcitur ex quinm coluumu 10'; SW45 pcntaqonn ltilicct 17 5. 8; ex quarta columm triangulnficill» 10'; 5#45 cat 46. \‘ni cum quarto trinngulo, fcilicct IO. Nam] per 10'3 5~45 diflin. columnzl hexagorm tctmgonica quinti loci,c0alelcit ex wfifl quinque hexagonis tctmgonlcis. Tales autem hexagoni con10. 40 175-215 {lant pct cliflin. ex quinque pentagonis ciufllcm loci , 86 ex totldcin triangulis loci quarti . Porro quinquc pentagoni quinti conficiunt per dill. columnam pentagonam qummm. Et quinque trianguli quartimquiualent column: trmngulm‘ PROPOSITIO n; 4.0 Lm 4;. ‘ Omnix colummz bemgomz mguéangultz .47"me aggrczyto 9): (01:4an bemgona tctmgonirzz collaterali, (9' ex cubofipdtz'mro/[g pmccdentibm. Excmpligratin, colummhexagom~ nequinm gull quinti loci fcrlicct 5o 5.3:quiualct aggregate ex columns. 16‘45-61' hexegona tetragonica quinmfcilicet 125. 8664 cubo quarto, 16.45‘61 {cilicet5+.quadr1toz'1ue quarrofcilicet 16. Nam, per dil'li. x6.45~61 columm hexagonn :equiangula quiuta confht ex quinque 1 6.4.5 -6t hcxrgozyis :‘equ-imgulisTaleS autem hexagoni com ponuntur, 1645-61 Per 3 2.". lruiusfllnguli ex coniunc'lionc fingulorum lxexagono- 16. 64.225.305 rum tetragonicorum eiufllem quinti loci, & totidema'lue quldmtorum qunrti loci . Setl quinquc qrmdrati in quarto loco valcnt culmm quartum, 86 quadratum eiufdcm loci fimul. Er quinque hexagoni tetmgonici ex quinto loco Ebciunt, pct dian. columnam tctmgonicam quintam . Igiturcolumnl hexagona mquiangula quinta , valet aggregdrum columnrt hexagonx: termgomcrc quint;e,cubi (1mm, 8: eiuf- (L‘m quadrati : quod ol'cmdendum fixit. QED dcmonflmtio, ficut quiuro loco,im & alijs QCCOITHDOLLLELII‘, ad confirmau- dam propofiri veritatcm . COROLLARIVM. Et pro column-o. hemgona tctragonica, {ubflituerc pores quicquid in prmmims,tali columure oftenfum el‘t azquiualerc. Sic concluderc pollirm, quod columm. hexagom xquianguh :‘Cquiualct columnnm pentagomm collateralem , column-am triangulnm cum filo trimgulo , Sc culmm cum {no quntlmto prsecedentes . cmtems mquipollcnzias omitto , nc pluribus, qu‘am dcccgnegociuln ugzun. PROPO‘SITIO‘ 46.» quartet & trinngulo. Igitur columnahexagom tctragomca. Omnir colmmm hexagram wquiarzgulx co.zgment.zmr ex mdice collatmlittznqm‘m are, (9-H congcrz'c pixeceicurix trim- quinm pcrficfitur ex columna pentagona c111inm,& ex colum- gulx co/zmz:1.e,fiz£j} triangulijexcuplic;zr.z.N1m,per diff. mli 5 co- na trianguln quarm. 8: ex zrinngulo quarto : quod ernt oftendentlum ,1vrc'1ue pro qumto fac‘him lic pro cxtcris locrs pnoribus , vel pollc-rioribus nrgumcnmrc, ad dernonllrancluxu propoiitum. Et pro pentagom columm. fublhtucre pores ea: qum F17 IO .-5(7.I-6I' 10.60.1-61 6%10. 60.1-6tIo. 60.1-6r' cEtralibus vnitatibus, 8(1Excuplo triiguli prxcetléris. Exépli IO. 60.1-61 gfa,colfin1‘hex1gonl :cquiigula quit; 3 05.9 difficéltruitur ex lumn: coilruitur ex hexagonis mquiangulis; llcmgoni :ruté ex .-___-_,. guiq; hexagonis aeqyuiigulismoc é,_quicuplo ipli'6r.q_ufti loci. X 2. Tales 305". |
