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Show n LIBER PRIMVS. ARITHMETICORVM 3O fcilicct Columns. pcntagona quinm cum duobus quadratis quintis, Per prmccdcntem , :‘cquiualet triplum Pyramidis rpyfl: quintrc . Cu mque m‘is pyramis éomec‘r,‘ pct 40.63: combinationc duarum pyramidum , {cilicct hexagonm tctragonicrc quinrre , 8: qundmrm .c‘lnartz‘ci; iam of'ccndcndum crit, qubd {can}; 17.pcr 4.05. pentagonx quintx, qua: {nit vm. pars combimtionis L8; (upcrius dic'hun aggrcgntunnrriphlm ci'c ipfius diéhc combi- fimilitc‘r l‘cliqua pars :yggxcgui , (cilicet columm trianguh qunrm cum duobus trimgulis quartis fimul , Pg 50. huius, triplum Valet pyramidis trungulm quarm'fluodécfi rcflduum combinatioms. unnobrem,quoniam dust panes nggregnti, ‘ nationis : quod hand obfculx" conf'mr . Nam VM pars iliius aggregariJcihcct columm hcxagcm tcrmgonica ql,1im3,c'. m hexagono [no quinto, 8: rimgulo quinto . Pct przccdcntis =corol-‘lari-L1111,xqui11alt-t triph‘z pyramidis retmonicm quintg: pythcxmgg. 3i 1 25 l prr' UV? jr).*‘ dunbus Partibus combinationis,fingulx fingulis triple fimt: qure vm psi-mum com binationis cfi . Nuc 1b". ,rcliquu pars propraca,perprim1m quinti Elcmcnrormn, 85 totum nggrcf gimm torius combimtionis triplum valcbit: quod filit dcmonih'mdum. 8: coiem whogifino pro quo llis alio affignxto 1050 Vti'nlllL' ad robomtionem propofiti. ‘ l COROLLARIVM. Ft pro dag/0 qn :dwti coflxtemfis ac pmccdcmfi tringuia , :5.quadratus quintus flab? :76 pate: benzgon‘1m @~ triznguE/m: collatemlcs : quol). A‘j' 25.0.5.{ ro.A.A, niamfimt ma; :mrlcm. Nam,pcr vndccimun huius,qmdmtus quintus valet duns triangulos,qm‘ntum 8: quartum. ({gu‘e duo quadrui quimi cum trimgulo quxrtofimul vafcnt cu- 10.A.4 mulum qmdmti thintifirianbruli quiuti,& duorum triangu- lorum quarti loci . Sud , per 19. quadratus quintus, & duo 15' D ' 3' rriunguli qtmti confidant hcxagonum‘ quin'tum :ergo hexan 10. A: +- genus q‘uintus , cum trianguio quintc» valcblmt :duos qua- ", 3‘ 4, dmtos quinros,& triangulum quarrum: Scidco Proillis {ub- fiitui Poll‘unt‘in Prxnmfa propofitionc. ' hung. 5'. +5» P‘ROPOSL'rIO 66. om; calm-2,41 I) emgom .c guizngzda czm 128x1g0210 tetmgo- nico collatemi , 6372/, 11.4953" txlmgw'is , collatem/i [CL/ice: (3" Ecru- comma? prueimtbpamcr I/xzmpz‘x,\trzplu flzcztfim pyramzdzs bexxgon.e. ML 5.~£. Excmph gum ,dxco, quad columns. hexagona-xquianguh Col. l1:x. zguxgo; us- quinm , (cities: 3 05. vni cum hexagono tctmgonico quinto cub' 4 .45. Cumin: trimgilo qgiuco xy. 86 trimgulo qmrto 10.7 L. 46+ * coniunéh , Emir tripmgm luv pyramidisquimx, {cilicct I 1. 5. U '+"‘ ad quodofbndcndum i1c pcoccabflolumm hcxagona :zqui‘ angula q:1in:1,per 4,5. huius libri, xqualis ci't cohlm me tctm- heflgpn‘m y.4; +xr§ang.5.15.+"13:18.4..10' gonica: quinm, cnbo qxurto , & 1.11115!er quarto pariter ate-Ccpris . His ego 1ppono 11315501111111 tctmgonicum quinruzn, trinnguhnn quinzum, & trimguium qmrtmn ; atllu: it; d:monlmndum crit, quad tomzn huiufnmli .1g;1':-:1tum er colu‘xml hexagon; tctmgonim quinm , cube qu 1H0 , quak dmto qx}.1rto,hcx.lgono quitumtrimgulo qumm,3€ triangula- q‘ulrto‘umal , triplum. elk Pyr‘unidis hexagon .equiugulx. 93133" aggrelgrm , {allca cubufls qmrms cum qu;1(,i.1‘3.[0 quart‘ofik Irri~ angulo quarto, fimul Iumprus, per 6;. hums, valet iumhrcr triplum pyramidis quadrant: quart: , qua" inn} CI: combinau tione refidun pars cfl: . Itaquc quoninm dug yams 1ggrcgnti duabus comb'innrionis partibus iingnl; fingulis {um triplg: 'iccirco,pcr ptirnaleqllinti Elementorum, 8.: to tum aggrega- mm totius combinationis triplum crit : quod cm: demon- fimndum. Et nrgumenmtio :21 quinto loco ad aha ququis 10m *tmnsfcrctur ad conclufionem'propofiri. COROLLARIVM. Er pro (124012145 triangu/ix collatemii (y prgcedcnti , fitbflz'morc pore: qzmdmmnz collatmzlcm. Nam , per vndccin:mn,qm- draws qqualis cf: du'obus fimul triangulis, coll; :cmli,&' Prgw Ccdcnri . * COROLLARIVM. Rmflmz pro bcmgona tetrdgonico, c'r quadraro collateralibm, fidgflirztcrc pares bemgonum hfquianguimz d)" numemm im‘oarcm per 52". rhemgxcrm' collanrflz's. Nam,per g2.cxcmpli gratiachxngonus mquim- gulus quintuswnlct hexagonum tcrmgonicum quinmm cum i 45 hexa.:rq.% . , quudmro quarto. Apponnmr vrrobique nnmcrus impar 5. 61 pct 13. imlmi cum quintus‘at tunchcxagonus mquiangulus quintus LEM-"‘2 quinro vnlcbi: hexagonum tctrngonicum quinmm cum qm16 . [1.59 draro quarto 8(1'mpariquinto . Sad) per 13. quadmrus ,1." {par 5. impnr 5.5 25. &<i111parquintus fimul mlcntquadmtum quintum . Igitur 9. 9 lleagOnuS :tquiangulns quintus cum impari quinto \‘alcnr htcxagonum tctmgonicum quintum <36 quadratym quintum fimul [u m pros : & perindc iii-dam {ubrogari poflunt. |