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Show ARITHMETICO RVVM culzlijofquamls,1cum ltcm due r'cliquia pars aggregatflfcilicct ; mus, [SP 0 P, LIBRI PRIMI, PARS ll. 4-! A" q‘uarto.£Io.primigcncris,c6ficit 515.113 m' If: ci‘t mm per 77' na- us pam .13nimltaqucquoniam dua‘ purges aggrcgan zldcucomcr PH" (unt x mpl lxs isfingulx fingu primigcncris formiszvidclicct colfim pémgona 5",cubo 4°, 6: (3m 4°.His adiungo duplfiD" quinti,& triangulfi quartfi, :tq; ita dcméflmndfi crinquod rotum id aggrefiatum cx columna pEtagona 5‘, cube 4", qmdrato 4°, duobus quadra- quadrato & A10 quarti;,:rqualxs cf}, Pcr6 altcra Par? Eon] mafia. tamidis quadrata: qtmrrarqux {Luz combin‘arion um aggregarum toflusdcon} mi quinti Elementorumfi? tot' unlfk cmu f Cub' 5' dcmonl‘trand binationis,triplmn crinquod fn‘lt m locum tranchlctur and alxu vxs m flratioiquinto ad que o s l ‘1‘ l o .80 . confirmmdum propofilum PR 0 P ftlz will? Omnis columna quadrata centrally cum duplo quadr x 25 s.‘Exc. mzdz ; pyra a n iplzzmficztfg l Cub. 4‘9 X teralis prfimégmeri: conlunfi u du- oyf mLz qum s rali gratin: columna quadrata cent pli %LB" 4964' ' Ploouiml quadrafi cx P" gcncrc,l1oc elbcum yo.fac1r 555. 16 D- 5' P, 15' , 19 9 '1 ;=- > ' I" I H A 5+ P ., 0° 59 15 .15 g 31' 49 p9 IO 7 fic COCludl'tlll'. t X quod triplfi cfi {use pyramidisfcilicc 8 5.516 lat cx tnlms o:1f/ cr 77‘,c ta,p s quin rali a Colfina quad‘rat ccnt 3 {Llnt co ((1:3 4 e cub _5°, cgbo cct c:l1 is,f form ris primi gene hco qua' mtu qum lfinx quadratz)& quadrato 4... Hx‘s app s qlllualctduo tfi:&altcrum quadratfi qu1ntu,qm,pcr I \"K' triangulos, quinmm,& quartfi'mtq; ita oficndcndfi crit, (13 (on? talnaggrcgatfi cx calm quxprog coubs) qlmr'co, qunguo 4o,qua_dmm qumto,&' {n.angulls‘y 064 8111911 gcncnséam-l a lS qmmz. ~Un.. litcr mplum ell: pyram1d1§ (111ngan cenn midis pentagonal: ccnrralis qumtazf. IO 5.qd fic (femont‘trati C . , Colfina pcntagona ccntralis quinm pct 775 céfiat‘ex tribus 0' O 5 1' tria uadrat", 3°____ 7C .4- Vm pats lllius agrcgatifxubus,q ls guadmtx gnm/ld pyra uf trlpl ng: Faci fimul - M ti loci,pcr 635, ; rcllquafars agcmq slr nom bma com pars vm fuit uq t;,q Cub"4_9 49)" l 6.4.. X Lat" 43 15. xis quintis,& A" 4" fimul triplfi fit Pymmidis pémgonx cé- 9 D 5 tralis quintz.Vcr|'1m pyrnmis hm61 per 7 5R huius,‘c6{ht ex cébinationc duorum pyramidum primi gmcrisfpcnmgm Cl" 5' 50. m: quintxfic triangulx 4", & px‘OPtcrea dcmélh‘andfi crit. A+'P‘ qubd memoramm nggrcgarum Prgfluxvcébimtionis triplfi 10. cfl.Hoc paélo: vna pars illius aggrcgarifxolumm PEtagona cum duplo quadrnti ex 5" loco,pcr 64,5,fiml'r qquat triplum pyramidis pémgonm 5‘"- ,qua-Lcfl vna pars combinntzonis. Ité rcfidua pars aggrogatidlcubus, quadrn tus,& tria ngulus .quani loci, fimul :tquat,pcr 655,triplfi pyramidfi E1" quar- P]. x Pyl" Q jap' 51 1‘ r 75- T tz,quaz ii ell rcfidua Pars combinatlonis. Sic,quoniam dug . . . . c pattcs aggrcgatl ad duas partcs combmanoms , lmgulx ad fingulas triples {untzidcoper quinti clcmcnrorum primam, P 10mm aggregatu m totius cébinarionis mplu m erit,& 11min o y‘ 5 PYRD" 42 P9 i L3 0. PC 'litctin‘quocunquc alio loco vcrificatur propofirum. ex combmanonc qucpyramis talis , p6‘1‘75a hmus , ‘confiat . i gcricris, {ClllcetquadratgIqmtngzfi; PyLCl 5' 1'1 pyr. Q- 5‘ P i duarfi pyramidfi prim dfi Cfil',(}1 {‘up‘radlétu asgtc E 5 5' + ‘ uadmm quartz: Ii dcmonftmn - 85 nationé : q; 11c dcducxtux. am cabi diét prac ad fi fit pyr. an 4: Pl gatfi tripl .&. ngulus gn- (Col. ' j‘P 9 17;. + S g n o L 1 v M. (L110 autcm pacto column: hexagona ccntralis conficiat, ficut ,cztcrz column; Iuarum fingulx pyramidum,triplum fuz pyramidis fan's demonfiramm efl in fcxagefimafcxta‘ ‘ Pnorosxrxo 82‘. Omni: colummt beptagona rum hexagon!) primi generi: 29' quadrato collateralibus atqu: triangulo praccdenti conirmrfia, can ‘grcgatificubus,qundmtus,& trlan'gl‘llus quart! loc1,pcr ux 1"1mulfacit triplum pyramldls quad‘ratg qoanrfl cflicit trip/umftm pyramidis. Excmpli gratia : columna hepTagona quinta 5; 3. Ci hexagono quinto, quadlato quinto, pchoroll.7 6? (Col. *4" 2 a 505 * 5: triangulo 4" in 13° gcncrc : hoc cft,cum 4.5. 7. 5.|o.confic1t COLhcpns‘ Col.A"4'p 5; j 1.35. quod aio triplum CIT: pyramidi hcptagonx quintm , onfiradu d aggregatum totius célainanoms tr1plucr1t,q dcm ta,pcr coroll arium 7 6.huius,c0n{ht cx tribus formi3,c-x columna hexagona quinra CCnl‘l‘L-‘Lli, & ex columna quarm Frimi generis,atquc triangulo quarto. His admngo hexagonum :16 635, partcs fuir rcliqua pars combinationis: quam'ob‘rc dug mm lxfi fiygu onxg natl s cobl Pane duos ad a: aggregati tripl fun: : ot}m n,r, omm, prlm ad fingulos. Et idco,pcr qumrl Elc'monr fuii. Et fimiliter 5 quinto ad qucmuls locfi transfcrctur dcmonfh‘atio propofiti. P n o P o s l 'r 1 o_ 8 15 . . Omnis (alumna pentagon rcntrali: cum duplo qufldmfz col. latrrdli: , (9" mm triangulo prmca'ente prémi gencm, trzplum fizrit fim pyramidix. Exempli gratia : columna 'pcnmgona ccntmlls quintav155.cum duplo quadrati quint1.{.50.A81: c6 {cilicct 145.@9d fic dcmonflroColumna hcpmgona quin quinmm primi generis,ac qmdratum quintfi,& triigulum 40 '0 9: *59P9 4s-+ quartum. Atq; 1m dcmonl‘trfidnm crir, qa rotum hoccc ng~ [15" gregatum ex columna gum cantrnli hcxagona, colnmm ma gula quarm primilgcncriSJIiigulo quartoficxagono quinro, A49 ‘ ‘ quadrato x LA94'P' 1.5 10 + |