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Show Pyr.A‘" LIBAR'I PRIMIE, PA‘R-SJI. ARITHMIE'TICORVM'A 4‘2 4; 1+5 )I‘.8 )"7 tat? Qumc'l; per, corollarium 749 huius,tali's pyramis quinta, P 465 V LPYr-Vh'r‘j" confi :1'1tur cx pyramidis feptangul'x quinta: , 8c pyramidig ttinngul-J: qulrtr confluinationc: [am of'cen.lcndfi crir,qu<‘x-d 2.0. 7: ' diétiag‘grcgatfi dié‘tre combinationis triplfi crinhoc vizlcli- "F6317 in ,2. licct'piilon pars illi us aggregati, (alias: colfina {spran- gula quinm cum hexagono prim: generis quinto, quLll‘CLKO 1 1'5)" , Pylhcpnja r45 quadrato quinto, & alio triangulo quarto , {Emu-l squiualét‘ triplo'pyramidis hcptagonx quimxfiunq; percorollarium‘ ex comliina.‘ 74'" I'mius talis , quinm pyramis 'conflituatur li'quin- centra ona héxag rPyr-*- 5fl 7- ‘ tionc duarum pyramidfi,fciliccr cx x25. Jr ra,& trifigula quarta primi generis: Ii ofic‘ndcndfi crit,quod né m'phi combinatio aggregatfi ad dié'té mox a dudum diéhi . . . . . . aggreganfcxhcct colu LPWAh 4-3 P cr1t,hoc fcxllcct 13216}on pars 1111115 no prumvgcncns hexago cum quinta is central na 10- X na hexago arium ptimgm coroll quinto, & quadrato quintofimul per is quintqzqug Ccntral n; hexago dis pyrami 66‘ triplum facit ars cft ‘vm combinationisltem columna triangulagcfi duo Ens triangulis quarti loci,Per 50i huius,triplum facit pyramidis triangulx quarta'fln rcfiduum ell combin ationis.Q13 rc cum dux panes aggrcgati, duarum partium combinationis, fihgulx lingularum m'pla: fint : 15 per primam quinti 9 Euclidis: totumc'1; aggregatum totius combinationis triplfi erit. In hoc quinto loco : & fimiliter in omni alio , quod cit Propofitum. . COROLLARIVM. .. Et pro bexagono primi generz's e9" qtmdrato collaterallilms, fubflituere pores bexagonfi rcntralem wimparcm collaterales. r Nam,per corollarium 2." 66m ,hcxagonus centralis Scimpa fimul fumpris , valent hexagonfi primi genexis & quadratfi collaterales,hoc ethin quinto loco, huius cxcmpli. Pnoposu'xo V 83". Omnis columna ofiogona, mm hexagon/z _primigenerfs,'aa quadrato collateralilzm, duploq', triz'zguli pmccdentis coniszfuz, c317" 5= ' 355' facit triplum fim pyramidix. Excmpli gratia, Columns oéhmCOL!)la 5 & cum qua 4.95. % "01A" 4." Pi gula-quinta 405. cum hexagouo Primi gtncris -tr_iangt\1i 5.duPloquc 2 cum :35 45. c6 ell, hoc quinto, X drato a l- .40- LAI9 49P9 + IO. *9 5‘) Pi 45- . :19 59 Pl + quarti, {cilicct cum zo. conficit 49:5. quod aio triplum cl . pyramidis oélqngulx quinte: , fcilicet 165. QLodfit oftendo. Columna oétangula quinta,per corollariu m 7 Gat Confli- tuitur ex duabus columnis, feymngula quinta: triangula 4‘ pmm geneus,& trlangulo qualro. H15 ago allocm he) ago nfi primi generis,& quadratum quintfi: ncc non duos man ' gulos quartos.quo faao, dcmonl'cmndum exit, quod tctum A4"? A49 P] ifiud aggregatumfcilicet ex columxm fepmngula quiutmfo‘ 1.5. lumna triangula quarm primi gcncris, triangulo quarto,hc 1.0. X xagono qumto, quadrato quintefiuplcéue trianguli quar- ti,limul triplum confummabit pyxamidis oCtangulx quin- - ll . , l quinvt0,& quadrato 4." fimul cfficit,Pcr prmcedcnté propofi r 5 ti0_n€,tripl(1 pyramidis feptangulx qulntr, qua pars ell vm, cabinatioms. 1:6 refidufi aggregatifmlicct columna triigu- la. 4" primi generis,cfiduplo trianguli quarri Per )0" lull/us, Col.{j.4" PD'; 445 l 40. V L'A49 P9 112. *. i9 P9 mplfi Elcir pyramidis trlangula: quartr: qui ell rcfidufi c6- bmarzonis. Itaquqcum duet partes aggregaridunrfi parrum Cl :9; P9 combinationis lingulx lingularum tripla' lint,ii & per primi-qninti Euclidis,cotfi uggrcgatfi rotlgcébinationis triplfx cut, in hocquinto locogSc fimzlitcr alibi. {Lid} propofitfi. COROLLARIVM. I: z 5. +9 A . £3 probexagono primigencri: z'g‘ quadrato collutemlfibns fub .. 2") fikuere pores bexagonum centralem a" imparcm collateralcs. Nun. per co'rollarium 1‘3'669 hexagonus Ccnrmlis & impar fimul finnptiflalcnt hexagonum primi generis 8c quadratfi })9 V 49 p? 11),r.8h SI Pyr S" a 5 3 ‘ 165 collateralcs, hoc emit) quinto loco, per allhmPto cxcmplo. ' Pmoposxrlo 8+", .v ti: '3ti quadl‘am-cfi diélo nggregxro & vno Ltiangulo prxccden 0 7,145 m1 l'y'r-AI‘4'P' zO. A WA A '"_‘ Siwt'columna triangulacentralis cum qzurz'rati ('7 trianguli caflate'ralifi primi generi; aggregate commit, triplum conficit C-l face pyramidis. In Ctiam fequcntium columnarfi centralium ,' A Cl ‘ ' ‘ "---‘- h K, q pcfitagona c6 codé aggregato 8; duplo trifiguli procedéu'si b. g P l -~--~- m J 5- El h l" K "-""-" f1 :1 hexagona cum [all aggrcgnto 56 triplo triiguli prmccdétls' 0 i d- {3, h KKK" quim [opt-gala Cfi iplomct aggregato SC quadruplo rrifigul 6- g 1‘: 519‘}: >--- p quincu CY "giro f‘E" iplo co prxcedétiszqui‘juc ochngula 01 pymmirflis. f- g h hlx 1\ h K ---- (1 ploftriiguli Prmccdétis céifiétn,triplf1 elhcit [use . ‘- f' lmplc h, triigu é 56:0 columns: céL-mlcs colldtcralcs'aquid Exam plum\ gro loco 5° V angu oil-or fa gonn,ip d.llcxa l‘a quadramfipfa openragonafip + FYI-5 h. triangulus COI-S-D'S-A-f-Lla, &i'p{a f. oc'hmgula. ltcm g. quadratus 8: mrfi 8c cx 155- 25- 1 ‘5colum pfarum pmlcsi ciufdgm loci, hoc cit, Collat loci: "ES- 15- ‘ Sipfo gengrc. Ité per Enligulusuciufdé gcncris prxcalétis 2) 5' 7-5' ' 5diélif is column cs ccnrral 86 ex alia partc {unto pyramidcs pl1 collatcrales : Ipfiquidcm l. triangulafipfa m.qu.ulr.xt;,ic qt feptanguln. ipfiqu n.pétagona, ipla c. hcxagona , iplh p. 395- l f- 1)"- 555- 25. 15. 40-; +5 79" 4° 5- 15- 1)" 55*16E oiangula :quibus difpofitispllédédfi clhqubcl ficut,psr 1 0. 4 o, atfi aggrcg & huiusagggcgatfi ex a g 11. triplum ell iphus Lita. y ex COLA. Pygm xx. 7 , ~ , -, ‘M' aw ""'< " 41"" ‘NW ""‘"" a ~-"'"""" |