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Show us LIBER PRI-Mvs." ARITHMETICORVM ' Tales autcm hexagoni quinque per difficoagm Etfitur ex vnl- _ PROPOSITIO 4.9". ‘Omriw columna triangula 425114.111}: efl pyramidépcntagoni col- idtemlz Excmpli gratin, co'lumrm triangula quintZ ell: 7 5‘. COLA" 75 g E 7 5 PW qucm numcrum dico sire pyrmmdem pémgonam quiutam. 5‘ 55 r ‘- .ij‘ . Nam ‘per antepcremillim , columns. trianqula quinta valet Fir-El" 5‘ I U ex congmémtione 59 radicisuangj axis: & cx columnis quarti pycamldcm quadratam 5i ,8: pyramidé A'fquarmm. & per 356" tales dug pyramidcs conficiunt pyramidcm pentagonam m. ‘ loci,{cx,cum toriclcm eai‘i‘i rriigulisflcur Fuit dcmonfirédu is qucmu ad itur modab Er afiiimpti loci argumentum accom . pofitio ditpro conclu ficut : locum nlliguatum PROPOSITIO 0,quod EX'fiipll gratia,quinm column trinngula laciliccc7 §.dic 2.1 4 ~5 l.iquiamobrem Ipymmls pcmgona quinm valebit columnam A 5 . quod Fuit dcmonftrandum. Eodcmc'lue arguments Vtar pro-alio quouis loco,ficur propolirio fentit . 47". Omit columns triangula mqualz': ([11 aggrtgato duamm pym. fiziiium , fci/icct (Ilmdi‘dfx (olz'uremlir , ego triu‘rzgula: pmrcdcntis‘. XI! xquiunlct aggi‘cgnto pyramidis quarlratg quintglciliCct 55.8: iwrnmiclis triangulc 4" f. 10.1'ntclligammim quiuquc trinn: gulos quimi loci, lingulos lic ciifiinclos, Vt forniarionis (lifll. Folhilar.i.2.3.4.§.qui ism l7" (iimccnfiimut 5" colummm 1.2.. triangulam. cx llorum R'cfilio chipio vuitztrcmtcx [criio riantuort mrqun quifi .2... mo1.1 flz'c .6xpo cx quarto 1.2.5 ‘ ' Pnoposirio 50". .Oamm columna trianguln, cum duplofui triangnli, acquimlct ‘ triple pyramidzix triagulz collateralis. Exépli gratia,columm IA" quinm 75. vné. Cum duplo {ui triangulifxum 50.dico q, ‘a‘quiugler triplum A" pyramidis quiurzefig 5.Nam,pei'ante ‘prsemitlain , columm A1" quinm valet [res pyramidcs trian- "gulaszf. 5" .& ducts quarras. Apponantur vtrobiquc duo tri- angu‘lx quinti . Sc ficnt columm 5" , cum duobus triangul-is _;"_ lunul nccepta :cqualis tribus pyramidibus trianqulisll 5" ,Clualms quartis, V1151 cum duobus triangulis quiniisi l‘cd 5 guli :xb vnimtc (lifl‘m'izi, 8; yer Hm. {nugmnirs quai‘mm py‘3 A mmidcm trinngulam. 13-: X‘C‘lllqlL 'vnims, duo lfiinnri/ifircs (-5 5-PyT-U-5 ternarijfiuzituor qmtcru' ij,& quinquv quinaiijJioc cliqui- cuuqu: qitmlmti {criuim Ali vuimtc diuéoiiti: é'x' per (iifliu. 75 h a conl‘m'ucnms quinmu‘, Pyramid m qua-311mm. iraouc imumi .a‘" muns. 1mg cx 1c. z c10ml:t 11:; irimguli 1 ll'll c-x nullicui v bio-Pli-L-l fxC‘YlTS'vlrl 1 l 0. xi? ‘uln columna L:- r:loci m' licerqui quics lumpro , ipib. Vld‘ quiiidlct Cumulo pyi'autixlis qua ' .mr qui 1‘ , nc pyi‘umidi! 51 triangula: quartm :quod fiiit ofiuidmdumfiimills cl} cuiuslibetultcrius loci arguinmmtio ad vcritatau‘; propolid . PROPOSXTIO f Du - 5 55 75 la 48". Cmmk (alumna Margy/.1 aqzmlix cfl riggirqwto trfum pyramidum triangularmwfiiliat1722145 col'atcraz'm , (y damn? pmccdr‘nicolumuatriigula quinta. . .7 j. '31 tumuExcmpligratin,dico,quod . - . ~ , . trmngularuquuiumt, pyramidu mum 55 "3'5 xquiualet agnxcgato C la r Num, 1(‘1' )r.rccti<:ntcm J columna rrlnnyu L3 Siciu l310 (11.1.1133. l in x quinri 8; pyi'amidem zoA.4 quinm xquiualct pyramidn'm quadrati 5" mini- 1° Ala 43 pyna'q'f " H 20' «~ - io. mtib. fingulisfislqui eflquinta radix:& ex triiguli quarti umfa g‘ulor ti‘icn la {Excup fcxmploJinguli. Scd quinquc talin {L105} ciunt, per diff. {Ex columnas triangulas qmrtas , {cxfiuc triangulos. Igirur coluui n1 hexagom :tquiigula quinta {urgit triigulam 45. Scd per 345 huius,pyramidisquadram unlat pyramidem trinnguli quinré,& pyramidcm trinnguli 4. lg? columna A" 5" valebit pyramidé tIianguli quintfi,& duns pyrd" (93‘4". quod fuit dcméflrid fifhii iyllogifin us ficut hi6 quinto loco, im 8: vbiuis infcruict. flcut propofitio c6cludit.PRO- ' dune p‘ymmidcs .1." cum d uobus A1" quinrisfzciunt per diff duas pyramidcs 5" . Igitur columna triungula 5" cum dud‘bus rrinngulis 5" valebit [res Pymmidcs trinngulas quinras. roZJriigu/a 5‘7 5 quad fuir‘demonflmndum . (Mg: argumenmiio ad omnem ml:9 59 colJriigu/a 41.40 {alium locum accémodari Porefl, ficut propolitio concludit. triungulw: +9. 10 : . PROPOSITIO 51". "'5 0mm: cuIm/x wqum'l}: eff pyramidi bemgome mquiangu/x col- laterali. Excmpli gratin, Cubus quintus {cilicer 1 2 5. qui 86 (77120"? 7! "Idem numcrus ell: pyramis hexagoua xquinngula quinra. "7"" ( n a 'Qod liC oilendam. Cubus 59,pcr 47f :Equnlis eff aqgregato 2:33 Perl‘ 4' ' 30 "columnarum AW quinrae & 41" , necuon 36 rrianguli quarti. '5'" LTerA‘" 4" . 20 :At per 4 :3 pyramis hexagona :cqniangula quium requalis cf} \ aggregato pyramiclis pcnmgonx quinm: : pyrdis CI" quarta', & pyramidis triangular 4.". Dcmonlh‘amlum Cfi igfnoliis, i . . . - FPW-QE‘4=30 quod hmc duo priedic'h armrcyam {nut mtcr {c azqunlm : 11c Col m'ig 7mm. --‘ Db"? "1-4" 0 APP"4O cubus 'cmm per communcm animi conceptum Qqucturwt . 4o 86 pyr" hcxagonaxquiangula 5‘ loci, fiutinuic-cm :Eqmlcs. - Aufcmtur ab il'lo quidcm antyi‘ewato columm triangula j" : DO U ab hoc vcro aggregate pyr" p'cnmgona 5‘ lampndé pct ante Pmuulfim :eqimlcsdir demonflrandfi crit,quod duo refidua 1ndc.f. aggregatum columns: triangulx quartz: 8: A" quarrj; X 3 hinc I L'PJ'V'A" 5" I0 |