OCR Text |
Show 36 . ARITHMETICORVM Pnoposx'rx o 74.". Omnis pyramit cEtralis con/{at ex radius tollatemli tanquam axe , (r ex tot pyramidibus triangulis primi generix pmcedenti- LIBRI PRIMI, PAR; 11. 4 lemmiqfe: 11‘ Gcmm. , xlxl.41|1llly :7 , ,PjrainidesCentrdcx. lIEIllfllilr‘ ill‘4l‘l5l63m7l lil617isl'9lm 'WE'I‘.14|18}.11] '15f19[2;127[31|55 +tz°>l»30_i40!.50l 'ulsfli‘jjl 7519351 ls+I4+ls+164l7¢i§§ l 65! Ssl'w's l-Izs_lx45l165 quadruplum, in pcntagona quincup3um , in hexagona {ex- 6|56_{91['126||6x| |Ill [.146 |le lzIG {2.51 |286 cnplum , ficut in 59." fafium c1}. In hepmgona feptuplum. In oélagona oauplum. Atquc in ex diffin. conflabit , ficut VTI-gn-Efiflfiil 1175 lzsi NIL37 15+; U99 I455 [TE-{(Eijo4i188 [572. | |i60|344i428 $512. 159616"o 9 llmégjjsgsls IV |569 169 I609 I729 {349 I969 5m Iochuotfunt latera pyramidis centralis. Quad 39‘ .huius s dc pyramids ccntrali hcxagona dcxnonflralxit : hzc prqfcn dc omni Pyramidc centrali concludinfit dcmonfiratio vtro. biquc CR cadchtaquc in omni pyramidc {umcnda eff radix collateralis : fed in pyramidc A" fumcndum cfl: rriplum ta pyramid-is triangulzr primi generis przcedcntis: in quadra in 39.3 Propofitum. Excmpli gratin, pyramis quadrata. ccn~ tralis quinti loci CR 8 5.qui numcrus conf'cat cx radice quirk tafcilicct 5.8: quuadruplo pyramidis A1" primi gcncris, {cilicct cx 80.8: fimilitcr in cam-is locis. COROLLARIVM. Manifeflum cfi igitur , quéd ficut Pyramis centralis quadrata fupra triangulum pyramidcm collateralcmtita & pen Iagona {11pm quadmtam : nec non hexagona fupra pentagonam, 236 hcptagona {upcr hexagonam : & oaogona filpcr hepmgonam {cmpcr addidit prmcedcntcm pyrami-- dcm triangulam primi generis . Sicut vidclicct bafis ccn- rralis {'upra bafim collatcmlcm latcrum vnitarc pauciorum, addit przccdcntcm primigcncris triégulum. Pnorosx-rxo 75‘. Omni: item pyrami: centrali: confiat ex rat pyramidibm primi generix; ex quot bafilms primi generis eius;bnfi5 confiarc ofié' fa efl, (y ciufdcm nominix atquc loci. Exempligmria : pyramis hexagona centralis quinta,fcilicct 125.conflat cx quinti pyamidé hcxagona Primi gcncrisfcilicct 9 5.66 at 4‘ pv ramidc quadrata primi gcncris, {cilicct 3c.qu0niam fcilicct' bafis he xngona cétralis quin ta,fci1icct 61.confiat cx hexagnno quinto,fcilicct 45.86 ex quadrato quarto primi generisflcilicctla VI: in 70 ‘.oficnfi1m fuit 2 quod quidcm dcfixonfiratum cfl: in 4.0" huius , quoad hexagonam pyramldcm : & fimilitcr hic gcncralitcr dc omni ccmrali pyramidc oficndetur. Scd in horum cxemplum cxponemus in tabclla Pyramidcs vtquuc, mm {cilicet primi gc‘ncris , quém ccmralis, in quibus propofitionum vcritas apparct. Pyramidcs _1-c_)-,-lzzg|38;]550 {71; I [$051670lS;g|tooo['i1m]1;;o "Wt A191 at? low *"I 1 A" 1 a": ION" Mew-105'}V Pxonosrrno 67". s collaterali , tan-A " \ 0mm colummz centralix wagmcntatur ex radio fuig', triangua- _ nx. colum 'quam xxe, z'y' ex congerie pmcedemti: triangu-lx ' m. plica multi latcri Ii 22: prime genera in numerum dc pfis izhxc cérml , Qggd 46‘ huius,oficndit dc columm hexagona efl'. tiohic 8c ibi cadé omxfi centrali column: toponit; 8! dcmonflra is: {ed it} columns. ‘ teral colla radix cfi da (Smé mg; in omni columm uc A" in Prfimo‘ ' fuié mnar triangula,c6;crics prmccdétis triégulx colu rara in qufgtcrquad na colfi mln ariu tcrn generamuliiplicrmda cfiin gon: in {cna-" hexa , per narium:pro columm pémgom in quimrium fonarium.‘ inroé gonl oélo pct , ium rium , per hccrtagorm in feptcnnr pli gm- Excm m. ofitu prop 46. in flaw bit, confh ‘Arquc in ex i‘ffin. loci,cfi 2. 2. pin Conflarur cx raj tia: column; ce‘nrrali quadmm quin-ri congcnc prxcedcmis triangular co‘l‘umvl ' ' dice quinta, fcilicct 5 6c ex quadruplicata',' hbc 'nx fuifiue trianguli in primp genera , fcilicct 50.is columnis. > ,& in cgtcr cfi , cx 2.00.8: fimilitcr in cx'tcris locis ROLLARIVM. CO ‘lis quadrata {u- Vn‘dc manifcfi‘um cf}, quiyd ficut columm ccmsa & pentagona {11* teraléfim ‘Pr'atriangdlam ccntrulcm columnam colla pcnmgon:up,& thmf'o fupra gom hexa ac non Ncc : ramm quad pm ‘?"‘"" icmgcr‘ ad 1: h?"§ r fupe ona oaog mi. {upra hex‘agonam , 8c angulo- BURN gcncuovm cum praecedcnrcm columnam triangulam infcxcbar. corxollar'idm rial-lo: idem dc Pyramidibus ant: przmilfie 5 P n o I 0'V 1 |