OCR Text |
Show 2.8 PROPOSITIO 65‘. Omniy cubm cum quadratic e3" triangulo collateralibm' com H ic paum defimt. _ ~ { If ' I l- xmu Ryandum cm: quodl iunfim,triplum efi‘icit fuce quadmm pyramidl'o‘. ExemP1? graf(‘75.60[.A" 5‘ . + tia: quinrus cubus ef‘t : 2. 5. (1111111115 quadratus 25. qumtus trinngulus 1 5. Aio,qu<‘)d horum aggregatum triplum cit ad , A" a cub" 5' 12,; - aggregatum prxdiétum xquiualebit duas columnas trlani. L15. A9. 5'. ‘1' 9 AS L57 gulas, {cilicét quinmm & quarmm , & qmtuor fimul trianL gulos fcilicét duos quintos & duos quartos. Igitur demom {‘tmndum crinquéd congcrks talium dun-um columnarum 9 & talium quazuor trinngulorum , CR tripla ad pyramidclfi a" "5 ' quadratam quinmm. Scd cum per 34.5 huius,pyrnmis qua} (monn'a. ‘ . . 25 rPyr.D.; pymmis Pcntagorfa qulnra? P" 56; 2 conflat Fx comb1_natio- ne duarum pyramxdum, {Clllcet quadl‘nras gumt; <3: tmngu1‘2 qugutqfirgolcfi dcmgnfiyanfiumquod dxaum aggrsggqun triangulasfiquintam , & quarmm & triangulum quartum. Item per vndecimam huius , quadratus quintus azquiuale}: duos rriangulosfciliccr quintum & quartum. @gmobreni 25 ) I! _+ ? (111073113 {manguhs trlangula quartagrlangulo $1!"th quams , fimul mplum CR pyramldxs pentagona: qumrm. Scd 7,," O "5% ‘1' ~ Pyramidem quadratam qt!inram,fc1licct 5 i.qubd fic pater: 40'60" LIo. A . 4.9. ---' Cubus quintus per 4.13 huius , mquiualct columnas ducts [19.5'J-xo. A". 4" .0‘59 gg V ‘ 19 PRIMV'S. LIBER ‘ ARITHME‘TIC'ORVM- ILPyr.Ah.:_ 7- zo-* CR EUPIUFU hPlF combmauogl- quad fiC {MINA/113 pars "1115‘ ‘ aggrcgfifl , (Ohm! cubus qumtus , cum quadl‘flfo' qumtg) 5‘trlgngulo qumto fimu? Pct prqccdcntcm, cgquahs CH: mph) qumt; quadrat; pyramxdls , : 35.p)'r.A_‘"‘53 ,+ dram quinta confict ex combimtione dmrum pyramidum PJ‘V-CH' 5 5; triangularum quimx «Sc quartxziam ofiendédum crit, qubd Lzo.p}'r.;\.‘" 4‘ _ congeries prrdfim duarum columnarum 85 quamor triangulon11n,cfi tripla ad cmnbimtioncm diélam duarum pyra- ~ midum.E tconfht fic. @0d per 50" huius columna triani gula quinm Cum duobus triangulis quintis (imul conficiunt ‘ '1‘ V H2c multa dcfmtt , qua: non fimt in exemplari manufcripto. ' triplum pyramidis triangulse quince : & pcr candcm 50"i columns. triangula quarra cum duobus triangulis quarti3 fimul accepm, triplum facir pyramidis triangulaa quartz: .. Ergo, pct primnm quinti Elementorum Euclidis , rota conigcrics dunrum columnarum 8v: quatuor triangulomm,tripla crit ad totam combinationsm duarum pymmidum : quan- _...._‘_. ._.__;.._._. doquidcm panes fingulx parribus fingulis tripla: (um. 86 , Per-13' I7 5 to]. O .53 ' hoc crat dcmonfimndum£t fimiliter pro cubis caztcrorum locorum Confiabit propofitum . ' 7' Pnoposn'xo 64‘. , 0mm} coJMmm pentagorm cum duplo quadrati collateralt} 1 2 5.6145". 59.4" fimu-l fizmlpmgriplum "dale/r [$1.12 pyramidiy pentagonae. Exegxph: .. P . A . r 4.0.(0.AL‘ 2* Lgxqtlafo‘ Llllamll‘pcnmgonafriupnm 175 mm duplo qu; ‘arl ( Wm" 2,. 0c L tcum 5c. wt 27. ;. quod tnplum cfhpfius L1 o.gl'_4_9.._>§< Pymmidis pcntagonx quinrt; 7 5.qn0d oftcndimr fic.Colfiné. Pgnmgom quinm :t'quéfis 6?: cube quinto per 43" columnc; trmngulx quarra: 8'5 triangnlo quarto limnl acceptiszquibus appono vnum qlliadmtum qumtum:l& pro 3.1mm quadratq qxfmto, RPPOHO L105 umngulos qumtum On. unILUlD, Lllll pL‘f per 575 P" 37. 9, fcilicct penra1;. KNEW oficnden- py.bex.5 gong quimc dum eff, qubd {upra difium aggrcgamm CH triplum huius cdmbinatiOnis : quod 'conftabit. 1C. Vna par51111u5?gg1r€gall9 , Ci ice: 7,3,0! , |