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Show 1'6 ARITHMETICORVM . pyramidis quinta , per 3‘g5‘.corl1‘ftetiex pyramid-c Ugangula lam -:'qult{‘u' q11i11t.1,& cx (lUPlO pyramldls rmgu-x quaint. vt pyramiiis hexagon: quln‘ra cgnf‘tct cx Evramlucilxlfngua cum quinm,&cx ra'iplo pyramld‘n mangulg- 4 a.Et hm: 1tlr, ramide D" quinm , 8: ex yymmxdc trmngula quarta' '. '& per ytaxn1d1 Pmprrt‘n‘aillhm pyramis llcxagona 5" fupcmddatp ncs in cam-is locis, verifimtur propofirum. fetagona: 5" pyrmnixltm triangulnm qugrtam :non mmus ex gamn? sggrg mleat th eggun (11‘1" gona hcxa pys" r Vt quitu 41". trium pynzmidmnfcélicct pentagom 501111117711", ac triangula: (9' ficut plecns Propohtio concludlt . l'nov 05111 0. quadram pmcca'mtium;. Excmpli gmtia,dico qubd pyramis hexagnna :rquianguln quinti locif. ( z j. :equiualer rres pyra- 39". (uplo. Hmc propofirio facilimc Idc'm‘opflmt‘ur ea 1p'fius. l 1, pyramidis hexagonx,&hcx§gom ful dlfllrlmgpllbus. Excpl Pcl' graria, pyt‘s hexagona xqmangula 51100, {FLICCLIZ} ftxus 3. 13, I, l 9. difl‘. confiat ex vmrate & cx quatugr Icquggtflbus 1hexag 6. 36.13 7_ :cquianglxlis. 'mlgs autcm hexagonl pier d1 1i5111gL11§0F an: L10_60_ 1.6 1, ex fingulls vmmnbus &cx przECCtlcntl'buS A finguhs excu: plicatls, . Vcrfim linguli rules A" ( qm lunt quatuqr ab vnl- midcs.{.pcnmgmmm quinmm 7 5 . vni cum triangula quarta, fcilicct zo.&' quadram quarta, fcilicct so . Nam per Pl‘xCC' dentcm,pyramis hexagona mquiangula quinta tequiualer duas pyralnidcsfiilicct hexagonam tctragonicam collateralcm 9 y. 6.: quadramm quarmm , l‘cilicct 30. Par 37"1 autcm propell- tioncm huius , hexagon; [crmgonica qulnm :cquiualct duas, {cilicct pcnmgonam quinmm & triangulam quartam pyramidcs, {cilicct 7 5.85 2.0. Igirur hexagona mquiangula quinm xquiualcbit trcs , {cilicct pcnragomm quinmm , trmngulam I 25‘ tatc,con(lruunt, Per dit'fipymmidcm mangulw} ‘lfl . 8: per- quztrmm,& quadramm quarmm , llcut fuir dcmonfimndum: indc fexcuplicati conl‘truun: fcxcuplum pyrgmldxs maxlgula: quartz . Igitur diéla pyramis llcxagona 53l copflablF ex & codcm {ylloa'ifino in omni cafu confhbit frmpcr pro v politum . Pnoposn'xo 42.". 0mm} colummz quadrata, fine cubm, componitur ex duabm quinquc vnimtibus, 5-1 fcilicct radlcc, 8: ex pyraxmfhi [mu- gulm quanta: {excuplo 1. cflquc mlxs radxx quah 2x15 131211; pyramidis conflans ex vnimte verticali1ac quamor vmtat'lbus centralibus hexagonorum pyramidem ipfam integrantlum. Er fimilitcr per quotcunquc pyramids, ficutpro 5" fifC-hlm Gilt, ratiocinarx Pollhmus ad dcmonflrationcm propoll r1. Pnoposx'no. 4:."_ Cmmk pyramis beiz‘agmm mqm‘angula conflrsfitur cx aggregate pyramidzk hexagmm tetmgonim collatemlm a" pm we. en1. pROPOSlTl o Omnv'lv pyramia‘ bexagoncz aquiangula 42111441115 cfi aggregate }2y 1"" quadmta quiuga, dupnq; {nagulz Pytamldxs qualtx: 0mm'»: pyramia hexagom azqufzxngnla. conflat ex radicgcollatcrali,tanqua‘m axe, (5" ex pyra'mzdzs trmnguloe proecedemlsfex- 6 vvmmuxcnnfliruunt pyramidcm quadmtam quarmm . Igitur fymm 13 hexngona :cquiangula quinm c6fl.1bitur ex pyramide chngom tetragonica qumm, & ex pyramidc quadram quar[mquod emf (lemonfimndum. Similitctper 527‘ 86 diflinitio- ex py. ; er anrcprxmilfim pymmxs pcpmgqna 5 conflctur 1‘ 6, 1,7, L Y B E R P R I M V S. hexagonis tctmgonicis conf‘truunt,pcr dlffi. pyramidem hexao 80mm rcrx'agonimm quintam : & difl‘i quatuor quadmri ab columnix triangultlt, fi'ilicct collarem/i (f pmcedcnti , (y ex pmcedcnritrimgu/o. Excmpli caulk, dice, quéd cubus quintus {cilicct 125. componirur cx duabus columnis triangulis, {cilicer quinm 7 5.8: qmrcaflcilicct 40. 84 ex triangulo quarto, {Cilia-r IO. NM'ILPCI'difl‘. cubus r1115 conficiturex quinquc quadratis quiuris : tales autcm qmdmti , per vndccimam huius , con (hm: cx quinquc triangulis quintis & cx totidcm x-I If: pymmidix quaclram. Excmpligraria: Pvr‘axms hexagona quarn's. Vcn‘xm quinquc trianguli quinti, pct difl'. faciunr co- 6-7 mluinngula 5‘ loci fict .cx-congcric pyramychs hgxagonc rt;- lumnam triangulam quinmm : quinquc autcm trianguli qunrri , Elciunt columrmm triangulam quarmm & vnum [ri- 4. 15-1 9 9. 2 8-3 7 16.4§---61 _ " 30'95 "'5 tragonicx 5x, 86 pymmulls [1‘x quartx..Na Pct dlflilpvramls hcxn gem mquiangula 5" confiat ex vnltatc 6c cx .4, {cqpfn- tibus hexagonis mquinugulis. Tales autem .1." hexagom 11ngllli,pcr 32-? huius propofitioncm , conflat ex {mguls hexagonis tetragonicis collateralibus , 86 ex fingulxs quatpqr Prmccdentibus quadra tis. Vcn‘un vnitas cum quamor clxc'hs hexagoms ' angulum quartum. Igitur cubus allhmprus quinti loci acquiualcbit aggregamm duatum Pyramidum rriangularum quin- tz 8c quartg , & trianguli quarri: ficurdemonfh'andum filit. E: finn'li argumcnto, quod pro quinto loco , pro quocunquc allo Prose-dam ad confimmndum Propofitum . P n 0. lo-xo.t;-25 IO. 1 y-z; 10.15-15 10.15-2)‘ 10.15wz; 10. 4o. 75~-xz |