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Show 22 ARITHMETICORVM ETBE R PRIM'VS. hinc autem aggregamm pyramicfis 1]".1,‘ ,\& pyramidis trim 1o-------A‘1 4'~-xo. angulz qutttes, funt 11111 can 131111113. : (1110;! 11c pgttct. .I‘.:1: Itcmc'lueipfe 5.11111Ir1'p11'cnns ipros 1.0. 5: 25. Facitipf'os 100.‘ anteprcmnillhm turtus , columns. (tangy; {lawn , .tq11.1.111_1 hoc aggregato pyramis quadrata 4‘ T1 & fiemonflmndum fitipfe 16. vtc'luc diflrercntia ipforum 80. 8: you. fit ipfe zo. v'tc'111e differentiaiflbrum mo. 66 1 z 5. Fr1pf'e 15. quoniam diflercntia p1‘0dtlfl01‘un1 producirur ex 111111t1'plicirein differentiam muItiplicatorumJgirur ("Herc-mi; 11116111111 cubomm 64.& 12 ;. conflal‘litex congerie trium numerorum 16. 1.0.8: 2 §.qui qu1den1 rum in hocexéploquadmtus quintus, par'tc altem longior quinms 8" quadratus 4.9 : qui cum , per 315 huius, Ezciantfimul accept: hexagonum :equiangulum quintum : fequitunvt talis hexagonus fitditfercntia 21113015; Cuborum: hoc efl,vt cubus qtmrms 64.01111 dic'to hexaqono filpcrerit, qubd pyramis triangula term vna cum A1" quar to quinto {cil-icet 61*. coniunétus conftitnat cubum quifitum mqualis eft pyramidi ttimguhe 1,?" :qszd tandem conf‘tat pct diflin. 1p fius pyr‘illS (fungal-.13} quippe (111.2 alTumpto {empet {equenti triangulo ptozrcnt {equcntem pyra1111dem .1 (LL13. 125. quod dcmonflr'andum in hoc exemplo nflhmpfimus : fimiliter 1n omnialio Cafu id idem d‘emonfiraturi: ficut Al' +9 .4 (3 I la pfl: py1‘a1nid1 pentagonx qturt e 1 54113441113 (unenlplnuiqna quitta , per 36i , :eqtulis aft pyrmmth quadmmzl quart: , 86 Pytditrianguh‘c Katrine. QL nobrc111,colu 11113 tt'langt1114." , a Y'yr.[‘..+.---pyr.'j. +3 .. 30. V1131 cum N'quarto , azqutls exit 5111111110 trump, {c111eet py: (311111115 {1" quartz, pvtmmdis trinngulx: [crux & trmngull 4i.05}c11den1{111n aft 1git'ur,qu<‘)d diftus cumulus mquahs efi pyr.A'-‘4_‘ aggregato pyranndis quadratx .4" & pyramnhs trlangulx Tyr. A" 5= 10 10 A" 49 10 4x.Auf-etatu1' VCUnun,(CihCCt tam 21131110 Cumulo,qu1m ab argumentatione, ficutin quinto,im écin quollbc: .1110 Pue- cedenti vel fequcnri 10co,fcm per conflabit propofitum . COROLLARIVM. ng N 1 A M igitur finguli cubi ab vnitatc ordinati fi111t fingulis pyramidibus hexagonis xquilaretis ab V~nimtc d1- iE}27}64 X 3 7...~ fpofitis , collateralibus :eqtl.11es ; propterca manifeftum cf}, quod cuborum diflerentix fimt pyramidum p1rd1€ht1111t differentijs fingulae fingulis mquglcs , hoc at}, 113115 hexagoms ,1, xquiangulis. Ac,(1cut ex mhum h:mgono1‘um ad vmtatcm fuccemua coacetuatione pyram‘ides prxdié‘tcc per ordinem 61---. proponitur . I COROLLARIVM. HI N c ergo rutfus manifefium eff, quéd ficut hexagoni zquilateri ab vnitate continuati,pymmides hexagonas xqui- angulas,1't:_1 & cubos ordinatim coaceruant. PRovos1-1-1o 55‘. ~ ‘Omni/s part9 altcm longéorquadmplimnu cum 1121341235071- ficit quadratum colintcralii imp/wk . Nam parte 3111312. 1011gior,per nomm 11111115, céflatex prxcedcnti quadratofimq; radice. Igiturqmdruplicarus fitcirqundmplfi talis quadrati (quod quadruplum c‘finumerus quadratus) &quad1‘uplum 4{15---100 S"'-'~zo confiruunturfita 8: cubi procreantutfiumc'luc: 1Pfi hexagon'x prrzdié‘tre radic1s,h-oc cit, duplum radicis huic quadrato dc- I 1-1 I cubotum gnomoncs ab vnitatc continuati .. PROPOSITLO 52.3.. bitqltaquc parts altcra longior quadruphcams cum vnitare, eflicit congcriem ex quadrato quodam, (111131061; (11:: radicis atque vnitate confcé‘tam. Sed,per 14i hui11s,tnlis congeries cf'c quadrams fequens: Igitur patte altem longi'or quadrupli~ cams cum vnitatc Facitquadmtum : qui CL‘Im impar figpro- . Omrw': cubm cum fequenti bexxgono .cquiangula coniunfiw conflimit cubumfequentem... Hrec propofitio c6111: ex pm;cedenti corollario . Sed & :t‘dter hic ipfam dcmonfh‘abo. Difponantur numeri fic: vnitas 4.8: 5.1tem horu1n-c1uadrati 16. (Sc 2. 5. (Sc patte 11mm longior ex 4. in 5. {16mg {c1hcct 10. I 8: 1 z->5.propte're:1 nrcc'fli: eftwt differentia ipforum 64 :35 80. Item comm cubi 64.8: 1; ;. dcinde ex 4.1a 1.0. hat 80. 8: ex 5.1m zofiat 100. @ibus dil-pofitis cfi'n 64.fit cubus quaternatij,atq; 1 z 5 .cubus quinarijpflzfdédum 6&3; 6.1.. +9 cubug 4.5 cum 5° hexagono zqmangulo coniunéhls conflat Cgbun} 5" 16.20.2; differenm 11310111. 64.. 80. 100. 125 12;.q116dfic pater: Qfi,per 9" hu'us 4.120; 16.& 20.pe1‘ 1oi huius Left diflErétia i‘piotumfo.& 2 5.atq; Pf: 4.1n111tiplicans 1131705 16. & 1.0. 1.14:1: 19105 04. 86 $0. Itcmq; ptet vnimtis additionem , eritomnino & radix eius impar. QB" fcilicet con Prat ex prazceden ti radicedupl'icata cum vni- tate,& Pet indeefl impar ipfius parte altem longioris collae tcmiis. Exempll gratis. : numerus 50. pattealtem longiot [exti loci quadrupficatus Cum vnitate Emit 121. quadratum Vudenrtrié 11in unparis. Nam 30. 1161' nonnm conf‘mt ex pmtcedmti qmdmto z 5. (cilicetquinto , 85 ex quinm mdice 5.q1mdn1plum autem ipfius z 5. cfi‘100.qund1‘ntus paris in {LXFO lerO. 0113deth vert‘mius radicis (cilicct 5.6": duX 4. plum " "*‘vixzrx-fia-‘w.v,~W . _ 12. t |