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Show ‘ ARITHMETICORVM 54. dodecahcclro pentagon'x: cnim pro cubo quadrant -. pro ,quo lcilicct fin: corpro Crt‘tcris triangulre ca pienda: funt 4 s. ormc conf poris ipfius bafibus 87. Pnoposrrio cfi pyramidi quaOmni: offabedrus primigeneris wqualis gratin : oélahccirus drat; centrali,fibiq'i collaterali. Exempli ,quod is idem numcrus all, quintus , primi gcncris cl}. Aio «v ‘ Nam per 7 5i 8: & pyramis qundmm ccntralis quinta. r ex cluabus Pymcitu huius,py1amis quadram quinm confi ta, {cilicet quinra & quar miclilms quadmtis primi generis , quo loquimur, oélalicdri,1a- ' 56 cr diffinitionem ipfius, dc ijfdem diélis duabus lis oé‘tahedi'us quintus componitur cx us quintus cfi pyra. hcdr oéta r lgitu bus. midi quadratis pyra alio quo vis midi quadratc; quintet: cqualis : 8c fimilitcr in loco verificntur propofitum. PROP 051-110 88. gcncris wqualis (fl aggregate ex ofiabcprimi cubus : Cmni T-CH ("PV pyramidis pm- per 36‘ THY-OS: 55- dro primi generis collaterali,»duplo¢; triangulpe . et 1 2. 5.:rquacedcntzx. Excmpli gratinzcubus quintus, {cilic la :1 5.vna cum duplo prm}. 'l lis rfloélahcdro primi generis quintoJiS 2.0. generis , {ClliCCt Cum 40. ond flc primi m quart iclis pyi'nm P" "i l pyramiI oflc-nditur,per 5 1i huius,cubus quintus gqualis ell *4 ‘F 1 is hc-' pyram 31116 .415 per x: quint ngulx mquia onm hexag di 11; 30. idc pyram ex garum aggre valct xngona quinm qquiungula 1m 11‘ locif. quarti ibus ramicl s p} duabu ex 8: a, quint ona pcnmg FYI-A" 4 m quadram & trianguln Primi generis.$cd,pcr 3 6H1uius,py L. 20. aquadr idum Pyram gate aggre alet equiu 5" mis pen mgona pyrfiraf per difli. 192 (Juintat,& trinngulw quarry. Igiuu' pyramis llcxagona qr! 55 O&all€d.;9 1.1.1111: cubus ipfi a‘qualis valcbit aancgmum ex dunlzus py 35 PVT-34‘ mmidibus quadratis quinta & quaita ,k& cx duplo pyrami7 S- 32.4% Wm $0 clis triangulx quarranCumc']; Per diflinirioncm duae preedifilo: pyramidcs quadratx céficmnt oé‘tahcdrum primi gene- ['15 quinrfitiam 8: ralis 03.1116de quintus cum duplo Pvra midis rriangulz quarm: fumptus, adxquabit culmm quin1um: quéd crat demon (hand 11111.8( psi-indc ficutin quintO: 11a in quouis alio loco conflabit propofitum. .. .PROPOSITIO 89.1; Omim zmpar m quads‘atumfcmndxflmciei , hoc cfl, [entralemfibz tollatemlcm multiplicatmmroducitgnomonem collare- ralcm m ordine gnomomxm ab 'L‘nit:tc c6témmtorum, an]; qua- drato: ex_quadram prim}: infe dkfi‘is 36mm: per aa'dwéonem fuscefiunm LI‘BRI PRIMI, PARS‘I‘L SS , qua: «:mm‘m [uteri/751mm com‘fitucntiuw. Prxmillh vnitate r ell 3 fecumius numcri {pccicm rcéprxfcxitat {ccundus impa 5.13310- fit 1 autcm quadrarus Centralis ail 5.1:): 110mm dufio dratfi {C111 6.qua 1 ficit tc vnita cum qui fecundus quippe Tia [5:111:13 [0:13 mo tcm notabo pri cet quaternarij. uod fic ollzcndozpoft vnim ab vniquc uumcros mum duos in 1163, in quatuor, in quin Hoc patio duo pri rate per duplam proportionem notatos. Iimul couficiunt huius m minumcri , fcilicct 1.2.. per fexm utem {cqucntis cmia Extr 3. licct i,fci imparcm fecundiloc -t qumlmti, {cilia imi ordinis {cilicct 1.2.4.fi1nt 1. 8c 4. prox centralis {cants quadr fill uiuS Gsih quorum c011gcries,per quod aggrc cf'c, m cundi loci,{cilicet 5:113un dcmonl'cmndu ex 1. 854.. m cric cong in m catu gatum ex vno,& 2.. multipli m ipfo~ rétia diflc cl'c hoc , loci di fecun onem producit gnom vnitaus ri1n 1n,p toru rum 1.8: 16. qui {um quadrati qmdm o,fciliccr 1 snappe- tis,& alter quaternarij.TaliS cnim gn01n m quadratu quadrati fecundi : fitus vnimti, conflituit 16. ordinibus, duo primi, Nam in hifcc quatuor numcrorum ntifi,fcilicct 1. z. 4. fcilicct 1.2.. fun: difl'crentice trium feque ucntium,fC1liorreq quatu : 66 rurfus hi 11:: fun: differential entize quinquc cct 1.2.4.85 8.8a adhuc hi quatuor {unt differ idcm in nu- doqu quan 16. rum, fciliccr 1.2. 4. 8. poilremo entix {um continue meris continue proportionalibus dificr iam vnitates,fic11t fint : proportionalcs, & Prima: differential cfl aurcm proccf- ch ri. numc m primi ordinum finguloru & vno z.primi ordinis {us demonllrationis: aggrcgatum cx 1.86 Lin tcrtio ordinc. ricm cégc Cluéhlm in Vniratcm, facit ordlnis duékum in 4.1310: Item aggregatum ex 1.86 z.primi aggrega- 12. Igitur talc ducit 4.8: 8.in tcttio ordinqhoc CH, ericm 6x 1.864.. l10C cong in €tum 5.du all; tum ex I.& z.hoc {cilicet ‘Pro tertia la co. cumulum 1. z. 4. 8. Vcn‘im mlis cumulus faci: 4. S. 16. 6c periudc is , fcilicct ipforfi 1. 1.. 2.; quaruor numcrorum, cflt, in 5. produce: cumulum differentia- rfi quarri ordin fcilicct 1. 8c 16. hoc ell, facit diEc-rentiam cxtremorum , um.QLod filit demo 11v 15.gnomonem fecundi loci prxdié‘t 5. duplus s impar, {Cilicct firandum. Item dico quod tertiu l.15.producct tcrrifi gnoalcm. centr m ratu in tertium quad unfius .f.cum 1 6. coni moncm ex Pracdiéltis , {cilicct 6 5.qui ell, Excit in- atus facit quadratfi noucnarij, qui tertius qmdr .in ft: diéto genirum. tercio ui 81. quadratum cx quadrato @d haud obfcuremec difficilius oficndam Hoc proccllh. Polk Z 4 I 4,. 6. 9 3. 12.118. :7 6.54.31. 16. 24.; .__.__---- 5 15 w |