| OCR Text |
Show 56 ‘ARITHMETICORVM. Poll: vnitatem notabo radiccs proximas fecundi & rem" 10 57‘ LIB‘RIiPRIMI, PARS II. Eodem penitus proccllu demonf'c‘rabimus,q; quartus im, c1 , {Cilloct z. & 5.qui,Pet fexmm huius, coniumfti faciimt temum impai‘emzmoxduco z. in (c, 8: in 5. ncc non in 931.117. duéhts in quadratfi cétralem quartfi 2 5.6flicim 7 5. (c, élc {161114. 6. 9. continue proportionales in rationéi {0111 1.8.: 5. 8: Rurfum , cx quatuor multiplicationibusP {Cilicctcx duéhi 2.111 4. &in 6. & ex du&113.in 6 & in e ' fiant quatuor numcri fimilitcr proportionalcs 8.12.. 18. 1;. E: ndhuc fix quinque multiplicationibus , {cilicct ex 2. i ingulos diolos 4.8.12. 18. 2.7. & ex 3. in 27. fiantqtiinr: 9 } 69 tfi cétralé.l.4l. ptoducit 369. gnomoné (1.1mm; Cu 2 56. 5 infiniti‘i. in lic & : quadrati 5i ell CGI'eituit 61. 5. q quadrants wv.._.____.__-- quc nuineri ‘16. 14. 56. 5-4.. 81. in cadcm mtione continu a pfgfloar:1:)n:.cs.1Atq1w his con{-fi'tutisulcmonllrandum crit (11' ‘ DaleamJl ex 2. 8: 3. lClllCef 5.:crtius \mpnr multipgigntum in aggregatum ex 4.8: 9. hoc CE, in 1 1. qu,od per Enigflltgrrgg(julaiji‘arus ccntralismroduoit differentiain ip [em'um N. ' :wlocjsi igno'moncm ex hls,qualcs diximus mun ex} 1;} kirzi {CPUIDI Elcmcnrorum Euclid. quome-i "kingfisllilllglum z.d3. prilni ordinis, nafbniitiir nu- mmcominuug ium 01 11111111,1dc11co finguli ordines {at tiplicantc i"diam-13110901uoncxn $1"an 84 quoninm ex mul(mm... Pmdu‘gigmm-n' [inulripucntomm,producitur dif- {dhcct z. 3‘ 3. {milling-111‘c11c07du0 numci‘i primi ordims, nis,[};1'1icctip{omm l E11151; mung-(1111111 fequentis ordi< 'Pra quarto 7950. I 3 - 49.12.. 16 27.36. 48.:64 81.108.144.192.256 rentie {01111;} numero 8_ "i. 13rumz q411:1 ~ 9i&11111 NIP?" 1111,1151, qui 11{f§f icqurlur hl' "CS, film follicet ipdiffequin uen ‘.‘ 7. ‘cc ecus 1 quinque {um dlflrcntix quog 11111610111111iequcntium, {Cilicer16.24.;6.54.-81« ipforurfnvr6mg]ulus 1pfomm 8. 12.. 18. 27. fit difcrentia . \ 1 . , 1..ext-remorum. Vndc demonlh'andum erit giggdiefiinulnphcauone aggl'egatiipforum z. 3.1n congc: cctimp 0111111 4.. 86 9. hoc cf} ex duétu 32111 1;. terri}, {cilipans in retrium quadratum centralcm producirut frillmufilyg 11;?1un18. 12.. 13. 2.7.hoc modo. (Luoni' am ex :- 111:1; 2m; 3.31:1:fif3237-‘Per z 5" feprinxi Euclidis(quoforum 2.. 5.51 aoore ~atum Ii Pffopffi‘ea 6X 4""! aggffg flmm 1P di Element fins, 8"):oruxb; 3.1." , 8? er c‘dp fifz .1 cm omm‘ muonem 8JLPCY ,lqnon Pnlzmm 1a ex 1{CFLm‘ . in 9. [0mm 1. 3. mail-e 7. programs cx 9.1m aggncgatum 1p- Prim-13f. .d' ht, 'gatu‘m 11.) 9111111 18.27.Rur{11m ergo CX 5.1.11 (:Cun 1 Euclldis [cquitur,vr ex aggregate 1pforum z. mercjsgreégamm ipf'orum» 4. 9. 5-31 cumulus quaruor mm m . 11.18. 27. (goal fiut dcmonflrandum. 1, 16. .. gnomoné quartfi, qui cum quldrato noucnarij iunétusl. 6+. 80. 10.. cum 81. céponit quadmtfi ex 16.1Eilicct 2 :6. IEE limilitcr 256.520. 400. 5001' offendemus, q) quintus imparf.9.du&us in quintfi quadm ‘1l3 [5 17 l 9'111 | I; [Isl I7(|19leparcs 114. I9[16 |25 [56 I49[64.[‘81lloongdi‘atiprimi. II; [13125 I41|61 | 85 [113l1451181l @gdrati ccntmlcs. 1l15165l175l369l67111IOSI1695|2465I5439l Gnomonés, .Pnoposxrio 90. Unufquifque diflorumgnomonum aaqualis efz' aggregato trii gulorum centralium ab vnétate per ordinemfumptort4m,(y~ tot quot fun: vnimtes impari: coltxtcmlis. Exempli gratiaJ 5.gno mo poll vnimtem mqualis ell: aggrcgato trium trinngu orfx ccntmliumf.1.4_.1o.quoniam ternarius cf'cimpar collate-mlis ipfius gnomonis fecundi.At 6 5. gnomo {equens aequalis ell aggregate quinquc triangulorum , fcilicct 1.4.10.1 6.3 I. quoniamf. 5. all impar collateralis dic‘lo gnomoni. 8c". tic dcinceps in infinitumlit quoniam tria. talia. triangula , pct diflinitioncm componunt pyramidcm triangulam cmtralé terti) loci, 8c quinquc talia ptcediéfa trinngula confiituunc impyramidcm triangulam quinta loci, & {1c deinccps per Pares locos in infinitfi : proprcrea propofitio pfis hoc dicit. COROLLARIVM. Quod tales gnomoncs fun: pyramides triangnlx cm- protralcs per imparts iocos difpofita: in infinirum. Cuius 65.3110- polirion'is &: corollarij demonllmrio hxc ell. Aio,qy Q1191! mo terrij loci,cik pyramis triangula ccnimlis quinm. ,1. triangulum radixllquinmin 31. in g. Ducntur pater. flc Producfitur quinrx,& ipfius quintfi qni bafis cl} pyrmnidis quimi '1; 5.colfina.f.triigula quinta huic addo qua drzrtum conflicur quintfi.{.15.3c primx {peciei.f.z5. & triangulum 1 9 5.q3. pcr 7 9i huius,triplfi ell: pyramidis tux quintxpro‘ dué‘tfi 3131 ex y. in 3 1.cum dic'kis quadrato & triigulo,lum.f. 59. conl'mt Ptu,cll xqualc produflco ex 5.111 59.quoni:1m ,R ex 51. 5. & 3. hoccfi, triangulo quinto : imparc tcrtio ,fihoc imparcm 1.116111 in radio: mli 'mdicc tcnia: 8: ex C a Eodnu v... ‘"-;§M«@W ,fi W |
