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Show co produé‘tum ipfum ex 5. in 59. {cilicet 195. triplum erit gnomonis 65. flair autcm 8; tripium pyramidis triangulx quinrx : Igitur gnomo tertius & Pyramis ccntmlis quin- ta filnt eequalcs. (god crat demonftrandum. Sed i‘cfiat oftendcre , qubd triangulus imparis loci cum ipfo impure 86 cum radicc collaterali ad imparem faciunt fimul triplum +6.5. confidcrctur continuatorum crcmcnta , qua: crefcunr pct 85. tcrnarium , iam alternatorum cmucnta per duodenarium +109156. augebimtur.Ar in {Erie imparium quis nefcir crcmcnrfi ficri per binarium , &in {erie radlcum'per vnitatem B demq; in +166. {cric pofircmn quadratarum ccntralium , quoninm finguli confiant ex binis Proximis quadraris prim-x fpscici , quo- rum diffcrcntise Crefcunt per binarium , quia videlica con- flntur per additionem cominunm imparium,ideo diffEren- quadrati ccntraiis , qui collateralis cfiipfi radici. Hoc cit rias fortiuntur per qmtcrnarium crcfccn tcs.Sic nihii rcfiat, affumpto exemplo , quod ; I. cum 5. 6c ;. Exciunt triplum ipfius 1;. quod (ic oficndetur: Difponantur quatuor {cries numerorum , {ingulx ab vnitatcinitium capic‘ntes: in quarum prima finr trianguli centraiis locorum imparium , {ciliccr l. to. 3 r. 64. 6c in ii-cunda [. 3. 5. 7. & cxrcri impares per ordinem. In tertia radicss naturaiis progreflhs I. z. 3.4. &c. In poftrcma I. 5. 1;. 25. & cxtcriquadra- quod ad dcmonftandum propofitum facict. ti centralis. In quibus id quod voiumus facile conflabit. Nam cum in exordio trcs vnimtcs tint 1 J10 [51 '64. ]109[l66[255[316]409 [5l4iTri5g.C€rrales locoi‘fiigpa-EE PR.0P05i'rio,9I. "fies quadrdti centrale; cum quamor 'vnitatibm fumpti, fun: mun/es qlmtuor trianguli: centralibu; cum tribm 'um'mtz'bm fimul acceptix m eodem loco. Nam triangulus centralis confint cx vnimte &t1‘ibi1$ triangnlis primg {Pecici pricedentis loci. (mgdmrus verc‘) centrdiis conflnt ex quamor trimguiis primc; {pccici prazccdr'nris Ioci,& ex vnimtc. Q1311} ob rem , quatuor trianguli centralcs conflabunr ex li.t1‘L‘:ngu lis primx,& ex quaruor vnitatibus. Tics vcréquadmti can. x] 31 5|7l9l11[13 l15| 175119[Imparcs llllil415l6l7|31 9 110 lRadiccs. 1| 5|13Iz5|41|6x [85 |iI5|i45 [181]%adrari ccnrmles. traiis COnflnbunt ex 1 2..ti'iangulis primes, 86 ex tribus vnita tibus. Igirur, Ii apponantur hic quatuor, iliic trcs vnitatcs, éonflabitveritas proPofiti. PROPOSITIO 92. triplum quartzer trium fubfequérium tres ad primas vm'.» rates augumenta fuper ipfas vnitares faciant duodena-- Tre: pyramides qzzadmm centrdlex'mm q/mtiwr aribusfitm: pmftmt wqualcs quatuor pyramidibus "2.17214qu centralibm cu rium, qul numerus triplus 6ft ad augumcnrum, quo in tribus axibu: in eoa'cm loco finm/acceptis. Haec conihr cx prmcedcnti : quoniam pyramidcs coniiant ex balibm , illx quzidi‘aris, hm triangulis, 81 :1er conihmt cx rotidcm vmm- Imus Iinqulx. uafc cfnn ex .iggrcgatione :L'qualium coaccmcnnfi‘xquaiia , confiat propofitnm. '17:: quarta {erie {equens vnicatem exccdir ipfam vnitatcm ; iam idco ncccfl‘c crir , vt aggregatum trium corollariumflkilicct 16. 3. 2.. [it ti‘iplum ad hfic fequentemficilicct 5.1mm quonmm augumcnta 'trium in tertio loco (cquentium {upra trcs przccdentcs..conflant 2.4. E: augumcnmm rcliqux in qnnrm I‘ W M menta,facillimum efl: oftendcrc. In trianguiis quidcm ii M \J Pct triplum tertij gundmti ccntmlium , qui nunc eff. 13. "BC gnomo 6 5. fir ex 5. in ipfilm unper Prcgmiflhmlam iccii SDJUdLUI i301 lus , (cilicet quintus csncraiis cum ipib quinario (Sc remario, quoniam quinarius ‘cfi tertius impar, conficiunt fem~ 19. («ww wuwv w .A v. n o crefccntia {cmpcr dcmonftmbimus. (bod dcmum in di- +51. 46. flis quatuor {cricbus numeri {Ecuudum talia proccdant (re '11?de spol u; WV xgq augment: 'iiic pcr duodenarium , hic pct quaternaiium mm duéto ex 5.in 3 1.cum quad-taro quinarij «Sc rriangulo quinto , hoc eflz, cum 2.5. 8: cum 15. Ht, quoniam 31. triangu- --0¢\n~ 4. gi‘cgatum trium iliorum , (Cilicet ; 1.5.3. em 8: triplum di- éti rellqui, fciiicct 1;. Et fic deincc‘ps in infinitum, proprer +10. NN-uu-g xquale fit produéizo ex 5. in 5 Lin 5. & in 3. hoc d} , pro. 4) progr'cflionis Facikconikatfllgo fit,vt Pruniuc‘tfi ex.5.in 39. LIBRI PRIMI, PARS II. 59 quarts. {cric fupra. fimm prxccdenrcm CH 8. Idcirco & ag- +1. WI» Q\l »ARITHMET'ICO'RVM‘ '[UOIL‘HUIJUOD mV 3:5 CI 58" cf} ex 5'. in 5. fit diétustriangui'us quintus v1 5. ( vrtcx reguia |
