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Show LIBER {cilicct Squippe qui per tcrtiam huius,eft duplum prxdiCtG.' 4." radius. Sic & pro alijs locis conl‘mt propofitum. PR 09051 r10 603 . 0mm} quadratm imparzk cxccdit pmcedcntif impart} qua- 24. dratum in quadruple colkztcralz): park. difltrcntid. Excmpli gratiazqua~ drari qmrti imparis ,1149 . cxcalit quadmrum rertij 1m - 24 25 E 4 9 E 1 48 par-is, fcilicct 15 . in quadruple quarti paris 6.hoccfi in 24. Nam per 535 praecedcntcm 4.9. conftat ex pgrte altcm lon25.‘ I giori quarto quadruplicate , 8: vnitare. Et per candem vni& ate quadruplic tcrtio longiori conf'mt c‘x partc altera tatc. Igitur 49. exccdir ipfirm z 5.in quadruple differentiz, qua partc alrcra longior quartus cxccdit parts altcra lon- giorcm-tcrtium : Sod per prmmillhm talis differentia cfi pct numcrus quartus , fciliceté. ergo 49. excedit ipfum z 5. in quadruple quarti paris, 6.hoc ell, in 24. @od crat demon- firandum . (More ficut pro quarto, ita pro alio quocunquc loco Propofitum concludcm us. PROPOSITIO 61‘. QM fit ex qtm'ibet radice in pane altcm lo ngiorem collate- ralem fi conitmgatur cum qmdrato collaterali; conflabitur gm)n:o , qui conium‘iwx cum quadrato trianguli pmcedenMJMficét quadratumtréangulicollateralix. Exempligmtin: EX radicc 5.1'n quintum partc altera longiorcm {cilicct 20. fit roo.qui 5-20-100 iun éhrsAquadmto quinto fcilicet 2. 5. conflat 125. Aio,qu(‘:d 15 n. §.pohtus cfiEj‘°A" 4‘ rof.cum100.céficictDmA" 5‘ 15f'-‘""f' 27.5. Namqvcr 5 5i Prxccdcntcmfluod fitcx radice 5" in 5‘} farts altcm logiorcmfi ifigrttur ca [1" 5° , céfiituit 5‘3 Cul‘fi, Scd,p 555 przeccdétcm, 59cubus CG [3" A" 4‘ céiunc‘hls céfi< -100 Cit [1‘0 A" 5‘:Igf,qd fit ex radicc 5" in yfi qu‘l't.‘ alter; léqioré, 125 , ififlum cum [3" 5° : hoc t-fl,iplc nfius 12;. fi apponaturfl‘" ; 25 A: 4‘ .Cxoo.couficict [1'0 A" 5‘.C22 5.quod Fuit oilcndédum, in 5 ‘ loco c‘\'1uuilitcr in alijs locis conflabit propolirum. PRO- Drfpomnrur 33.; vmut. 3.98: quodquc d e Elimul tertium cubumzquodquc g1) k Ltlmul {umpti quartum cubum: quodq; ipfi m n o 1.) +11de quin< ,tum cubum iunc°ti conficiuut '. Itaquc dcinccps. Sit cum ipfoga b caggtcgatum r. & ipforum d c ECLllnrllLlS {.& iplbnun g h k l. congcrics t. 8: ipforum m n o p q. accruus u. crltquc dcmonffiandumqubd a. crit primus cubus, {cilicct vnitas. & r. fecundus cubus. & s. tertius. & t. qmrrus. 8c v. quintusdrocmodo. uonii ipfi a. b Cd :- Pg 11 k l m u o F q. . -----~ I {unt imparts numcri ab vnitacc pct ordinem difpofitr : proptcx‘ca , pet I 5" huius , ipforum a r s t v. aggregatum crit quadrants ab vnitatc in ordine quindccimus : quoniam poItrcmus impar , {cllicct q.quindecjmus c& in ordinc impanu ab vnitatc . Itaquc talc aggregatum crit quadratus , qui fit 51 vquinto trinngulo, hot: all it numcro qumdcnario. Talis ergo b C . , d C __ f f______l quadratus , cx praemilfi 58. erit xqualfs quinquc cuborum ab vnitarc difpofitorum cumulo . Et idco [OtuS a r s t u. g numcrus crit quinquc talium czlborum congcrics . Et per lr-~--- a cadcm ac fimilitcr oftcndemus, quod ipforum a r s t. aggro. l{»~--- l gatum cm: quadratus ab vnitatc dccmms : (qmndoquidcm l.- l. dccimus Cfl: impar : ) hoc cfl qtmdmtus qulrti triangu‘i : 1- qur cfl‘numcrus dcmriuszqui quadratus Pcr g8" prmcudcn- u tern ctiL congcriss quatuor cuborum ab vniratc ordumm- n"""‘ rum. ngmobrcm,cum ipforum .1 rs tv.cumulus fit quin- 0 -" qua cuborum :tb vnitatc continuatorum congerics : atquc ll ' ipforum a r s t.cumulus fit quatuor ab vuitute cu‘ooruxu :g- ‘1'"- l grcgatio :nccelfc cfl: Vt v.fit $9 cubus ab vnitarc._ Et Imulitcr Poll quim per cadcm oflcndctimus, pa 1‘ s. ht cumulus trium cuborum ab vnitatc: relinquctur t.qu;1rtus ab vn‘itttc ,cubus.[)cmum oflcnfo,quod a r_.fit duorum Cuboru cumul= , fupercrit cll‘c tertius ab vuitatc cubus . Cumq; a. fit vn t s -, ctit 8: Laltcr ab Vnirtatc cubus : quod crat dunon {trout-lam. Et fimilitcrdcincegsquro foxto, {cptimo cz‘tcrisq; in infini- tum cubis proccdi potcfi, ficut ptopofitio conclutilt). R01) 0' m Et idco zo.maior CR, quim 12. in iplb pari numel‘o quinto, cut'mm aggregati con/141mm . prdincm imparcs in indcfinitum l) C d c {1; 11k] a. u 0 o q. Ai0,quc‘1d b c. fimul {ccundum ab Vuit.tt-.-,Cubum autism. .1. lo. fit ex 4.141 s.:1t 12.6): 4. in 5. qux produc‘ta diffi'runt in duplo multiplicnntiszquouii multiplicati difl'crunt lunario. W m duplo quarts: radicisfcilicet 8. wod liquido con f‘tar.Na tam cubumzt:(t/l‘qumzicsi‘c,5mm rufmm. (1/ my fat fr: quwmm. {Lumguepo'f (39c quimw. Sex wt :31. reprcm jurimum .. 58144qu% 71710 o/urcs [amen am :4 ' _\n mm collatcralz'. Excmpli gratia,quiutus partcalrcm long‘or 20. exccdit quartum part: altcra longiortm fcilicct 12. in K/‘N [0715 iorcm in a'uplo pmccdcntiwadia}: , 2'? idea in ip/‘o parinu- did. 8 H x.) 1 59‘. L/wx\_) pROI' 051110 C7» m? Fayre altera longior cxcedz'tpmccdcnrem parte altcra PRIMV‘S.‘ P110 Hos: no L. '. 7713M: primum culmvz : :49 (‘eqmntcsi7;;p.zrcs§m:.f?,fi * ..‘ C‘QV-w ARITHMETICORVM -3 26 |