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Show ‘7"1. ARITHM‘ETICORVM PRopos1'r1o 105‘. Omnis cubm,fiue 053116517145 centrali: cum impari collateraIi coniunflm,.equiualet duplo terrabcdrincntmlix. Cum enim numcrus bafium oélahcdri ad 11111116111111 bafium tctrahcdri ‘fir duplus : itcmc/luc numcrus latcrum illius ad numcrum 1116111111 11111115 dupius. 131111 1111 par 2131110111113 {1011, vt vniras ccnrmlis Cum {Cl‘niJiIHYICEI'IS oé‘tahcdris finr ( additionc fa.éta) duplum vnimtis centralis Sc {c1n1diz1mctrorum tarahcdri. Sunt (4111111 IE1111'd13mct1‘1'o&1l1cdri[cx,& {cmidinma- I 2.5 4.6. 9 8.11.18.27 r I 4 - 5 16. 2.0. 15 ‘4. 80.100. :2; :g: :...-:s::-_~_.~._. ficit 11149le .zgzregltiwbomm primi generix collJtemé'ix (3' preredc'mix. Nam numcrus , (1111 H: ex aggregate mdicum duarumfciliccr propofiti loci,&: pmccdcntishoc citcx 1m igitur,(1u<‘1d 1d,quod fit (:1; g. 111 15.fc111c:;t 6V§.co11iun&um PROPOSITIO 108-". Omni; culms primigencrznmm pmcedcnti 614110 coniunflm, Cum ;. facit duplum ipfius 35 Exponamr vuims cum 13; dicibus z.&3 & quuh‘ati 4.& 9. cum medic proportionali 6. Itcméluc cubi 0&0 8c 2.7. cum duobus mcdgs Propor~ paricoihtemli in agqrcgntum qmdmrorum coll1tcmlis.& Prqccdenns. hoc cflfin quadrarum c;ntra1:m collarcmlcm, eff pcr 8 9" huius, qnomon collatcmlis in q ladmtis quadratorum. Er per 99i [1111113, talis gnomon cit cu'sus Cummlis. Ven‘nn mlis numerus cum nggrcgato mdlcum collatchis & przecedcntistc cl}, cum i111paricollaterali coniunfkus, cflicit pct pmmiifim, duplum aggrcgati cuborum collate- ralis 8: przcedentis, hoc sitcuborum ipfiuum 111d1'cu111.lgitur cuhus centralis cum impari collaterali COlliL1n&L15,fJCit ipfum tale 611110111111 duplum :quod eff propofirum. conficir coll.zteralcm tetra/1811mm cmtmlem. Nam , per 10 ;5 rremiflizm, culms centralis cum 1m pari collurer. l1 coniun Clusmonflnt dup'um tetrahcdri Ccntmlis. Er per prseccdcnrc-m , 11117111 0111115 ccnrmlis cum 111111311 coilatcmli comun- cx aggrcgam z.&' :.in .1. raggrcgacum ipibrum 8.1311 12. Non 1111:1‘ of‘tcnd'Im und ex 111810 2. 8c 3. aggrcgato in 9. fit ipibrum 13. 8C :7. aggregatumficut 1n 89"Hc1110nfiraui< mus. Vnde cx age'reguto ipibrum 2. & 5. 1n aggzsgato 1pforum 4. 8: 9. ho: 6ft , cx 1.111 15. fist aggrcguum ipi‘o‘ flus,efl1cirduplum nggrcgarum cuborum colhremlis 8c prq Ccdmtis. Iszitur talc cuborum duplunlfiquflm 1:1} duplo rc‘fraiwdri, EC perindc Cuborum aggregitummquak crit 1'le rum (1112111111 mumsrorum 8. 12.. 18. 2.7.. Dcmonfirandum 6111311111- , (111211 aggrcg 1mm talium quatuor numcrOv 077m}: tetrahedrus central): pore/l ejfe calms ccntrali: tcm'i mm. cum 311' va‘cgato radscumflbilicet cum 5. ficit duplum aggrcgariigiorulu 8.13 27.hoccfl',quod 65. C11 1. eff duplfi ipins 55. 1111: (1d Aggregatfi ipfonrn 18.8: 1 z.cf1 5.C0mun‘ Ctnnncfi 131111.111: agrgrcgrlto iplbm 8.8: 17. QLOd Emile dcma fivrur: Ni 12.11.191.111: 1.111 4.. Aripfc 13.111413111th 5. ".111 it deinceps I'z‘milirer‘ pro r8121111.55 . P11011051 1'1 0107". Omni: calm; central): mm impari collateralz' conisziur,can tri rctmhcdri quatuor Er 1dcirco ogvrtct :Idxjccrc ad (ummam 061211161111 duas thnfidimmctros, huc c1hpa1‘cm collaremlcm, & vnimtc-m , ad duplicandam vnimtrm cc'ntralcm} qnzz Cum p.111 ficit 11119316111 collaccmkm . Conlhu 131111: propofitum. P11011051 "110106". £xaggregato duamm proximamm radiumzinaggrcqatum qtmdratorum ex {is inw'tiplicato,p;"o;:'ucimr numems qué mm ip fl) radium; aggregate 10715141213125 fizcit dim/3472'; aggrgaté cuborym Mfume/71.. Egcmpl gram 2.& 111111111113: 111011111111 re. dices, qunrum congc‘rirs yquadran autcm 481' ~,. C1151 vero 8.27.q11;1d1‘a101'u111 cumulus 1;.Cul101'um vc1'645.Dico tiomlibus 11. 8c 18. 4n qu:bus proptcr proportionem numeroru1mquoninm ex 2.111 4.5: 8. 86 «115.111 4.511 1.1dcirco 1 3-4 9.12 .16 27.56. 48. 64. LIBRIPRIMI, PARS II. ,7; maior eff (11121111 4.111 aggregato ipfotum 2. 86 3.hoc eitin ;. ergo aggregatum 18. Sc 12. fupcmmrab aggrmaro ipforum 8. 3: 1.7.111 5. unrelggrcgatumigforum 18. &12.. cum 5. coniunfltu:11,fit:equ1lc aggregato ipforum 1&5 2.7. chi fuir oi'mndcndum.31111111161 pro duahus q111'l1113l1'bcr mud-v mis radicibus argumenmndo proccdam. Sicuc propo‘nirur. 9.Tn.n101gimr aggrcgatum ipfogc 18.13: 11.1‘upcratur ab aggrcggio 11110111111 8.& 17.C1u3nto 9.maior efl: qufim 4.5111 9.. . ma1or , rctrahcdro .Céntmli : quod cfi propofizum. Pnopomwo 109". Rhimi 557211131105 efl cub/4; 7172:6145, compo/husfcilirct 6x £1401: generfs (0'7att'mli {wpmcedem Vocamus autem hmufmoc11d1 011111111 mixmm : quoniam ex mixrum duorum bmum 11:":111 gentris complgimrur : ficut & qu..1dr.11us cannu‘ic conficmu‘ ex combination: duorum primigcneCum tis qu 11112110111111 , {cilicet colhtcmlis 8c prxccdcncis. 3c igitur. p 31' 11111311 T1111 , tetrahgdrus conflflst c1; collgtemh cubxs cgnflct prxccdcnn 911ml 5611-9115, cubis : 8!. ex citdcm ' cu us «no-1.1.1., mum-M''''' V " "*'*"Wm. .15 |
