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Show 32‘ ,, L I B R I . . P R I M I ‘ Pars Secundau. PROLEGOMENA. ,. .» I'D. angula tiflpcr/fria/is,quzimfilida, fit; pjmmir,fiu U ‘colmmm: :16 71M tar/7672' inprimo genercdr/fe‘mifim‘, O proptcr talzkférmx dtgnimrem, 71m mcrcmr rvn‘aéi- .0 gm tmfiari. 1mg,- quo aa' bexagomm wquiczflgu/am :' 3 0. g 0. , 0 25 formal/z, 1326 72071 repetc‘mm 64311511601 prgmf/fix pica 0 .0 0 0 marszmmflmt:fid pry/2W5 dzJ/jlgmtianilim, mtcm O O 0 190 0 & 0 0 e/JEZen/u do nmflemi‘z}: férmpiprimige72cm , mmc dc tantra/Mm; agemz'um .- a'e .. quamm Immem cflférma hexagoim xqui- . 00:00.. "LIBER PRIMVS.' Omnis potro pyramis' ccnttalis fit cx aggregationc ccntra~ O Iium formarum (m, nominis ab vnitatc qu; ad bafim [mm o O O {ucccffiué aogrcgatarum. thotc pyramis Iriangula,triangu~ o o o D larum: qmdraraquadmmrum,86 deinceps. Omnis dcmum 0 O O 0 columns. ccntmlis procrczbimr cx form; centrali collaterali (q Lu: fin bafis cfl) totics 4.. coaccruara , quota efl; in ordinc, . fiucin radiccm larcmlcm multiphcata.Harum Proprietatcs & coll'igantias nunc cxphcabimus. PROPOSITIO 67". Omnix triangulus ccntmli: con/fat ex collatera/i triangulo (y pmcedenri qrmdmto prim} generis. Exemplx gratin: triangulus quintus centralis {cilicctg I. conftat cx triangulo collateral‘i primi generisfcilicct x 5. éccx quadrato quarto, {cilicct 16. Qt) d fic of'ccnditun Trcs trianguli Primo ex ordinc,tcrrius. n quartus, quintus, fcilicct,6.1o.& 1;. fimul coniunflimonfi- 6 ciunt triplum mcdij , 8: vniratcm per 2.95 huius. Scd per fa 1o diffin. rriplum Luvsdij, hoc ci‘t,quarti trianguli, cum vnitatc, 15-- conficit quintum rriangulfi ccnrralcmlgimr quintus trian- gulus ccntralis conflar cx aggregate trium diam-um trian- Pro/winemur . gulorum tcrtij, qucxrri, & quinti.Cumc'1uc Per ni huius,tcr- 00041 DIPFINITIONES. rim 6: quartus triangulus componit quartum quadratum: f 0 ~> O M N 1 3 forms numeraria cétralis plana (upcrficialis c6‘ firuimr ex centrali vuimrc & cx I'Ot trifigulis pmcedétibus pri mi gcncris , quot (uniforms: ipfius anguli : vrpote triangulus ccntralis ex vnitatc 66 trib us triangulis . andmtus ccntmlis ‘cx vm'rate & quatuor triangulis. I'cntagonus centralis ex vnitarc& quinquc triégulis. chngonus cx vnitate & {ex vt antca diximusJ-Icpmgonus cx vnitatc & fepté. Ofiogonus ex min;tc & 0&0 trinngulis primi generiantcm {cmpcr :cqualia & an- qus vuiformcs confiitucmibus compaginatur.ltaq;,fi lubcr, dcinccps.Vndeomnis figura ccmrahs {upcraddit prxccdcnti figum n‘iigulum. Vtrfi, ficur in chagono geometrico latcra fun: {cmidiamctris mqualiafim lxic, in hexagouo numcrali vni tatcs angularcs mmum inter {c difianr,quantfi ipfx ab vnimte ccmmli rcmouenturzék' tres unimrcs proximg {cmpcr triiqulfi" zquilatcrfi faciunt: Gym in quuh'ato primo quaruor unimtcs quadratum conformantlu cgctcris autcm Formis ccntralibus, hoc off in triangulo, quadrato Sc pen ragouomuimtcs lateralcs magis dif'caut,quém diamccmlcs : minus ucro in formis hexa- fequiturwt quartus quadratus cum quinto triangulo {imul {umptus pcrficiat quintum triangulum ccntralem. @od cmt dcmonf‘tmndum : 8:5. quinto loco trunsfcrtur fyllogif- mus ad qucm vis alium :v: propofitio conclufir. PROPOSITIO 68". Omni: quadratu: central}: confi'cimr ox tlztolm: qzmdran': pri mi gcncfls, fcificet collammli (9V pmcedenti. Exempli gratia. mndmms gnt' citralis 4,1. céficit‘cx quinto & quarto quadmris prixuigcneris.f.15.& 16. (Educ pater. Per [1i huius, 4,1 25f qumdmt9 gm" confiat quuarto 8c: qnto triigulis primi gene ris Er 9 p114: cedété, trifigulus qntus CL'1 quadrato 4..primi gt ncris,céficifir triigulfi qntfi cEtraIE: Igitur quadmrfintus cfi quadrato quarto fimul xquiualéttriigulos duosfquartum 4.1 Primi gcncris,& gntfi cérralé. Scd triégulu§ gurus ccntralis cum triangulo quarto primi generis,Per difl1n.procrcat quadratum quintum centralcm : ergo quadratus quintus cen- tralis xqmualct duos quafimtos Primi genetis,fcilicct quin- mm <56 quartum '. quod {nit dcmonfirandum . & argumcn- gonum {equcntibusmr in 11cptagono (SC ofiogono, ut pou'hllat mm 5: q uinto ad qucm uis propofitum locum transfcrmr," {nus Gcometticarum formatum,quas Arithmeticx imiritur. Omnio Conclufio proPouit. Id idem dcmonftratur per 30"" huiuS. Y P n o P of 31 E 10 3! |
