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Show D E I S P H AF. R A; dicrtrumfiue ad pcriferiam pofitos . in Splivqris quoq; Circuii (quorfi iphmri. abfcmdunr fimilcs l'cs) prop‘ortiona metri {Phgricis dinmetris ms Portioncs . Tam aurem Ear-allclogrammum ad [uum trinngulu, mm co~ quém columna tetragom :id iuum fierratilc, (in-pie. eft Item 6 tiiplus lumna ad fuam pyramidemqufim Cylindrus ad iuumiConum py= cf}. Item duo triangulafiuo parallelogrammmdum colunmgdux ramidesfiuc Coni fuper xquas bufisconflituu {un‘r filfillgljs proper- riomlcszfi autcm {unt eiufdcm alrirudinis, {um bafibus proportion;les. Item nnguli in circulis,fiue ad centrum 5‘ flue ad Ecrifcrmm termia , ‘ nat, flint niiumptis perifcrijs proporri‘onuicsrefpondcn S I M I i; E s autcm‘plnnm figurre iunrin duplalmtione tium laremmSic 8: duo circuli in dupla rat-ione diametrorum. Simplia vcro {b-iida fun: in tripia ratione correlariuorum laterum . Sic é}:dure {phasing in rationc diametrorum triplicata . In cw teris autcnrh~ gurisfiueinplanis triangula, {inc parallelogramma con {Ufa-S, flue mo folidis pyrmnidcs,aut Parailc‘icpipedu, veI' coiumnns ceiiflra§.§Ciiiper collamrum figurarum ratio,ex rationibus-baiiuniék celiitudznu com~ . onctur . Vndcdi bafcs fuerim cclfitudinibus recurrocaefigums axluaa fcs cflc neceflc eitEt é contrario.. r Q". A N D o nurcm rcé'ta {ccat duas parallcios , tunc ram anguii contrapofltiflufim coalrerni, quiim extrinfccusv& inrrinfccus oppoliri {untinuiccm mqualcs . Er duo intriufcci‘fimul duobus reéhs anguhs mqualcs . Er Vna ex his conditio facit mquidifhntiam . (lipndo linen {coat lineam, duo anguli coliateralcs aur {unr recli, nut duobus rcékis aequalcs; Er omncs-quatuor anguli,3ut rcé‘ci , aur q-uatuor rcfltis fimui IIB‘ER VNVSJ fphazria . Si autcm planum {ccet S phsemm praeter Ccn trum , {'eé‘do erit ,circulus minor, ccntrum'lmbcns extra Sphxrx cenrrum , & Sphagmm {cams in duas ina‘qualcs 'porrio-ncs . Vndc circuli maiorcs omnes in Sithccm {unrinuiccmmqu;:lcs,&fe inuicem in {emicirculos diuidfit: quoniam com munc ccn trum habenr. Circuli autcm minores mquali- 'tc-r rcmoti a cen rro S phrcra: flint :equalcs‘Rcmorior autem minonAxis Sphxrfe (it eius diameter fuper quo mouetur.Et eff cius circuii,pcr cuius ccnrrum pcrpcndicularirer tranfit. Poli fun: axis cx tremmqum fingzvia xquaiircr remouentur :1 (iii circuli perifcria. Circuli‘parallcli in Sphrcm hnbenr eundcm axem,& eofdem polos, 8&8) con rrario . Circulus mai‘orin {thrra inccdcns per polos circulorum mquidiihntur : di- ‘uidit cos fingulos per mqunliaSi autem procter p0108,pcr inxqualia(cxccpto maiori :rquidif'cantur) arcus autcm coalrcrni duorum circulorfi vrrinquc requalirer i medio remotorfifimt xquales. Er rcmorior,maio rem patitur inatqualimtem. idemc'l; facir maior obliquitas i-ccan tcs.Cir culus maior duéius pcrpolos ‘ciroulorum in fphzcrn {c inuiccm fecantium,diuidir vrrafquc portiones corum per xqualiafc vcro con ringen tiuimtrnniitpcr punéhim conrac'his . Si duo circuli mniores BantingE30105 circulorum (equidifhm tium,vel tangant corum minimum. Tfic f wrum arcus inter {cmicirculos maiorum reccpri funt fimilcs: Er ma- liorum arcus arquidiflanribus duobus inclufi fu-nta:qu:iics . H I s praimiiiiswcnicmus ad Sphxra: mundanagintroduélioncm. widquid autcm {upcr ifio negocio tradcndum eff, aut pertinet ad principia, aut ad circulos, ant ad motum primum , an: ad motus [an .crmdziriosflxc fingula filmmatim ac Paucis cxplicabimus . xquales . Vndc quatuor quadrata iimul, v51, tria hexagom :rquiangiblaflcl {ex trianguia xquilatcra implcre poflunt torum fpacium, cone: curi‘cntibus anguiis. Qioniam {cilicetr nnguio in 5‘" rcc'his 693111116» Sp/mm primipia, 71Mflmt fix Pto- xagono valet vnum refrain (Saddam-pattern,» In tsiangulo valet lem‘zi com/uflona, duas rcrtins vnius rcéri .r Etvidcireo tam quatuor angulos quadrati, quhm rres angulos hcmgoni,& quiim trcs angulos trianguli , quntuor refills angulis :rquiualcrc neceiic CPL . Item, ii quanrimtcm angulorum pcnfims , iicur Hexagonos Cum in tcrmiftis-- triangulis , ira Ofiogonos cum inrcrmifiis quadraris compaginaros torum locum implerc ram rationc,quém cxpuricnria conciudcs. Hmc nutcm ex Euclidis clcmétis pi'r‘eiibanda {um 35: prmdiihmda his,q-ui afironomica principia Cdpefl‘cn: volunt . Scd 8c iinha‘ricas Tiicodoiij clcmcnm minimé omittcnda. funtwp-Sphere:mundanzr forim,circulorum magnitude, firms, incli~ nationcs,axes,& poli, 8c diuifio ixitclliganrur . ' S I pianum (acct Sphcemm pct ccnrrum , feéiio erit Circulus maior limbcns commune ccnrrum cum 531mm , camc'l; {ccans in duo hcmh {Bh'xrium Vgugm CE L I figumm eifc fiahxricam, & morum eius circularé. G7 "4%": {h Nam C0310 vniucrfa comprehenfuro congrun fuir forms. 2%: capaciflima ad motum circularem Facilis,&qure {cinpcr c ‘ inrm eofdcm {c limites continercr : 8: H1113 cfl: fphscrica. ‘9 Itcm 1i {ccus dict, caeli propterplures moms circularcs angeren rur,aur vacuum in cis reperircrurld idem {cnfibili compro- baturcxperimenro . @661 autem affrorum corpora filnt fphxrica, coni'mtquoniam quaqua verfum {pcftam rotunda vidétur . Item 51 necciiita tc moms ab excm plo cuclcfi‘is & elcmen tarijs formm.A crcmento 8: dccrcmcnro Lunx . T E R n A M cilia rotundam . Nam rotunditarem abortu ad 0cm. {um arguir anticiyatio orruum 8c occafiium i‘ccllarum per indicium A 4, lun aris |