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Show DE SPHAERA talem,Mathematicam,ac Theologinm. Atquo Thcolcgiu excedit igcul tatem humanam. Phyfica vero,propter 1:11:11'5'1'13 Huxum) incerta. idc1r- co commendatur Mathematics, & prcccufuo Af'cronomiu, proprcr Ctrtitudinem demonfirarionis,& {ubicé‘ti no uilitotcm , Vt mt Pi'olcmreus. Igitur Afitonomix principia tradituri , Pi‘xmlttemus (lurcdam geomw LZIBERVNVS.' j S o L t n v M cft corpus {ub triplicidimcnfionc contcntum hoe refi, quod longum, Iatum 8: profimdum cI'c . Perpend icularis rcaa in planum efl: , qua: rcé‘tos facit angulos cum rcélis in piano duflris . Pt . raliclaplana funt,quz1: quoquo Vcrfum & quantumcun q; produt‘h nufquam coincidunt . Parallelcpipcda {olida flint , quoru m oppofi. tzc bafés {unt parallelcc . Solidorum {Pecics {unt Pyramidcs , Colum. trica,& ncccflhria prccmnbula . geometrim PViflCiPiép . napriiinatafitque Polyedrx figurx. Angulus {oiidus fit ex concurfu trium,vcl plurium angulorum phnorumgquos media 6": quatuor rc- él'is angulis 61H? minorcs. Ex polycdris figuris folidis quinque tantum P v N C 'r v M eff (ignum quantitatis cxpcrs . Linea ef‘t longitudo iatitudinc carcns . Lincnrum quoq; alia rcé‘m , 211:1 Hem j‘ Superb Cies CR , qua: longitudincm 85 [atltudincm habct. StiporfiCICr‘tiiii aim Plain , aiia curua . Angulus cit linenrum concurfirs indlreéhis. Angulorum alius rcé‘tilineus , alius alterius modi . Recon} 1n rectum purpendicularis cfi,cum vtrinqi nngullos ficirmqualcs, qurrodh (hr:untui‘.Ar¥ gulus rcéto maiorgobtufus : minor autem ucutus dicitu‘r. i firminus 'c-tt limes, {cu finis . Figum cPc,qus: termino, vcl terminrs drtumuu T Cu< Culus cflc figura, cuius ccntrum 51 periferiot coqualltcr dil'catihunc dmmcm ter per ccnrrum ducm in fémicirculos' (huldit : rezfln vero proctor {cum trum in portiones inccqualcs . Rcéhlmcaruin figurarum quainm hint trilatcr‘agquazdam quadrilatersz, quasdam multilateroc . Trilmgulorum autcm quoddam :equilntcrum 2 quoddam Iioiccks, ‘quod uuomntum latent mqualia imbct : quoddam Scalcnum, quod trm inocqunlm .‘Itczn aliud orthogonium, quod Vnum ex angulis reé‘rum : aliud mniuygonium, quod vnum obtufum :- aliud oxygonlum , quodomnos :tcntos ImbetScmpEr nutcm mnius lotus opponiturnngulo 111110111 . ht anguh trcs Coniunéti conficiunr duos i‘eé‘tos . (Egririmtcrarum figurnrunr quinquc funtf‘pccics, dirarum, Rhombus, l‘xccjmtangulum, Piliomt, boidcs, 8C Trapczium . Ex quibus prmm 8: ficunon iunt :rquuntcrte folum Prinu 8c tcrtiu rcCtos habent angulos. Secunda 8:qu.1tt1 oppofitos angulos imbcnt :L‘qualcs . Tcrtin. 86 quarto Intern ctinm oppofi'm mqualiu. 1308':an vcro ncque mqui‘laterajnequc mqumnguiu cit. Room nutcm p.11'fliicii,{1ll€ mquiriii‘mntcs iunr, qum 1n codcm pic-.110 dcfcriptx quorfinncunq; & quantumcunquo protraéht coxitzlc‘cum non a .mit» tunt. Paralldogrnmm um officuius oppofim latcm :L‘qllidlfl'ilrlf. .qualr‘s {tintmquilatcrurum primac quatuor {pacies . Limircs & ownerdcnux lincarum {unr pu 181:1 . Cuiusliitct figursc rcfl‘ihncm anguh omn;s con- iunfl'i conficiunt tot pariu rcCtorum , in quo triangula diuiriunrut. Vndc quatuor a ,guii figurx quadriiatcrrc con Hunt q11;1rL10‘rL-&c§,qt1ia rcfoluiturin duo trinngula . Anguii iigmx pcnmgona: conflanticx tea flos,(1uonja111 fccatur in tria rrianguh, 8: {EC dcinccps. 501mm. m -q,‘ : 'M"m fun t,qurc rehularia dicun turgquoniam fiib azquilateris , &xquiangulis oquualibus intrst fc bafibus lingula contincn tut . Pyramis, {cilicct quatuor triangulis. Oétacdrum oé‘to.Cubus {ex quadratis. Icofae drum triangulis viginti. Dodecacdrum duodccim pentagonis.C onus €9ch- mmis rotunda fiipcr baiim circulnrem . Cylindrus columm rotund a, pro bafibus habcns circulos acquos 86 parallelosln his axis per vcrticé' 86 Ccntta bafium ducitur. (hi cum perpendicularis cfl, cfi ad bafim, Conus &Cy'lindrus dicerur rcéhis . Secus autcm Scatenus . Tam duz reéh'efcinuicem fecantesquitm omnc triangulum reé‘tilineum in vno inccnt piano . Sphztra cit folidum lub'vnn {upcrficic Conclufum , i qua. cen trum medium :Eq unliter difl'at . Eius diameter vol axis pet can rmm inccdit,vtTheodoiius .Vel folidum , quod z‘; {emicirculo fuper fixa diametrum circuniiué‘so,dcfcribitur , vt ait Euclides . Ratio {cu pro- Portio cl'c quantitntum citifdein genetis collatio . Similes, eccdem, vcl zquaics rationes fimt,qu:€ vel ciufdcm fun:nominiswelqualibet nominata rations {imul fitnt 1naioreS,véi {imul minorcs.Nominatur au~ tem ratio 31 numctis. Eiufdem .mrionis quantitatcs Proportionales dicun tut. S I M 1 L E s pianrefimiliterc'l; pofitx figurae fungquarum anguli {inguli fingulis azquales 36 totidem . Etlatem fingula fingulis proportionalia, chquidif‘mntia. Similia 8: iimilitcr collocam folida lunt, quae {11b Iimilibus {K'f‘iuflicm'numcri b1flb115,& parallelis continétut. Er fleri potcfl 'intcrdum , vt in .pofitione iimili planarum duo latcra. figurarumwtl bina congruant limul. Erin locations Iimtli folidarum, duo: bufcsnel binre,vc1 terns: communicent vni plano,rcliquis :equidi~ flzmti'nus.Corre'latiua Iatcm,vsl correlatiuas bafes , correlatiuis {ingu- las iingulis confcrendo . Item fimilcs Coni, out fimilcs Cylindri {unr quorum axes funt bafiumidiamctris proportionalcs, & rcéti vs} :3 ugliter inclinati . Omnes autem duo circuli,& omnes dux Sphmrac unt adin uicem fimiles , quonii {cmpcr habcnt diamcrros pcrimctris Pro- portionalcs . Item in circulis chords: ptoportionalcs diumetris ab- .(binriunriiiiiilcs portiones,qu:e fufcipiunt xquos angulosallllC ad Gem 5 trum, |