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Show 276 DELINEH HORARIIS firperflciei,planoc'1; prcedié‘tan quo k e.h x. (@o fir,vt reaa'linea in codé plano eonncé‘tens pi‘méht e 5.3.8: vlterius produéla tangat in {010 punéto g.comcam liiperficié, Se in eodem iplo pund‘o paraboles a g. periferiam tfigar in eius plano iacens. {Equalis autem cum (it h dipfi d LS; ipfze h k.d 3.:equid1flantes: iam xqunles erunt k 3.3 r. cumc'luc ipfa: k e.d t.xquidiflét5erunt 6: d 3.21 e.inuicé :equales,receptze {cilicet 5;. vertice {eétionis :1. ad terminum vmngentis e. 8: ad ordinatam d g. Sicur fiieratdemonl'cridumEt lICCC propolitio ell 3 5" pi conicorum. XIIIEIfiid fi receptee ex diametro Parallels 2‘1 vertice adpfiéhimquod k .1 e piain & ad ordinatam flierinr :eelualesgfie retire, m-‘*'r qua‘ a punflo ad extremum orclmntx duCitur,1n i! {0 ex tremo tangit eriferiamlixc ell conuerfa. preteetlentis concl-ulinonis , qure facile oftenditur ab impoflibili: Ewell 3 35 primi conicogz. XIII. 5121 pfifl-o-quopiam in diamerru extra circulum, elliplim, velhyperbolen linea dué‘ra prriferiam mngar , & £1 punélo mans ordinate: ducntur ad 5 4? flli Fog . "a l". C" ° diamerrmn,tunc receptc; ab extremitatiltiis dis: mem adord1natam,erunt p1'0}301't10nfll('5 receptis ab eifdem extremitatihus ad punéhi prxdifiumRepeto efidem dcfcriptionem,& idem per axim A"? h k L Etordinata in circulo,ellip[i,ve-l hyperbole litd goug- per 2" prrecedentium lemv matum,ponatur diameter flue circuli,{iue Ellipfeos h g t.cuius peri- feriam in Punéto _g.tangat redo linen gx.& ideo mquidifians diametro h L8: in piano A" vtriq;:rq11idilfnns k c.coincidésq;diametrofeéliob nis propofitx spud e Sic enim,vt prius,planum,in quo {untk cg x. ta'get com} firperla‘ms k g. & reéla linea egmnger le&ionen1 apnd g.pL1n€ci11n.Veriim in ellipli & cireulo tranfiierfa :1 d.coincidatreliquo lateriA" epud bin hyperbole vero,eidem lateri {ii- Pra verticE Produéro; erirq; :L b.diameter fefiionis 'tranfuerfa,in quo centrum z. Quibus 2&is &intel- leéh's demonfimndum erit,quod lieu: eff b d-d a. lie erit b c--e a Hoe paé'co. Ducatur per punétfi a. ipfi h kmquidifians linea m a Lipfi quidé h Lapud Punaum m.ipfiq; kc.apud l.pun¢‘tum coincidens: Sic enim,proprer xquidifl‘itiam linearum h b.a m. AA‘fd b h.d a m.en'1tinuiCem eequiangula, & proor"u laterum:hoe elUiCut b d-d aJie inm h d-‘ (1 111.110: efl,{ic t d-d m. Sed propter xquidifianriam linearnm k e. dz. LIBER TERTIVS. ' 2.77 d t.AA‘"a k e.a t dfunt flmilia 8: proportionalia laterum : Itemr'luc AA" ae 1.3 d m. fimilia &proportiomlium laterum. Vnde fietfieut t d-d m.{ie k e-e l. Verum adhue,Propter :equidil'mntiam lineari‘i k b.a 1. AA" l) k 6.116. limilia 86 proportionalium laterum. Igf k c -e Llicut b e-c mCmareJicut b e-e afic fier b d---d a. quod fuit demonfirédumfit hnec ell propofitio 36" primi conicorum.& {imil'r ol‘tédi potefi 372 tertij conicorum v‘l linen. eadb. n6 diameter, {ed {ecans Circulum, ellipfim, hyper-balm , ac etinm parabolen Ponitut. XI 11. Contra verb,fi in circulo,ellipfi,authyperbolanrceptm 2b cx- tremitatibus diametri ad ordinatam flierint proportionales recepris ab eifdem extremimtibus 1d pfiéhim quodpii diameter extra feé‘tioncm: tunc linea dual 31 punéto mli adextremfi ordinate: in perifi-ria sec ell conuerfa przmillEe,8e ab 1n tali extreme ranger pariferiam . impoflibili Emile oflenditur: hoe ell,de[lru€tis 5ri)5.Atque in conicis aft 54‘ primi . In omnibus autem his 4°‘conclufionibus procefli: Apollonius inditefiemos aurem in duah us ISLE: deméfirario nol‘tn ficilior ell : (311 ill: plane defcriprione vtatur : qua in re Apollonius ceeteros ingenio antecellit . Er notandum,quod to demonfiratione circuli,necelle ell vt conus h k nfir {calcnus & Aha k bfubconrmiifi A" h k LSlC enim,per 5i ptimi conicorfifec'rio a g bfuper qua dill'c- rirur,circulus erit.& tfic bafis h g t.Elliplis crit. Eeee 4‘" conelufiones aliter,quim Apollonius, quod pulehrum fiiit, of‘tendimus. X V. Item nomndfi q) in circulo,cllipfi,& hyperbola,linezr d 2.2 [3.2 efunt continue proportionaleszhoc ell portio inter ordinatum 84 centrum: femidiamcter tranliierlh: & quse 21 Centre ad tangentem, ex diametro recept;¥.& ell: 37" primi conicorum . (De c‘orziugmk dame/tn} flexdmm, deg; tangen- tiémflexa/s/MM ducmdér. Cap. f. A M ex difiinitione coniugnrarum dimmerrorum eonflnt Parabolen coniugnms non hnbere diametros verum it'qllidlllffllltfs , v: in primo capollenfiim el‘t. Circuli were COQlUgfltf-(llalnrfrl lcmper' lc inuicem ad reé‘ros diliaefmmt nngulos : lecus emm vtraque nli‘cz'ius parillelos per medium lingulas {flare non potel‘tquod ell proprium coniugamrum diametrorum . SL1FCI:LllCl‘g0(‘lL'CCHIUgQUS Cfll}‘l€()$, aur contrapolimmm dumetris delcribendis Reg-alas trad/tires]: m. 2.. Ello iraqueelliplis '3. b c. in qua dam lit distinctive 3. d. V010 tn mill Ellipfi (icleribere diametrum céiugatnm ipli a d. Steeaiwo per $935133 iplhm 1 (Lin punelo eeritq; z.centrfidleé‘tiom-sduca gal] dderwmilri- , h. 6" (6 b c.6151; in piitfto {.9 mediL'i ditudLEt p puéla c Educ: teem 541% lJumeter S 5 |