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# Title: [Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ (shelfmarks Leibn. Marg. 0; ZEN Leibn. Marg. 0)
# Folio 117, page id 797435492:0189
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P E C Y. XV II.
Triogerens haud aspernanda. relinquantur isitur ei extera, mitii
suttecerie, quod veriorem Phaenomena detegendi déclarandique me.
thodum adnitus lim aliquatenus enucleare. pergamus ad alios casus,
haudita pertractatos.
XIX Objiciatur speculo MI B N D recta F AO, rectX C A (per
speculi centrum C transcunti) Derpendicularis; adverto, ( Fuerit ipla Fig. 189..
CR major quam C2, quadrans diametri BD; quod rectX F AC
ad. infinitum utrinque protra tx ad totum circulum (ejus ad partes
intelligo concaras limul ac convexaS) imaso absoluta. (quinetiam ima.
s0 ad oculum in ipso centro C constitutum relata) exit Fllipsis. item
si C A minor CiC, quam CZ, quod iplius F A C imaso absoluta
(vel dicto modo relata) constabit ex hyperbolis oppoliris; (i denuo
C A iplam CZ adaequet (vel F C per ipsum L eran(eaT) quod ad
parabolam ejusmodi consistet imaso. Sed modum transgrederer hxc.
jam asgrediens demonstrare. Expectent isitur. 1)
 ai
I.: R. D ea, quae Tub finitam praecedentem propoluimus demon.
LaCranda necessariam, alioquin notabilem, Conicarum Sectionum
proprietatem imprimis ostendemus.
Sic triangulum A C F, rectum habens angulum ad C; e inde. Fi8. 190.
finire protractis lateribus A C, AB, in A C sumatur quod piaM, cLIM
ctum Z, ducaturque ZC ad C si parallela; inseratur autem angulo
CXC recta CL aequalis ipsI ZC; dico punctum indererminatum L ad
sectionum conicarum aliquam contistere.
II. Nempe primo, sic angulus A Temirecto minor (vel ACC
C E) erit punctum Z ad ellixlin, qua determinatur hoc pacto: AN-
suli LCP semirecti tiant (ad utramque rectxe CF. partem) liguet
i rectaS. C. P ipsi A F. occurrere, pura ad puncta H, et 5. ab his
2d.