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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 29, page id 797435492:0053
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L E C F TTI.
3. Non absimilicer in Pyperbola, (cujus itidem axis BD, Foci LI, R;
reliquisque velut antea prxepararis) ostendetur fore perpetuo NR.
CR:: B. D. HIK. unde SiFueric (ex Lyperbolae constructione) BD. Fig. 270
HIR:: T. R. Crit etiaM NR. CR:: I. R. quod sI radius MN ad
CBparallelus retringatur in NR; hoc idem accidet, ut nempe (IE
NK. CK:: P. R. quareradii M A retractus per Byperbola FOCHI
EransibiE.
4. Ouod vero ab Ellipsis aut FIyperbolae cujulris Focorum alterutro
quiliber curra incidens radiens in alcerum reflectatur, admodum facile
dilucescir. Nam in ellipse, perpendicularis NC, in LEyperbola, Lan-
sens NVT bilecat ansuilum FIN R. unde pater propolicum, IIX0
extra nostras oleaspolica cursim ex lerissime perstringo; nec tamen
ut eo multa purem deliderari.
Revertamur in orbitam; _ quidem derelicris his generalissimis,
ac abstracristimis, lemmarum vicem obituris, ad particularia descenda-
MuS. Adplanas vero superticies (vel earum loco propter inlinuarar
ancehrac causam subrosaras lineas rectas) inflexis obtinsentia radiis pri-
mocontemplemur. Eriam quoad has Catoptricis primum, urpore ta-
cillimis, brevistsime defungemur.
XIII. 2. Parallelorum sibi ractiorum (AB, M NI) reCHX (F F) in. FiS. 2 2
cidentium reflexi (B a, NI _) sunc etiam libi paralleli.
Nam quoniam AB, M N ex hypochesi sunt paralleli, erune anguli
ABF, M N P pares. ErgO sunt anguli a B F, u N P etiam pareS.
Ouare rectae a B, u H sune Parallele.
XIV. 2. Sit recta A. B L recta reRecrenti F F perpendicularis; cum
hacvero promanantis ab a cujusvis radii AN reflexus a H conveniat
in Z; dico tore BZ = AB. Nam ans. ANIB = ang. a N F =
ZNTB. quare liquer triangula BVTA B NIZ sibi muruo aequilatera
tore; e esse AB =BZ: . P. I.
2V. 3. Einc, omnes ab uno puncto, diversentium tanquam ab altero F18. 29.
quodam uno prodeuntes.
Ouoad punctum longe dissitum (luo parallelos ad sensum radios eja-
culante) patet e penultima. Oudud punetum e sensibilirer finita di-
Rancia radians, ex ulcima patet, quod omnium ab A diversentium ra.
diorum reflexi procracti concurrunt in Z; adeoque videbuntur ab. c0
PTOMAnATE.
t r de