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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 47, page id 797435492:0259
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L. R C F. VI.
DEXHO erGO DTIXBE L DHXRO =D F XHIO; hoc cAE
DHXBE L DHXHO - -DEIXBL =DE X IIO; transpo-
vendo isicur eA DH X HO -DF X HO =DIIX BI = DIIX
BF. hoc eAt FHIXHO = DH XFL; vel F HIX CO. ]. FH X E1B. 39.
HO =DEX FL J.. F:TIX FL; quare, dempeis xqualibus, eAt F HI
26O = DExEL; vel ZG XGO =DEX FL; cum itaque
DEx FL Ci quid decerminatum, constar lincam OBO esse hy-
perbolam, cujus alymerori L. R, 25.
V. Si MO capiatur ad alteras recta B C PArTES, CtiaM DF.
BF ad alteras punctorum D, B parres accipi debent; uti Schema Fiz. 40.
monstrat; nec abludie modus demonstrandi.
VI. Consectarium. Si recta BO angulum AB C. secet, per-
que punctum D ducaneur atcunque dux rectA M N, X Y rectam F18. A1
BQ incersecantes punctis OP (quorura utique sic O propius ip-
si B) erit MNT. MO =  XY. XP. Nam per O descripta con
cipiatur Bxperbola VOB (qualem jam mox artisimus, sic ut inter-
ceptae rarionem habeane illam quam M N ad M O) erit igitur
MN. MO:: (XY, ZV) -1XY. XP.
Coroll. Diridendo eA HO. MO =  ZP. PZ.
VH. Ouinimo si plures linex BC, BC angulum A B C secenE; FiB 42.
e a puncto D projiciantur rectae DN, DY (quae rectas alteras
intersecant ue vides; quarimque D N puncto B vicinior;) eric
NF. HOYP. VX.
Nam NF. EOmy ZF. FV; _ FO. OM - FV. VX: i
BituE CX XqUO CA N F. OM = IYF. V X. II
VIII. Eriam exinde Paret, per B (ad partes alterurras) rectam.
duci posse; ita ut e D eductarum partes ab illa rectaque B C ad.
interceptas a rectis BA, BC rarionem habeant minorem quapi-
am data.
Nam SUMaTuT P ( == PZ; ergo connexa BO hyperbolam O.
BO rangit; e liquet a rectis BC, BC. interceptas ad intercep.
1a5 d BC, B A minorem rationem habere, quam habene inter-
ceprae ab. hiyperbola O BO ec recta BC ad ealdem; hoc est mi
norem data quapiam.
IX. Sic rursum angulus rectilineus A BC, et punctum D; icem B1B. 430.
dinea