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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 48, page id 797435492:0260
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L F C F. VI.
linea OOO ralis, ut s E D uccunque ducatur recta DO, secanS
ansuli lacera punctis M, HI, habeat D M ad NO semper eandem
rationem (pura X ad Y) erit etiam linea OOO hyperbola-
Nam ducatur B L ad BC. parallela; CIEque DL. DF: : . X:
Se per F. ducatur F R ad AB parallela; secanS BC in Z; de-
mum per O ducatur OHI ad B A parallela.
EA jam DL. DF:: DM. NO:: LM. CO Cob similia erI
angula DL. M, NCO):: LM ZDH. GO X DH item DL X
HIO = LMXDA (ObDL. LM:: DHI. HO) quareDL. DF::
DE ZHIO. GO RDHhOC CA DEXHO, DEKHIO:: DI. XIIO
COrDH adcog. D E X IIO =G OxDHI. hoc estDE xHIC. LDF K
CO = 6OxDF. . GO X F HI quare (cormuni sublato) est
DEx HO = GO X FHI; seu D F XIIC = GOX ZC. P2-
ret ieaque curram OOO eRe hyperbolam cujus asymprori Z. K
LC.
Coroll, Si rario data (ic requatitatis (CenD M = NO, ) ip(X AB,
C B asymptori erunt.
Sequentia quaedam, quia magis id perspicuum ridetur, AIC
brice monstrabimus.
X. Esto positione data recta ID, in qua punctum designatum D.
Sit irem curra D NT NTcalis ur in ID sumpro quoxiam puncto C, et
ducta recta C N ad polirionem datam lR parallela; cum adsumptis
determinaris rectis m, b; Positisq; DC = x, _CHI = y; CIC
conistunter my J X y = X X 3 erir linea D NN hyperbola; qu
sic decerminatur; TUMaNEEDM, e DO Chinc inde) Pares ipLLm;
_ per M ducacur M L ;ad L K parallela, Factoq; b. m:: m. MC; SIF
MZ = 2 M C
2m m.
ZM, Z T alymptori.
cum per Z, O traducatur recta ZT; erunc
Ducatux enim Z S ad M O parallela, cui occurrat N O in R (quX
_ ipsa Z T seceEIn P ). _ connectatur D V. Fst ergOP N = H C
+ ON - RP. Verum eAM B. M O:: ZR (M C). RP; HOC
M 
CA m.::M - X. RP:
MX.
ersoY
nem, MX.
m M m X
m X X.
adeoq; RC = R P
L. y. Unde PN XMC
Verum C ex hypochesi) eAt my
E18. 43
mn
F m y a. X y
18. 44.