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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 46, page id 797435492:0258
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l E C Y. VI.
DH. L. N -- HIO:: L H. LB::) LHI. HIR. CritDH X HR =
HOXLH; hOC CADL. XHIK = L HKHIR = ROXFHI . IIR
XL IL. UndC CTIED L XHIR = ROXL HI, vel ZIXF D = ZK
XX O. ergo constat lincam ODO esse PTyporbolen, cujus ASYmpTOIr
7. A, ZS. Breriuis hoc ostendi posset, producendo rectam NI LS.
NNam est DS =D M -=D O FOM =N M F OM =ON. Simi-
tex quartam ec nonam brerius demonstres licer.
Ouinimo siM N ad D C quamris eandem perpetuo rationem Dona-
cur habere (pura datam R ad S) etiam linea ODO Fsyperbola exic;
Elempe (2 cumm Hat R. S:: L B. LZ; _R. S:: DL. DF; _ per
Z ducatur Z S ad BC; ac per F cransear R P adZ A parallela, cum
ZS conreniens in Y; Crune PR, ZS dictae FTyperbola asymptoti
quod jam sufticerir innuisse.
Flinc intranscursunoro facile contici Problema (quo problematum
confectionesista Archimedea, as Vietea ope primae Conchoidis peracta,
ad Sectiones conicas rediguntur) Pex darum punctum D rectam lincam
ducere, sic ue anguli dati AB C lateribus intercepta ductae rectxe pars
aequetur datxe T. Nam descripta hyperbola OBO; centroD, in-
terrallo datam T xquante describatur circulus POO hyperbolam in-
cersecans in O; e producatur DON; Herq; M H ==BO =T.
Modus aurem hic generalior est, e concinnior eo, quem in Opticis
eradidimus.
IV. Sic angulus A BC, et punctum datum D, sic etiam linea O
BO calis, uc per D ducta quapiam recti DN, sic anguli lare-
ribus intercepra MH ad recta BC currique OBO interceptam
MO in eadem semper ratione (pura Z ad Y; ) erir linea OBO
hyperbola.
Ducatur enim recta DL ad CB parallela, ipsi A B OcCurrenS
in L; secenturque DL, BL punctis F, F, ut lEDL. DF:: X.
Y:: BL. BF; tum per F ducatue recta FR, ad B A. SC per
F recta FS ad BC Parallela; concurrancque rectae PR, FS pun-
etoZ; denuo per punctum O ducatur OHI ad A B parallela. Jam
ob DL. DH:: LN. 1O:: LB + BN. HIO:: DE X LB
. DF X BN. DF X HIO. ItEM DLXRO = DF X BNI
(namDL. DF:: MN. MO:: BN.KO) _DEKLB =DL
X BF (obDF. DL :: BF. LB;) exItDL. DH:: DL X BF
= DL X RO. DE X HO; hoc eADL X BF L DL X
RO. DHx BF. V DH x HO:: DL X BF + DL X K O.
218. 38.
Ei8. 39.
E18. 39.