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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 49, page id 797435492:0261
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=797435492&page=261
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# Lines: 39 recognised, mean confidence 0.81
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MX X
ut X g 
l. B C Y. VI.
= = . ergO PNXMG = Z =MDXZO.
vel PH. Z O:: CAD. MC::) OD. ZP. OMapEOpter est
PNXZP = Z QX OD. Unde palam est curram D N N esse hy. F18. 44.
perbolam, cujus a lympTori L. N, L Z.
XI. NotetuE; C xequario sit my = x y =  X X; cadem ha-
bebitur hyperbola; tunc solum puncta C 2d ParteS D M sumUnEuE.
Ouin e si xe quario BIC x y = m y = = X x; purcta C uIETA M
capiendo, proveniet hyperbola, huic ipsi conjusata.
XII. Sit Friangulum B D F; _ linea D NINI calis, ut ducta ut-
cunque R Had BD Parallela (quae lineas BF, DF, DNN secet FI6. 45.
punctis R, C, N) connexaque recta DH; sIt perpecuo D AI prOPOr-
tione media inter RN, NVC; erit linea D N N hyporbola.
Per D duCaTE D R ad D B perpendicularis (secanS ipTam R NV in F)
de sic F HIad D B parallela; rocentur que  B = b; DE = d; F1I
=f; tuM DO = x; _ON = y; Estque d. f:: X =OF;
X fX. Y
unde-
= -= X X -. yy = 2 F C X C LV ,s. DC g F GN9
bX
=DN9. Porro est d. b:: FC. OR: : d --- X.R C = b - ,  Un-
a
de RN = b  , 1 y. Et ided b g-
NO =DN9 =.
2 fx
d
Xe
-+ - y y = RN X
3 - + X X - ) - y y. quareby-
d
4
bX
2f.. B X X. quod SI BONatuE m = = F. ) - b5 erit m y - ∞ y =
M
XX. Unde liquer D NNI esse hyperbolam, qualis habetur in pex-
cedente determinata,
Not. Si angulus DC. N rectus Fueric, eranescente rumf = o erie