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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 136, page id 797435492:0382
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d ui ea b
in int
Series quarta.
1= 1
a_ -  CC == n n.
a3 -F CC a = v3.
at . CCa a = nt
Sit recta indetinite PrOtenSa AH, S huic perpendicularis AD.
hiat autem angulus R A HI Pemirectus; cum urcunque ducatur (Z R
ad AD parallela; _ Facto AC. A C:: AC: ZR; Per R intra
angulum D A R describatur hyperbola R Z K; (IHE denNIO CUEYX C L L.
A MM, AN NealeS, uE inter GZ, CK snc media C+L, bimedia
CM, trimedia CH; ha propoliro deserrient. Nam si AG (vel
C2) dicatura, erit R = = a ) - -, _ 6L9 = a a -] 66; 8
OM cub = a3 t cCa; eC N94 = a.  cCaA.
Noto
P. Delignantur radices, ut in praecedentibus, posita AF. =n, _ ducta
EF ad AII parallela.
2. Si AP = A C, erit P Z ad hyperbolam R X K ordinatarum mi
nima; unde s A F (vel n) = PZ; nulla dabitur eadix in primo
Gradu.
3. CUrVa C LI. est hyperbola aequilatera, cujus centrum A, semi-
axis AC; quae  ordinatarum est minima; alioquin (I ME C, Cem-
per una vera radix habetur, et unica.
4. ReliqUx AMMI, A N N sunt hyperboliformes ad intinitum
excurrentes; unde semper una vera radix habetur, neque plures:
5. Si tuerir Z a = ZY Z; YC == ZYZ; XY = = L R, e per
puncta a, 6, 2, traductae concipiantur hpperbola Chaberites _ ipsee a-
symptotos D A, AH) a n, 6u, vr; crunt tx ipsarum currarum
C.L L, AMM, ANNI asymptoci. (Similes etiam asympeoti con-
veniune lineis posthac describendis, quanquam de illis conticeamus.)
C:. Fdinc in secundo gradu a )
2an; in terrio a)
-- = B3
in
ab. - js hue
E18. 2YI.