# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/797435492:0344
# Permalink to this reading: https://leibnizlegible.com/page/797435492:0344?run=74
# Title: [Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ (shelfmarks Leibn. Marg. 0; ZEN Leibn. Marg. 0)
# Folio 110, page id 797435492:0344
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=797435492&page=344
# Source image: https://digitale-sammlungen.gwlb.de/content/797435492/jpgs/default/00000344.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 33 lines, status machine
# Lines: 33 recognised, mean confidence 0.83
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

21O
∞18. 26C.
E18. 167.
e F C Y. ZI.
d  ar da sn
LULLe
et instirutum sit particularia nunc aetingere.
 L. qualibus lane haec generalia consequentibus, admodum pro-
Clrerec cursidum Peess compinsere (amico tamen morem se-
rens dr s ceen luorexam ad Circuli T angentes Secdinos,
speclaman honnulla, perasue de lupra poliris emersentia.
EE
Ie demum et (I
Praeparatio C ommunis.
Fsto cirtuli Onadrans AC B, GUAM LAnSANE reCtX AHI, B C; 8
in productis HI A, A C TumanEuE AK, C P lingulae pares radio C A.
e asimptotis A C, C Z Per R descripta (IE FpperbolaKZZ; asymp-
totis BC, BC per F h, perbola L F. O. Sumatur etiam in arcu A B
punctum arbitrarium M, per quod ducantur recta CMS (tangenti
AHI OccurrenS in S) rectaM T circulum tangens; recta MF L ad
BC parallela, recta MP L ad A C parallela. Sit denuo recta a C x
qualis areni AB, ex ap arcui AM; _ recta ay, E u _ ib rectae a6
perpendiculares; quarum a y == A C; f E == AS; pb = CS; I a
MP.
I. ReCta C S aqUatHE RCCEX F Z; adeoque summa secantium ad
arcuns AMI pertinentium, de ad rectam A C applicatarum aequatur
spatio hyperbolico AF Z. R.
E.C enim C F. C A:: (C M. CS:: ) C A. CS. adeoque CF
XCS =CAG. IrEM CFXFZ =CA X AR =C A g. ergoC S = FL.
II. Spacium auE (hoc est Smmmatancentium in areu A M ad re-
la ap applicatarum) guatur spatio hyporbolico AEZ R.
PAFet ex hujusce Lectionis 9.
FI5. 16,