# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/175906937X:0317
# Permalink to this reading: https://leibnizlegible.com/page/175906937X:0317?run=74
# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 293, page id 175906937X:0317
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=317
# Source image: https://digitale-sammlungen.gwlb.de/content/175906937X/jpgs/default/00000317.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 48 lines, status machine
# Lines: 48 recognised, mean confidence 0.87
# 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.

L. T B. II. C A P. III.
diametri tran(versae sIC D = bb, erie quadratum lemi-secunde diz-
mecri ∞ + a a = = bb. AEqui cum F B live BLI. L IIF SIE∞ = a + =b,
e BG sive BII -- IIG∞ = a = = b, eric quoque rectangulum
FBC ∞ = aa = = bb, nempe  quadraro semi-secundae diammetri;
Cire, ut Veceres loquebantur, aquale quadranci higurx ad trans-
vertum axem factae: ideoque puncta A e B ea ip Ca lunes quae vul-
50 oppolicarum FIxperbolarum Foci lire CEmbilici nuncupaneur.
Clnde apparet, ex pramissis recte interri, quae sequuntur.
Corollarium 1.
Si ab alsumpeo urcunque in LIyperbola puncto ad
ucrumque CEmbilicum rectx duCanEUT, CATUM MajOF
minorem longitudine erantrerli axis luperabit.
Fciamsi veritas praecedentis Corollarii ex antedictis omnino
constet, cum tamen illud a Veceribus, Recentioribulre, quod
Sciam, non nisiper multas ambages lonsaque difficilium Theo-
rematum concatenatione hactenus demonstratum sic: id ipsum
hic demonstratione unica, e quidem breriore latisque simplici,
aliter oltendisse non inurile Forre judicabitur.
Ectoisitur Fyperbola qualibet CC, cujus cenerum LI, Eran(-
verlus axis FG, atque CEmbilici A _ B, adeoque rectangulum
FBG ut _ C A F semi- secundae diamerri quadrato ae quale. Du-
etis aurem ab altum pro quolibet currae puncto C ad puncta A e
Brectis C A, C B, ordinatim ad axem applicetur C P, Hacque ut
quale rectangulum F FIM. UInde cum (IC =, uE
Scabt.
HIFgadO AF, ita F F C ad C Fg: erit quoque, per compol. 12-  per 10
tionis contraria, ut
TIFgad (HIFg. I O A F, id CAt3, 2d) FIAg; itA P P G ad F F. C candi.
 C Fq; adcoque + ut
FIFgad HIAg, ita (TIFg. L FFC SIVC 5) HIEq ad HI Ag - denrium ad
FF C, F C P g. EH autem quoque 5, ut
TIFqadTTAG, icaFTFgad HIMg. OuocircA 7
FIMg∞ HIAg. L FF C5. L CFq; hoc elt, addito utrinque LI F g celentes ad
SeuHIOq. erit
FIM 12 quinei.
ex Byeoth.
Primihujus.
3per 6 se-
+ Cum SIEVE
un2 antcce-
VMaM COn-
SCg., IFa 0-
MDCS anTC-
Omnes
conseq. per.
5 per 6 se-
curdi.  ex constructione  per 22 sextt.. 7 Per 9 Cg YL quinst.