# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/175906937X:0338
# Permalink to this reading: https://leibnizlegible.com/page/175906937X:0338?run=74
# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 314, page id 175906937X:0338
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=338
# Source image: https://digitale-sammlungen.gwlb.de/content/175906937X/jpgs/default/00000338.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 40 lines, status machine
# Lines: 40 recognised, mean confidence 0.84
# 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.

374
E L. E. HI. C. U R Y A R U M
SeUI AM SE  = Parameter que sectionis   erit rectaner.
lum sub Parametro de recta DO contentum ∞ d X. Cumque
idem illud rectangulum aeguetur quadrato applicatae OF vel
. OBE, id est, Z7: eric;
73
∞ d X.
Octaro calu, ubi, manente rerrice in puncto D, diameter
est in recta DP, quoniam AD Peu B K est DC, _ R P ∞=
erIt PEuna (Sire BF - BK -L R P) ∞y -- c + =, _PF al.
cera (sire BF L BR - KP) ∞ y +c- =. Cum que Cocatu
altuumpEa (IC PTOy .+ = -c vel prOy -- = FC: CricutraquC
PF ∞Z. POTrO CUI DP SCU AM SIT ∞ =, aC PaLaMeteF ∞ =
3
eric rectangulum sub ParametrO _ reCtA DP contentum D d X
Cumque idem rectansulum ae quale sit quadrato ucriusque ap-
3. Plicatae P F, hoc est, ZZ: eric quoque ZZ ∞ d X.
Nonocalu, ubi vertex est in puncto L. de diameter in recta
2Ovel OP, quoniam, uc Tupra, OF est ∞y -  - c, atque
OBF∞y - = FC; aC reio PE una ∞y - c- F =, aC P F al-
cera ∞y. + c - =, siE que eo ca(u Z a NUMPLA PFOy 8 = 8c:
erIEOE, OBE, atque utraque P P ∞ Z. PECUMDO AUEDP
seu AM lic ∞ =, at que DO TCu AN ∞ =: erit OO vel OP
Choc est, obserrata juxta Regulam triplici distinctione, DO
vel DP B D, atque etiam () D --DO vel DP) aequalis
ex
efs
 E a d atque etiam
ad
.UInde si eadem O vel OP
mulciplicetur per Parametrum x=, erit rectangulum ∞ dx
8 ff, acque etiam ff- d x. Ouod quidem rectangulum cum
aequale sic quadrato applicatae OF, O B F, aut utriu (que PF,
D: hoc ett, 7Z: erir quoque Z7 ∞ dx 8 ff, atque Z7∞ ff - d X.
Dux quidem omnia lune, quae hic demonstranda crant.
Ouod aurem ad aequationes superioribus norem casibus
conversum correspondentes spectat, ut linea Parabolicae de-
Ccribaneur, quae sine Loca guae lita: Poliris iildem, ut supra, per
punctum