# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068196:0503
# Permalink to this reading: https://leibnizlegible.com/page/00068196:0503?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 254r, page id 00068196:0503
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 255v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=503
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000503.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 79 lines, status machine
# Lines: 79 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.

sit Parabola ACC, cujus vertex A, axis AB
ordinatim ad axem applicata BC sit AB, X
et BC, y et latus rectum a, fiet
raX = yy;
GtCB: BP = dy: dy
et 2adx = 2ydy seu dx: dy = y: a. jam CB est y
ergo BP est a. Ergo si sumatur AO, aequalis ipsi a
dimidio lateri recto, erit e centrum circuli parabolam
oscutantis. Cujus dimid Et A visecando A0 in F, erit
F focus parabolae
videamus jam quae sit differentia inter Curvam
Circularem descriptam excentro O radio AO, vel a
et parabolam cujus latus rectum est ra. ita scilicet
ut latus rectum parabolae et diameter circuli
coincidant sit corculica quato 2a Centro igitur
seuAt
radio A OA describatur AE arcus circuli et sit BE
ordinata, fet D, et fiet vD = 2aX - XX. Ergo
chard Ergo BEqu vb + XX seu BEqu + ABqu = 2aX
seu = AE qu. Ergo AE =  2aX. idas id
itaque _ AE chorda, aequatur ipsi BC ordinatae
parabolae
si jam EAE ponatur esse portio circuli
talis, cujus chorda EE aequetur distantiae
foci AF; rem ad calculos redigamus
sit aS AO, 1000000 et AF 500000, et
useu BE, 25000B vit AE seu fiet
seu 25, 1000 jam 2 fiet BE = a
quia BE est BE est =a seu B, hoc loco est a
fiet Aaa = 2aX - XX. seu XX - 2ax + aa = aa- aa
Doeb Xa, 18 E( EB, et 2aX = aa, 13. Ergo
y seu trax ∞. a, B2  B jan 3 = 1. 732050 et
jam 13 = 1.73205080 et X
53 erit = 056602540
erc et AB seu X, erit O. 13397460, a
seu fiet X - a = 8 = = d Y15. A et 
et X = a + LaVis = a, 1 + 3. 872. Ergo AB = a, 1 = 0. 968-
seu AB = AO, ∞. ∞2 8. 032.
Ergo differentia inter
b
B5 ∞B 10
10064 = 0.252 = A2 = Bct
et BC se inter, 0. 25 et 9.252 est 80
3t a Xx si sit BE.
c
0
E
Ve
e
10 fraiet X
5916
25Of 12
=a +a 35 L a
et AB = 84. AO
6000 et AE = 84.31
5000
916
34
14 (21
1004(250
50
0000
90000 = 2. 84, 30 = BC
= BC- 502
5012515
Ak I 6 X 72(301
2
300
300
= +
XX - 2ax taa = aa = L aa
1.000
0. 968
0. 032
(01032
ermo disferentia
inter BE et BC est
1teo so
0