# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068199:0343
# Permalink to this reading: https://leibnizlegible.com/page/00068199:0343?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 172r, page id 00068199:0343
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068199&page=343
# Source image: https://digitale-sammlungen.gwlb.de/content/00068199/jpgs/default/00000343.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 77 lines, status machine
# Lines: 77 recognised, mean confidence 0.75
# 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.

ydy = adx - 4 X dx
dx = ydy
a x
XX - 29X +94=
 yy +49, et
q qux = 
qy Lgy
seu
X= q f99
yy
y= R2aX = a XX
sit Ellipsis A BF cujus axis AI. Centrum
in ejus medio C. duo Foci S, F
FL semilabus rectum a AC, q
SL + LF = A 24 Ergo SL = ge29- a
FF Et SL2 = LF = SF
V
= 499 4gataa aa
ergo SF = 2199 - a9 vel si SF sit f
fiet 49q - s,: 49 = a seu a = 4 - (: 49)
seu differentia 242a = f: 29, seu differentia inter latus
traus versum est recte seu distantia focorum est media
proportionalis inter differentiam lateris transpersi et
o recti ipsumqus latus transversum vel latus rectum
truusverium
es differentia inter latus rectum, et ipsi nte
latus transversum pilateri transverso, distantiaque focorum tertiam propor
et
et ax= a-as ationacem.
Honale
strea AI
et . ax = a 1 21) Area in Ellipsi est sit AB, X et PB, y, fiet
Vaa = qy
sx
AdB
yy - 2aX - = Xk eritque area ABP = (rax-xx dx
SA
sut s qu- 2x Etu A5
sa est
ACA SC = 1
qu yf+sy dx, et quia ydus= ax quax quaereus  per y
XX . 29X +99 = 4 94 - 2 HH fit X = 9 - Y9q - 9 H)
et x = a - 3gg - 9 xX = a - Yaa = = XX)
ergo ydque = (adx = adX H raa -  Hy Ax seu de- Idy: saa-  yy
Angulus exprimatur ASB exprinatur per rationem SB ad. BP, seu
4+
S
Area vero
2 (9+ =
qtas seu SA vocetur 9 fiat 9 - X: y= Z: a et E(g - X) y + sydx =coa
quaeritur relatio inter Z et co. Tollatur y fiet y - X: Trax- A xx = Z: a
et L(9. X) rap -  Xx + (Scax. a XX c) = coa prioce mod. Ex priore
aequatione habetur
2. fel enim g9- 29X + XX :, 2a X - a xx = ZZ: aa
ZaX -  XX = g. X, a: Z p
et
fint Z(99- 29X +XX) a. Z) + seXa: Z dxida
sed (g- X)) aa = 2 aX ZZ = a XX Z
+ggaa seu XX - (daa +2
la  2Z
aa F a
(l Cait a 7417
e
X
sen aaXX+ a ZZ XX = 2aa9X - 2427
+
paq
sen XX - 2 a c 
aa ta
aagu aat qu
aae (4 au + 4 2
aa +.44
s
aat
aata aatra
(l lang + a35) daages an
1