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# Piece: https://leibnizlegible.com/api/records/536/text
# Catalogue record: 536 — [Aufz. zu Differentialgleichungen]
# Incipit: AB, x BL, y AP, v PL, p. AT t. TL = θ
# Date: 1676
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=536&katnr=58113
# Work: https://leibnizlegible.com/work/00068102
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 7
# Folios: Bl. 30r (from the shelfmark LH 35, 8, 7 Bl. 30r°): 1 page, canvas 15, page ids 00068102:0015 to 00068102:0015
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068102&page=15
# Lines: 52 recognised on 1 of 1 pages, mean confidence 0.80
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# 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, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 30r — 00068102:0015
# Source image: https://digitale-sammlungen.gwlb.de/content/00068102/jpgs/default/00000015.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 52 lines, status machine
BL. y
F L = 6
vV - 2VX + XX + yy = pp
u
++2tx + XX F yy = 0b
Exelis nalet tata relationes inter Y et p seu inter AP, et pL dari
miror
et X dx + y dy = vdx  t ex Sed hoc non pcedit
ax: du =  Y: B- X quod verum. ~
n
+X: y
sed x. si idem tentemus in ot. 2. non succedit quod miror
nam sit X Xdx + ydy ++ dx =0 seu dx: du =. y : t -x sed
loc est falsum, un potius dx: dy = F =x: y. Inde ergs
n
ex VV = 2.YX + XX = p,
sit aquata vdv- xdo = pdp
Hinc si v - x daretur ex p rationaliter dabitur relatio inter AP
et PL per quatraturam ratonalem, qua inventa atique deinde dabitur
Lex AP. seu intersectio circulorum. Sed alia ratione res sil
sed in fallor per quad raturam non rationalem.
Nempe
si Bp seu v - x datur ex p,  fiet _ relatio inter ydy: dx seu BB
4Vu pL
et inter yrdu + xidx quoe etiam reducibilis ad quadraturum
nempe sit, V - _ = pp: a (exemplicansa) fiet cx aeg. 2. do- dp: p.
seu V ap: p
s
a
(1)
sit sed ex eq. 3 et 4 fiet ydy: dx = yy dyta
o
seu ax + 2 dg. ax + a0 si L3 quai + di. sen dx- andus t saarg
(10
Ayy
seu dx =nd dy + (raa 7y du
2
3
29
Agy
Generaliter v- R . p. sit do = p dp: pre seu v = spap: pe
re
at si  ut ex aeg. 3 et 4 fit ydy:dx = y say + dx. dx. unde
evolvendo oritur aequalus  quadratura formulae radirem quadra-
licam habentis, quae tamen habeti poterit aliter er quadraturam rationalem
ex ay. 12 Hoc est magii momenti Haec inet hobus videtur valde subtilis
differentiali
liquod imperfectum est in nostro calculo V. 9. non ex hibet
quod variantu seu geminalis x et y tamen ipsae X + dyg: dx sunt
liaplices. Item quod contra licet facere x simplices G eminatis V.
cilicet horum perfectio aliquando pendebita Geometria situs.
b