# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068074:0032
# Permalink to this reading: https://leibnizlegible.com/page/00068074:0032?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 2
# Folio 16v, page id 00068074:0032
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 17r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068074&page=32
# Source image: https://digitale-sammlungen.gwlb.de/content/00068074/jpgs/default/00000032.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 65 lines, status machine
# Lines: 65 recognised, mean confidence 0.82
# 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.

si
X: a = (adz: 3
et y: a = AZ: V. siet
dy: dx 2 dEH Z: V Fingamus: (dz: V de  de et
fiet dZ dv: v + Sdz. v ddv = o seu (dz. v= dz do: xddo
sed ita posten in aeg. data res reducitur non fautum
ad dv, dZ adv, ds, sed ad 7, n, du, az ady, adzu
quid sic sic:
X: a = Sdz: Z
2)
et y: a = sdv: Z
dy: dx 2 dv: dz sit s Sdv: Z dZ L de. Ergo
dedque: Z = - sdv: Z ddzue sed ita in eandem relabumu
difficultalem, nam et Z ad est. Itaque via paginae
phaecedentis melior
pro calculo lineae isochrone. Grave
escn i bdam tegtemdi unformiter ucvedere purto A
BY BC7.
AH, b. AC, E
sit Rda ydy + rAx: ytr = a Sop + y: Fa b.Y. seu
 S et reducento omnia ad y. a,  et Y: a, et dyrdr, siet
y: a dy: Y + r: a: Syia tr: 4 = S1 + dy: dr: Y b. a - r: a
seu (2) y: a dy: dr + r:a  1+ dy: dr. y: a + r: a : b: a = r: a
Sit r: a Sddz: dzu y: a = ( ddz: dv dy: dr  dzue: dv
et quia
progressionem arbitrariam assumere licet, fiat E ad Z. d dv de et dde =0
(12) V.a
Ergo filtt Sadzue: dx dev = 0 seu Sadz: de  aaZ:  dv= ua
s
per 6 et 11
ont
Aequatio 4 ponatur explicate c et brevitatis causa pro3 Sia, y: a, dy: dx pune 5, 67
e fiet sGri e 66.77 + 2. 6+ pone 4, 5, 6, 7. et fiet
6.7 + 2.5,6.7 +5= 62+5 4+ 5. 7+6.7: 4-5 seu
4.6. 5 +2. 4.5.6.7 + 4. 5 - 6, b. 7 - 2.5, 6.7 -5 = 6 +5 +5. 7 +6.7 Et differen
C14)
tiando fil 4. b. 7. 2. 6dy 4746 + 2. 4, 5. 6. d7 4 5. 7. d6 +6.7 d5 4 4. 5. 25 - 6.7 d5 - 2. 5. 6. 7. 6d74746 - 3. 515
( 2.6d6 + 2.5 d5 +5 dy + 2. 5. 7. d5+ 6 dy + 2. 6.746
vel si placet, quaeramus valorem ipsius 6 ex aequ. 14, et differentiemus tollendo 62
fiet aiquao  (16) quam differentrando tollatur 6 in aeq. 17. ubi erit at, 5. ddv, daz du, d
unde rclatio inter dZ et lD qua dploria 9
Itellatur 5 per aeg. 12 et (irl aeg. (18) ubi du, dZ ddv, ddz.
caeleum si exaeq. B
tollas 5 per aeq 12, habebitur in ea ipsius sddredu seu ipsius yra vator per 1
laeterum ty aeq. 13 gatur y: a seu 6 per 5, seu C: et dq idy n aeg. (10) ubi sbti
sollendo dB, ope aeg. 19. fil aeg. (20) abi q: a per satz: dque et cognata a Z pendentia
compendii causa i+ dy: dr sit , 8. et 8b. a - r: a sit 8g. et ex aeq. +
sed aeg. G. etiam Y: a
Ele)
mer
6reibE fiet s g F(6. 7 +5 = 8 5 + 62: 9 seu 67 + 2. 5. 6. 7 +5 = 85: g + 8. 6:9. seu
(16
612. 16 ru - 12411) 6. 6. + 2. 5. 7. 36 =  5 -9. 52. t. Ergo  8∞9. 9.7- 8. . 8 + 9. 7 b2. 9
est
7) =8
72- 8. A
sit ditluratiendot ta de compendii causa sit n- g = 10 et fiet
6= G A.g. 10+ 7.9 -7.9: 10 seu d6 = 10d5 = 5 d1o (8- 910 + 7.9 45 B- 9 d0 + 10 d8- 9. + 2,7. 9. 1d9 u. 9d7
10. 10
et do = - d5 et d10 = 2.9. 9 d7(7.7d6 - dy. 5. Et ex11, 5== dv ddque: dzddv 7 = d2. dv,
et
8= 1+ dg: dv 9 = b: a - lvadzu: dzado 10 = bs b: a 1Z: v - dz adZ: dvddv
L10 = 2b. a dy. dv - dd2: ddv dv olaze- dz. dav: dv -  dd qdq. de  dd z. dv + d zddv. dv, 
si faciumus 2bia 1 fiet deo = 1. du
b = FiLrII - 1V