# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068201:0344
# Permalink to this reading: https://leibnizlegible.com/page/00068201:0344?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 172v, page id 00068201:0344
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 173r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068201&page=344
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000344.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 100 lines, status machine
# Lines: 100 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.

a
avv - aab, avv- aac aequanda Bto m quod esse poterit 00 8DD, si
sit avv-aab = 00Z et aav - nac = 73 D
Faciamus V = 11 2m + 123 smn
C = 310) al + 303 Van.
D = 410 tal + 403 san
sint l, m, n p varinates indeterminatae simplices velut . Xt..
vy = 112 lin + 2 112. 123m VIA
Fecimus v 12 Am +nsun
8 = 204 p + 213 iIn
00 = 3id al + 2. 3103 a VIn 004 = 310. 204 alp = 213. 315 ab Vla
1237 MM
3ost an
305. 204 ahp 213. 303 an
2. 213.310303 aln, 2. 24.310. 3 3 a p..
9D = 48 al + 2. H0 4u3a Vn 87D = 418. 204 alp + 213. 210 al In
403 an
4032. 204 anp 213. 405’ an
Ex ratio:, eb 00 ex avo- aab fient 12. Im  - ab = 20g. 310 Lp F2 . M0. Josla 2. 213. Mo Josabm 2. 20 9 3o totap..
nauos
204.303 np
 9.  Sed alteratiam ope signt ambigui
aequatio l
123t nn
ob ZDV ∞ avo- aac fiet neum
fictentrrundae homoeopto seos causa melius
=ac 2204. 40 lp + 3. 213. H0. 403In
12) 2. 213 (310. 303-410. 403) I + al,:9 204 (410- 310)  + 204 (405 - 305) n. Et ita habetur p sine m
ut tollatur litera m, et fiot  20q (403 = 309) b
sed in habebitur componendo aequationes 1 et 2 addendo in unum, fietque adeo
m 20+204 (210 + 316) p + 2. 213 (310. 303+ 410. 403) ln + ab, :, 2. 112 l +2. 123 n
ubi pro p posset substitui valor ex aequ. 3. sed quia alium postea inveniemus commodiorem velorem ipsius p
204 (+03 + 3031) n
Ex irra (ob 90Z = avv - aab fiet 2. 112. 123m = 213. 310 l + 2. 204. 30.303P
eo differemus.
tiona
libus
213. 303n
ob477 = avv -aac fiet 2. 112. 123m =~ 213. 410l + 2. 204. 410. 43p
213. 403n
p= 213. (410 - 315)l, :, 2. 204 (310. 303 - 410. 403
213 (403-905)n
Et aequationem s subtra hendo ab
aequatione 6, ut tollatur m
habebitur p, et fiet
is valor ipsius aequetur priori (minus simplici) ex aequ. 3.
compendio 410 - 318 vocetur 115, b.c. vocetur g
403
03 
et fint 4 2n 20+ 61 3 + 2. 304. 615 ag = 43. t. ndIl 4 2.213. 207. 118. 705 In
213. 20. 705 Mp - 4. 213. 2 +. 6134
si eset fieret 613 = 110.,05 seu +613 = r2o 613 = 7 10. 705, seu 310.305 -2 310 41. 305.403 =
410 403
41. 403+ 310.303-310 93- 305.410 sou 310 403 + 303 410 - 2. 310. 210. 303.403 =0 seu
310 403 = 303 210. Sed video id non licere. Nam C et D haberent inter se rlationem
constantem contra intentum, itaque .718. 703 - 2.613, erit
410. 425 1 310. 303) - 310 403 303 418  (2) 318 30 (2) 410 405 + 4. 310. +o. 303. 403
Ac proinde ex equ. 8. fiet
403t + 303t Mn = 2. 463. 303Hn (2. 310.303, sR. 315. 403 In (9415. 403n
seu + (10 + 31). Il + (403 3.3) un (P(E2) (310. 303+. 410. 40) In  2. (310. 303 + 410. 403) ab (+ C
alet esse -
=(2 (2) (10. 303+ 310.403) ln
Rursus ex 5 et 6 in unum additis, fit M= 213, (305 + 405) N
213 (403 - 305) (310. 303)
410. 907
(+318. 310.303 P 318. 410. 403 + 410.310. 30 418. 410. 403)
310, 310. 303 310. 410. 403 +410. 310. 203+ 410. 410. 407)
(4305. 310. 303), - 303. 410. 403 + 405. 310. 303 (= 405. 410. 403)) n
F303. 310.303) = 303, 410. 403 4 403 310. 303 + 4032. 410. 403
4. 112. 123. (310. 303- 410. 403)
( 310. 410 (410. 303- 310. 403) l. 4 303. 403 (403. 310 -410 303) n
id est  L3, 310. 410 (410. 503 - siv. 403) L + a  303. 403 (103 3 - 410. 303) n, , 2. 112 123 (31a 303 110 4to3)
 id est  2.12. 123 (310303-410. 403)
aro 387l. 400 5 205) un +. = (316. 105 0. Aor. ) In 4 2 (30 303 o. 405) (ab tac)
213. (310 4 410) (310. 303- 410. 403) l F 213 (303 + 4032) (310. 313 - 410. 403) 12
M = 4. 112. 123)
112 l + 123n
(i0) 213. (310+410)l + 2. 204 (310. 303) p, : 4. 112. 123
Et pro p substituendo valorem ex aq. 7. fiet
M = 213. (418.  310. 13 )1310. 303)l
seu me are
(11) 213
4. 10403..
213. (a1St. 315)  + 213 (410. 403 5 41 3. 1054 310. A0 7 310. 305)n F 4 (310. 305- q0 105) n 
jam novum valorem ipsius p repertum in aeq. 2 substituamus in aequ. 4. fiet
(4052 3032)2N 213 (405. 410  403. 310 f. 393. 410) - 305. 310)
+4. 310. 30375 1122l seu m 9. (310. 303 - 410. 403
-4. 410. 403) 2 123 n
1410.403
410II+ 310tll8 - 2. 410, 310ll 4 2. 415. 405)72. 415. 303- (4) 316. 305 b = 8. 318. 303. 410. 403 431 0.2o3 () a
Aequando valores psusd P ex aeqeu 
+ (403 + 303). MM
et pra p abstitato
40. 403)
2∞B aG =   2 ( (310.403 - 303. 410) En 4 (~) (410- 316) I(Y) = (e 0 110) (t05. 305 7
=4 ( (310. 403, 303. 410) = (.L (310. 363 - 410. 903).
2- 2 L) (310. 303- 410. 405) l + (+ (40) 509) nn 213
ac
ebbe t
d