# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068198:0329
# Permalink to this reading: https://leibnizlegible.com/page/00068198:0329?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 165r, page id 00068198:0329
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 164v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068198&page=329
# Source image: https://digitale-sammlungen.gwlb.de/content/00068198/jpgs/default/00000329.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 103 lines, status machine
# Lines: 103 recognised, mean confidence 0.78
# 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.

Assumo y: a = loXX + 12Aa, 1, 20X + 22 aa
axa  12
Ita per 1 et 3fiet
Explicentur y et X per a
330rV + 31RZ + 310 av f300aa
420 vv + 4uBZ qu ap + quoa a Et sit
(4) 10. 510. 510BV + 12, 6016012Z
20.510.510 bP + 22801. 6012
quos duos valore) ipsius 3. aequando fiet
aequatio nova (5) In qua possunt, occuriere  4 13Z 17. VBZ
Tollamus v, VZ, V, ita ut V non assurgat altra secundum gradum
NrZ, VZZ, BV, ZZ 
ob V fiet 1G2d. siosto = 10 ga  =  10. 420 - 29 320=0
ob V fiet
+0 (1. 510. H - 255103,0 31 of . 10. 410 - p0. 310=0
persicusto. TH. 20r 5id h0. 3H aoseu 10.4IL- 20. ao
Ponro comend Cssa ((.1100 Porro compendii caussae 
Ob VZ fiet
pro +1. 400 H12. 400 +10. 410 +k. 4
-20. 310 = 2. 40
20. 300 -12, 300
ponatus occ. 400 200 700 090. 410 (210. 410
uibi tamen ob bes aegu. quibus
Si +11. 400 -000100
+10. 401 +L. 401 +1∞. HI +12. H1 410. 20
220. 301 32. 301 f2o. B11 ∞2, 311 = 20, 320
001401 troj 40 oll. 4i1, 2I1. 411 020. 4
 infra certocasu ey orp 
v, v Z destruximus fit so20 = 0 et 010 = 0 et o11 =0 (∞) m atabeb
Aequatio ergo exvaloribu, aqaionum 2 et 4 aequatis habebut hanc fornam C DV + D aV + 8 a = 0 
 ve
ut sit coefficiens lpstus 2
et erit O = 6(. 2. 400 Z Y S10. 0B1 ABI a 2 tactoga L
512602.402.
D = Sci. 211. 4117 + 5o. 218410aZ
uit comprndio C- br t2oZ Z + o,. qolazu. +. sro. quoaa D. aui +. B0 404Z Z G = Bor. quqe 0+ 101 Z +Be quodni H
Ex aequ. 8. fiet V
+1Cg-40E
 
quaeramus valorem ejus quod vis
continetur, ex plcande O, D1Z
eritque ((DD - 404)7 ((ed1B1. 4 1 Z , 2. B,B BH. o ma a aBa  neE
Lagbo. Be. 402. gd .d a J. 701. Bor. 401.902.. orB tor 162...
sit datu fermula generalis sundata:
  v qoyt.    qu oe a tt  ato in. 4p 1 0080 horria
4. 702:B q.
xmazanaaZpaZ q coincident termini ultini seu absoluti. o Z fit 500. B0o t  100. do. Li S0. B0v. 401 a
identificetur Formulaesvinculo inclusa. ex ob ZZ et 3B, seu per Requationem inter duos cbefficientes ipsius ZZ, et aliam
haec multiplicata per 4. 60. e. 40 o Ha tar intu et en elidisuts I Acpliar coifficientium issuus ZZ
multiplicata per a). Ites positis
inter duo) cdesicentes ipsius Z, habebamtur valores simplices ipserum 420, et 402
pps qui in pice duabus aequationibus nec in se atte invicem dicuntur. Superest
unea aequatio snter solfficientes insios Z+, in qua substituende valores repertos ipsorum 400, 420 402
restabit aequatio un solvenda, quam segredientur 401, 410, AC, inqua bae incognitae ascendent ad seuodim
tradum. QGortasse ob abundantam arbitrariarum seu in Quate incertarum romui p, nova hypothesin com
modam assumtam ad unam vel binas sempliles reduci potast.
Et plarimum contrahetur calculus,
si in desa formala abesset qt seu esset  l =0, ita enim possemus facere Si1 = 0 et 802 =0 vel
et 202=0. ita tribus tantum indigebimus aequationibus
comparatilii formularum, eaeque etunt omnes simplices. Hunc orgo casum, ubi abest ut
quo quod eodem redit, 21 =0
nam quia jam posuimu  aturae sentrarum absolvere suffecerit. Et pervrode est ac si intio sentim praeter Temino
V, V3Z, V, destruxissemus 7t, et 7 3 et _ manente C= I: 220. 43 Z +510: 001. 1ga Z + 510. 000 70 a
cot. 002. 402
Et ex ag. 10 fiet
S(DDr 4O8) = Z(4. 6018,0. 401, 120423 + 6∞6,0. H0. H0. act Z - 4. 700. 6d. 100. 431a  - 4. 100. 606. 400 400a
fieret 3. 601. 210. 410, 22 et = 601. 201. 401 73 + 601: 200. 400aZ2
4. 102.801. 48. 402. 1. +)1.601 401. 401
sisdata tomula gererdli ana spaus as a  nultilicetur per (. quo doo. 4o oo, podibi poriori identisicanda
L (- 4. D V00- 400. Vuom7 - 4 Jo0. 800. 40o Jas na ZZ- 4. Hu Bov. 4. 400 parz 4. 100. 600. 400. 1x at )
Ex aequatis cz, fiet 801. A0r a500. 409p. et t Ex aequatis Z3 fiet (pro So1 401 a spostituto prius vatore invento
fiet 820 420 + 702. 4= 500. 400 m Et ex aequatis dZ Z (pro 601. 40ia substituto mis valore invento aequ. 1. Hiet
810. 810. 40. 410a (4  trop. 701. P00p 500. 400. 400 p - 4. 508. 820. 400. 429a f 4. 702800. 400. 402 a -- 4 7u0do, 1o 3uo n
in qua equ. pro pror 420 substitu chod ex aegu. 12+ Vulorem 500, 400m - 502 AP, ip, fiet
6102610. Aiv. qa 4 501 (Pp. n) 600 ita
100 4oep 4600 100 5 40ot p: A a  f 4. 6go. 100. 5od tora -  b
G  HIS agp beS SoI. AB dip. 1 4. gdo so01do (Ga
et eadem ratione in aesp. 13 pro 502. 402 ponende ex aequa se vatorem qu
 p
Eb fiet 403
Et ex aeg. 13. erit 826. 420+ f02. 462=
13: e 609. 40d. 601 aa p (502 - 500)
nm seotdum en per stad, fia tuiau 8B a1B. 2 q0 =
4, L. sp. 400aC
700Bo anp + folBop
=0, et habeatur aeqa si SH =  Si sit 80, =0 et 700 =
quos duos valores aegnanoo tur bBio. Ba 10 aap = 4. 800. 405 (700 Saa
 uae
hadou y
inii indeo non licere
factit 2140 seu
12. 41- 22. 31120
senlo. 4u - 20. 31 =0
firet 10. 20r v2. 17)
quod fingere licet, quaecum
st ratio 400. xd 3diter
+id 4uD rattor +. 102
22. g1B 202 7 30
278. 20 802. 182 . 102
fiet 610 614. H0. a 
W. 4i0.  i 900av  Bo1a X.
 ustiit dilus
ponamus 0 quud in data fotmula facia effici potest