# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068198:0147
# Permalink to this reading: https://leibnizlegible.com/page/00068198:0147?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 74r, page id 00068198:0147
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068198&page=147
# Source image: https://digitale-sammlungen.gwlb.de/content/00068198/jpgs/default/00000147.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 75 lines, status machine
# Lines: 75 recognised, mean confidence 0.73
# 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.

er
re adhabitissemus
(-D 1da  30n = 1310=
10= 13n + Ta 2, : 1310. seu +13A1. 13 na = + 1310l 2
1o C
13Hla
+aQ: 13
1320. 13n1a = 13n0la)
4t +1311. 13F0 Z +1310 a Z
1310,13H1
F13NOra (
310 - 2. 1310. 13X1. 1310. 1311I = 13A8Aa 2_ -2. 1310. 1310aarq. C
13II
= 51.60-50167
13 nopa
in pro 13Al. 13M0 - 1310. 13MC ponamus 13ApI et fiet
1310a44 = 13A n1 = 2. 1310. 13 10 a a4C, seu
1310 AaC_
4
Paa 2 2 (1) 2. 1310. 13n0 a a 40 + 13A n1fC: 13. (n. 1319 a 2t = (9. 1316. 13(
aaO
2an +2 14. 1292aamm
es
13am
2
a
1310 a
+2. 104132. 337aM 4 1a
+
slu
q
s a
3ot(
 = 2.1340. 1340 aa ZO . + i3 KnD - 2. BA Nr 1128 aY = 0
131OaC)
nI + 2. 1320a4 +2 13 n0 ac possit aequari quadrato
40
y = 13n0 aC aequ. radici hujus quadrati multiplicatae
dem quod cum n, faciendum cum II, fiat ergo
4
0 a2 -2. 13 (n0 aO = (13A n 12 + 2. 131 nc. 100101 a a 1000ia
4
10at 2136 a ( = (13XAN) + 2. 13A(p, 200 201 aa + 200. 201 a
a et. q,BaCMBCCN24aDCe
34044 + 2. 12 10 a C = 100. 1014
et 13A(,+ 2.13A0 a Y +2 1340 a) = 20. W a
=+13A (1. 100. 101 a4. Et ex 9 et 1 fiet  1310aY (+) 13ANI. 200. 201aa
2
=13710 a(
 ad = 112 aa + aD et a2 = p2aa + atque et a 8
1aa + a∞. Haque Et quia 12
Eit ex aeg. 10 et H quaeri 11Z, rmpe ex aequ. 10 fiet -13X 1 1310. 112 aa +2. 13(0 at
, 100. 105 a, seu 11244 = 100. 101 a L1Lni 2. 1310ah-2. 13 10 a Diy B 2. 1240+2. B3 n0
=200. 201a + 13A NI = 21346aG -2. 1340 a D, : 1318+ 21310. Et ex aequ. 12 fier
C
1340 at + 13 nCaD3:, 1320= 1310. Et ex Xg. 13 fit 12ad E (4) 13  N1. 200. 201a4 - 1340aO eNOUD, :, 1310- 1310
6, 17, sublata ir2aa, finul tres novae, quae pro varia combinatione vartari possunt, sed simplicissime ulopinior
17 tulli potest 200. 201, haberi potest. ratio naliter,  si 2ed roram 1gi ampndia. Ita non amplius oeus
rtus substituatur in aeq. 15. Lint ag. 20. jam aequ. 16 combinetur cum agg. 14 et 20, prodibunt duae aequationes
1340, 13n0, 134O, vocentur gro f 50, 60,70; et 1351, 13(I, 13_ vocentur S1, ,61, 71, et proi
et 13NNI  eut = 51.70.50, 71. Et 1320= 13n0 =50-60 = 3 3o( - 1) Et 1310-131O=50-70 -30 (n- )
C- 2. 1∞30 a((+ m) +30 U+ mm) et 13d0 + 13pose 50+70 = 2. 104-2. 1030 a(l+ 1) 430 (ll+mm). E.t
Haa L1 10. 31 al = 30. 31lm +, D. IIaa  ∞ = 10.  am + 30. 31, seu 100G1  aC 10.31 - 11.30, a (- m)
asit ). Im sit e lem sit f, l. nsit h, Amsit 
iet 112aa =4+ 10810144 e81 -Z. 509t- 2. 60233., 102- 210. 305+3091 Et 112aa = (15) Nec
IIheam
A11 = 10. 31 = 11.30, a (l = n). Compenlio 10. 31- 11.2
,2.10a - 2. 10. 3694 30 K et 112aa = 16) 481 = 10101. aC- 50dh+ 60a B,:, 4- 30C
0ag 4704D,: = 30h , Ex 49. 16 et 17 fal 209. 2014a= + 81. 100. 101 at eh 450a (Cg- ht,) 
vieb. Et
E seu 200. 201  (+) 10d. 101 50(RF -18) + (50h- 70e) D,:
a S0gu (eECht) = ∞. 90 eq- hF (60h.70C) Ad
Ds s. SI CCha 20) = 21 an 2 tohocgr 3G ax) (+ 81. 10 10t a) C- 5 50a +6B∞ B, ∞- 302) -9, th + 240a 5+ v10a 
190. 1o16CDhh)  +. 9(. 1ap. 101 2((0h.7 CC) aa
superest ad hnc una aequatio, quae fiet aequando 14 es 10 vabres