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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 187v, page id 00068199:0374
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(Xx + lmax + lnaa aequanda Eto Ugy. sit X-
20271214a y
34 20. 132.30) 42 = 40. 32: 30. fint X = 2030 25130 + 203rea ∞ Et
32= 31: 4
AlNX = II, 20. 20Z + 2. 20. 21473 + 2. 20. 220a Z7
aa
AlmX = lm, 20. 30.. 4 1. 20. 31
1 21. 30
+ln =lu, 30. 30 +2. 30.31
illyy = l, -40. 70 - 2. 4v. 4)
cta
30. 30(2+ 30. 5 az + 30. 3 raa
+1. 21. 21 a4 2  + 2. 21. 22 aZ + 22.22a
+1. 20.32
1. 21. 31
1. 22.30
42. 30.32
4 1. 31. 31
- 2. 4042
= 1. 41. 41
f1. 21. 32
l. 22.31
+ 2. 31. 32
-2. 41, 42
+ 22. 32
+32.32
=g2. 42
sumq 40.40 ll = (20. 20U) = 20. 3olm + 30. 30 ln sit = (20. 20l) + 2. 20. 5oll + 50. 5oll. Siet
Extermino
20 = 5-B 50.50l - 30. 303: 30 2.50 44t +40 = 20 +50
EB G +e  Ergo 4 40 = (50. 5∞ = 30. 30n + 30. 50m - (2,50l, :, 30m - 2. 50l
sit 4 242. gll = 22. 22ll + 32. 32lm + 32. 32 ln. ubi 22. et 42 ponendo valores,
ermino imqe
fit 4 40. 40. 32: 30.30)= 20. 20 (32. 32: G0. 30) l(+ 20. 3232: 30) Im + 32. 3El, et omnibus
divisis per. 32, et multiplicatis per 38, fit 40. g0ll = 20. 20l + 20. 3olm + 30. 30 ln, ut ante
Ex termino secundo, 4D. 41d = 2. 20. 214, + 20. 31 M + 21. 30M + 2. 30. 311. compendii
causa sit 2 2∞ Y 2. 20l + 30m = 6 270 et 20m + 2. 3on = , 80l, fietque
24 40. 41 = 70. 21 + 80. 31 seu 4 41 = 70. 21+80.31,:40. Ete
hEx termino ultimo idem fit quod ex secundo, nam prodit.
2. 41. 40 (32: 30) I = 20.  52.5 2, 21. 20(32: 39(+ 21. 3 2lm + 20 (32: 39) 31, + 2. 31. 32ln
qvisaque aequbione per 32 et multiplicata per 30. fit 2. 40. 41= 2. 20. 21 + 21 3oM + 20, 31m + Z. 30. 31 R utante
prodit ergo nihil aliud quam 41 = 70. 21 +80. 31,  40. ex dambus  termino secundo et penultimo.
ut valor ipsius 40 ex a primo et ultimo superest
32. 3 = 31: 43, exis.
suphest Terminus medius destimendis ubi ft pro 3rBonendo 31: 4. 30, et 22ququ et 12, et 4) licando
et (70. 2it 2. 70. 80. 21 31 493. 31 + 1 _ (3t. 13B ( = 2. 20. 20 (V.  30 u+ 2iUt2o f1. 4. 30)m +21314 20 3o (l 3 ft 2. 3o( l. 2o (+ 1 1a
 2, 2020(32. 30)D rs. LI 2,0. 80 ∞1. 4t. H 90 31 4040
N fictque = 4. 30. 76. 21U = 2.4. 30,70.80. 21. 31l = 4. 38. 80.312I1 =0
P4. 20. 40 21H + 1. 4. 38. 148. 21. 31lm = 4. 40. 3s I1
aenulus 20 30 40 50 31 32 22 42
quot
5
63
18 27 18
32: 30 4 2. 20.40 31 I
+Z. 20. 30, 403 lm
L 2013040
46 30. 40. 3e ln
A. . 30. 40. 3 ta
32-31: 4  22 = 20.32:30
22 =20,317430
24.18. 4. 9. Ergo 22 ∞18
42= 40. 31 : 4. 5
qy
Quia omnis res reducta ad tus aequationes praestari poterit in numeris
63 49
pro 20, 3, 40,50, ponendo numeras et pro 31 ponendo tnumerum divisibilem per 6, 
sit gn. Ita 31: 9. 30 dabil 66.7. 7.: 4.3 = 399 = 147 pro 32 et 21 30.32= 2 13.197
2. f3l. 32 = 31 4. 38. 32 = 31. E 32 = 31. 4. 3 31 = 42, 31 = 6. 7. 6.7 = 36 99 Jam
36-49 4. 3= 3.49 Ergo 31= 2) sed d hoc displiet quia jam habemu, ideo potius fint
+31 = 68,  18 et 31 =95. 4 et 31. 4. 3 = 99. = 99 9. 9. 4: 4. 3 = 9. 3 =27= 32
e
Ergo pro 31 ponamus 18, et pro 32 ponamus 27, et fiet 24. 3. 27 = 2. 9 = 18 132 =9 2.417
pro 40. ponatur 70, ut fiat 40 = 20+70. potro quia praeterea video ipsas l,
m n.  non sufficere: ideo sic proesdamus _ a hil + 12m +
8
574
ideo pro Ugus scrbamus tagu, sitque p talis, ut fiatioh. l + 12 m + 13n + p =0
eto 2Il + 22m F 23n + 24 p =0 et 31 l + 32m + 33n + =p = 0.
191
arsu
252
e
s,
vd
12. 23, 31 4 11. 23. 32 = 11, 22.33
iC. a 1 412. 1 1. 20. 323:3 413,. 221 = 13, 21 1. 412. 21
(162
( 228. 22E p
i
21. 2
i
st 
a
is
fit  canone
1t
2
6
 38
23. 104567
Siq
286si3
2qe
33486
17
16
D
a
ontcae
3079+31a 2+ 3aa a 302Z +31a 2+ paa 2.730. 32= 31
P. V( + 30. 41a + 4. 3 2. 90
30. 2 + 30. 3la Z + 30. 3a
C