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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 138r, page id 00068197:0275
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ea 1B.)
y 10 spem + uxtn +XFp yy Z 16XA Iom 4, 10. A LXtm Xtn Y, 10 12 Sxra, arp 1. 11 12 Extmetn
L=30
31
Et. 1e p
aequationes comparatitia  decem, cum arbitrariae adsint c2
o +Nyta astbre a + bo, 10 nitrc
C
11. 13(41)
∞, 10r erio b = 20+21+22 10m + en + 12p + a = 2om +rin + up. 10.1 = 20. 21 101 2022 
sineslvamue Ex aeg.  11, 10, 97 habebitur 20, 21, 22 tollentur, ne 22 11. 12: 21= (ex 10) 10. 12:20
ergo 11. 20 = 10. 21, seu 21 11. 20: 10  = (per 9) 10. 11: 20. Ergo fet 10 = 20 idemque firet
in caeteris, quod est absundum et glan ae qu. 7 et 8. videam, an hoc sufficiat, ita enim
In caeleris quad est aljurdum.
sed videtur res successuro pro casu triplicis aequilitalis
pi nempe y + a, y+ b, ytc, debearit aequari quadratis vo Z p  respective
9+aLvop ytb et y tC =  p
Nempe sit y- 10 exem e, t x+n + V
a
nempe
Nempe sit g= ta ot ri 1oram + tXin
a
y = 10 SXIm. XIn + 11 S ptm. Xtp + 1 Sx +n. XIp + 13X + 14
4
v= 20 + xim + 21 Sxtn + 22 Extp
(5
Z=, 30 Ynem + 31 YX+n + 32 YX+ p
= 40 sram + 41 Exin + 4u extp
20.20  F 20.20 m
21. 211.
22.2.
Vr= 120. 21 Tumgnm + 2. 20. 2 tumxop t 2 de Sumnip. Et esdem modo se habet Z et 1
Hinc 2. 20. 21= 10 2. 20. 22 =11 2. 11. 22 =12. Et par est
10d
Et quia pari puie se habent 30, 31, 32. vel 40, 41, 42. ad 10, 11, 12. Hinc
15)
(14)
fiet 20. 21 = 30. 310 f(2 40. 41 et 20. 22 = 30. 32 = 40 42 et
12
21. 22 = 31. 32= 41. 42. Porro ex 49. 12, 14, 16, eoque et ex 13, 15,17,
(17
(16)
(20)
21
fit 20.20 =30 30 = 40. 40, et 21.21 = _ 31. 31=41. 41.
19
((Na 20. 2 = 35 31 Ergo 31 = Nam ex 16 fit 32 = 21, 22: 31. (Ex 14) f = 202
Ergo 21. 30 = 20. 31. seu 31 = 21. 30: 20 (sed ex 12) = 20. 21: 30 Ergo 32
Ergo 30.30 = 20. 20, idemque in caeteris; cum par sit ratio
22
Hiac possumus facere v = 20 X+m + 21 X+n - Z2 IX+ p
Z= 20 (xIm -Z1 YXIn  + 22SXFp, et pL2otmtm 
Hinc ut resol ita satis factum est aequationibus 12, 13, 14, 15, 1b, 17. supersunt
25)
equationes pro jam patis faciemus et aegqe 9, 10, 11. Est ergo exhii est  = 12:, 22t=
ex 10)  11:, 2.20 Ergo (ex 24 et 25) fil 11. 21 = 12. 20. seu
seu 212 12. 20 : 1
2
unde fit 20. 20
Ergo 21 = 2bc: b = a: 20,
t
sit d= 20 trim + 2 Sn tE S ta+byu=vo e+ syus = LZ. Ex 5 et 6 explicatis rascuntur
Ergo 20. 20 = ab:c
(ex 9) 2. 10. 20; unde fit 10 12 = 2. H. _ seu
210 et2 2. 10. 11 : 12 et 21 et pari jure
30)
21. 21 = l2. 10. 12.12 et 22 = 2. 11. 12: 10
20
X +c
Y v = a + Te sX + M. X LH.
21. 21 n
22. 22 
20 d =a 20. 22 = b 21. 52 =c
22 = C: 21 = b: 20. Ergo 21b.