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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 5v, page id 00068196:0010
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primo
ax
do
Co = Sydx.  y = s(xrb. X+C, X +d) Otiol ax- 2f sry+ 2ytoz + h Nyi taK
sit X (ao) CaxL a sit (460), ax + ab = P) C12 Svy + 113 SvZ + 133 YyZ + 100 p)
(5to), ax + ac = 12) (212 (vy + 213 12Z+ 223 yZ+ 2004)
(6to), ax + ad = set (32 Nvy +313 10Z +323 (y2+ 300Y)
Fiet ob aequ. 4, 4 sgroze  2hlyZue tate = f2. 1. hop Avy 42. 13. 1ptrt . 13. 100
25 Vvy +2910Z + 2h FyZF ak
aqu
2. VI. 100p 1py, tr. 113 100p Y) B2BypryZ + 12. 1VV
2. I3. 113 2 (vy 12. 12. 125912) 12 13 113 B Ny) F 113. 11317
L + 123. (239
Eodem modo procedetur ob aequationes 5 et 6. +1.190p
ab
Hini comparando terminum Termino, nempe
coefficientes ejusdem irrationalis item rationales,
habebitur tet valor ipsius f, ipsius g, ipsius h, ipsius ak. Hoc modo
f = 112. 100p
113. 123Z
9= 113. 100B, h = 123. 100B aK = + 112. 112Vy
112. 123y
Et pro nota initialit B too substituendo 2.-
et pro prP, 9; pro b, c, fiet
f = 2. 209
f=
112. 113V
6213, 2232
9= 213. 2009 h = 223, 2009
212. 2239
212. 213V
Et pro nota initiali 2.. substituendo 3..
et pro 4,r;  pro c, d fiet
312. 30OY g = 313. 300Y h = 323, 300Y
313. 3232
312. 323y
312.313P
+123. 123y
+ 100. 100 p
-000,000 ab
af = + 212. 212vy
L +213, 213VZ
+223. 21397
+20040094
=0001000 ac
aK = +312. 312 vy
incipiamus a comparandis valoribus ipsarum f,gh;
ductis ab irrationatium coefficientibus; et ope aequa-
tionum inde ductarum inveniamus, Zue, y, v.
+113. I13VZ
+313, 313V3
+ 323.32397
=300.3007
=000,000ad
Ex ipsius f valore primo fit Z = 112. 100p - 212. 2009 - 312. 300Y -212. 2009-7 Exipsius fvalore
pr et aecundo
213.223=113, 123
y = 113. 100p = 213. 204
212, 223- 112. 123
d
tio
secunde
X3. 223 - 313.323 2
313. 300Y -213.2092 .... g....
212. 213 = 312.323S
V = 123. 100 p - 223, 2009 = 323. 300Y - 223,. 200) - B ..... h . . .
212.213 - 112. 113
212. 213 -312.313
+112. 213. 223 100p (212. 213. 22738009 = +312. 213. 223. 300Y (=212. 213235009
- 312 113. 123
+212. 113. 123
Ex binis valoribus ipsius Z fiet
Et ordinando +va o 32 idemque faciendo in binis valoribus
(1) + 113. 123(212, 2009
=112. 313.323
4212, 313.323
ipsarum  y et v, fiet
.=213. 2232312, 300Y = -313. 323)
Etbrdictanda +213. 2231 112. 100p
et permutando
12 et  13
313.323.
4 212. 2232113. 100p
- 312.323)
+ 113. 123.
- 212. 2231313.300Y = + 112. 12312137.209
+ 112.123)
= 312.323)
= 212. 2131323. 300Y  4 112. 1132223. 2009
+112. 113.
= 212.313dam
unde permutando + 212. 2137 123,100p
Ope harum trium aequationum, licet quidem invenire rationem duarumm ex in
= 312. 313
determinatis inter se, per determinatas, sed non omnum binarum quamvis indeterminatam,
0(3 et 023
alioqui V, y Z habeent rationem determinatam, ad unam eandemque indeterminatam
Piq sit e et r:9 sit co, et pro aequationibus tribus inventis scribemus has tres com-
pendio expressas 11 P + 12C0 - 10420 211 + 2200-20920 31V + 32c0- 304 =0
11. 21 1 = 10.21g = 12. 210 = 11. 209 - 11. 22W. seu F11. 22 - 12. 21)c = (11. 20- 10. 21) a
et pari jure (31. 22 - 32. 21) co = (31. 20 - 30. 21) a. unde per se consequitur (11. 3L = 12. 31 Xa (. v. 103
Non licet autem Et pari jure habebitur , non licet autem simul habere valores ipsarum P et Co, ergo
malterutra ut postremo evanesceret, efficiendum foret, ad eoque opus duabus hypothosibus. Sed quia malim pet
Et ex 1et 2 fit, 10. 269 = 11.201+ 12 20C0 = 10. 211 + 18. 22W, unde
2. 20 - 10. 22) = (30. 21 - 31. 20) 1p: (32. 20-30. 22): et aequande
has valores 10. 21.20. 32 10. 21. 22.30f 11.20. 20. 32 + 11. 29. 21. 30 = 12, 2021. 30 (10. 21. 22. 30)
11. 29. 32 + 12.20.31 =0 Hinc in aequ. 1. pro 20 ponem
1
+
tractari eodem modo, tollamus 
et co = (10. 21 - 11. 20) 1
seu F10.2131
12. 20. 20.31 + 10.202 et 10. 11. 22 10. 17. 2
arioria
u2. 2
1c. 22 - 1. 2134 = 10. 22- 12. 20, 4 et fit 11.22 -+2. 21 =0
inventum
et 10,22- 12. 20=0
= 21: 11 = 20: 10. Et pari jure 22: 32 = 21: 31 = 20. 30 unde 72. 1 = 31 : 11 = 30 : 10
rod t 2E,inut ergo aroportinales 1b, el, 12, ipsis 20, 21 22, et ipsis 30, 3132
(VI =100P
C c0 = 30Or