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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 288r, page id 00068196:0571
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(1)
Xa +G YX,: ya t yx =  = dy: dx
sit ∞ y+ a = e 105 + 1t + 12B + 13Z
V Xta  S+EIt + uV+ Z
et y = 405+41 ++qr v + 43Z
C
( et X  305 +31 + + 32v + 33Z
Et ex  305+ 31t +32V +33Z. 105+ 1IF +I2V F13Z: 405+41+ +42v + 43Z, 20st 21F + eI V+ 23Z
-90. -4). =9 43 et 4e15 fit a = - 120s + 21 F + 22V + 23Z
30P, 31. -32. = 33
quae dub ao quosduos valores ipsius a ex ay. d et 9 aequando fit 4 40 5 H1 F + EV F 13Z (0
134
13. 432: 433
40.
sunt aequationes 1, 374, 5,  et literae X, y, s, t, v, Z. quarum talli debent
quarum restare hebent duae, ergo tolli debent 4. jam per ag. 8. et 9 et
inveniantur set t; fiet es, et dissimulatis affectis per v et Z,
et ut compendio procedamus H 40 scribatur 140, et 1 Et scribatur 141 et 120.
sit +10-40 = 140 et +11-41 = 141 et  +20-30 2230 et +21 - 31 = 231
16
h
fi multiplicando eq. 17 per 230 et aeq. 18 per 140, et Ab illa subtrahendo hanc, tolletur s, et fiet
et 20 +
32 0 - 330
+ 141. 230 tZ ( 2300 +230a et 1140. 231 5 = C23F, 2310 +231 a
= 190. 231.
-1407 - 1400
-141, 230
= 141D = 141 a
et 231= 141 in nomta nm multiplicatore ipsa tolleretur
e
quidem a controbique sedt in multiplicatore communi feret  . 141. 140 - 140. 1452
(u) CY
ubi facitemus 230 = 140
et proinde tollerentur + et 1s nec earum posset inveniri valor per n et 
es s qu; 10 ubi positis aeg. 2, et 22 evanescunt , et F.
et fieret G Z= v +  quoniam 10- 4020- 30, fiet 40 = 10-20+30, et pursi
fieret autem = D, quod et patet
Quia per 22, 12 14, fit 41 = 11- 21+31. Ergo  ex 10, 26, 27, fit Z - v. 12- 22+ 32- 42: 13. B13343
ita in aeq. 7. poterimus tollere  X Z e q. similiter ex aeq. 17. fiet per 1n, 14, 2
per 21, 22, 11, 12, 1314, 26, 27 fit porro 140 = 20-30 per 21,  13. Et 141 = 21 - 31 per 2214
quibus valoribus substitatis in aq. 17. fit. 20-305+ 21 -31 F= (+a, quod idem
seu
ardisus prodiret ex aeq. 18. seu fiet s - 21 3t t + CoC XC lbE v. (2242: 12293
fiet 22 5=  1730a - 2t simulitae qu. 28 conpenduse sentemus sic
ergo subeta Eli jam  sed scibititatis his valoribus y et S inventis per 32 et 33, substatutis
in aeq. 7. redibit a ob valorem ipsius S. Cit idqe locis quatuor
Tentemus ergo
ita explicare _t et V, ut tolli possit a itaque suciamus + et sea  et vahtda
+64)  51a, et v h + 52 a. et substituendo hos valores in aeg. 32 et 33, fiet
fiet 38
 - 231  + 2351 a et ex aeq. 33 fit 2= = h. 12342: 12743 = 12342. 52a: 12343
30=
230O + 
130
perz
quibus valoribus ipsarum 5, F,    et V substitntis in aq. 7, videamus quonodo
ex aeq. 3. (5
6   250
in quotua locis solli possit a ope arbitrarinenu ponere  porro valores v etZue substtnendo
_ prisem cmultiplicatorem monerutoris debet esse o=. 3 in aequatibu valore ipsius O fiet
-12h - 12 52. a CAp + 13, 1274212 +135 12442. 52a. jam ponamus + 42E 73
 142. Y42.
3
irio
(39
2. 5 -60
4212343. 230 230 27
fiet 5= 61 h - 231 C + 60 a, et 12342: 1234342 70 et
1343
34513
fiet Z C -70h - 52. 70 a. Hi valores Yv, 7 5, t, ex aq. B, 3543, 41, 34 debent substi
4 135 12342
bui in aeg.7 et tolli a, quatuor logis exi pempe explicando arbitiarias ita
et 412
sed praevideri d, nullum sic dari exptum quia
 res eodem redit ac si o partio in aeqq. 3, 4,5b usi fuissemus liters asiem
ut restent soluius h, e
les generaliter co redit, data aequatione qua sint a, X, y du: dx invenire
R, et e, Generitissime de sine a.
Aest generaliter eo redit, sit aequ. dus t= dy:dx = X. y. a. et alia aequatio sit
aliquim alias duas in qua sit X v, a
e pryposita quaeruntur du ∞ dyodo _X   6Za et y-
H
X = ∞oa et y v. a. Ex 4 fiet dx: dque = Zoa (quod significat relatiorem Z a dari exrelatone Z. a)
H
et ex 4 fuet dy:  do= p. a. Ex.   b divisa per 5 fit dydZ: dxax=  a: 20a. seu sperq
A∞: dz et  valore ipsarum A et y substitato ex aeq. 3 et 4
H
substitutis in aeq. 8. fiet: alZa   a. Ea. v. a 0a: v a = dv: dZue. ubi 28
fit Za Xy. a : v. a
-
(10)
notandum si sit quacunque quaentetus :e dbe O: b =  D.a seu si
ratio
ipsiu Dad a, seu dari D O: b per D: a seu fore 6L) D: a. Ergo pro quantitas y: a habetur per
polam Z. a, adeoue s habetur per Z a, be similiter hy X et, dailq, et dg. dv. Ergo pro