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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 6r, page id 00068197:0011
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Et primum ope
es aelups
aequationum 6 et 7 tollamus y. Et quidem ecribendo explicatius aequationes
bex fier (yy+ 3by612by + ∞ bb aequ9bb +3bv + vV
+l
b
+=VY + 8 b0
+
ex VD
1b
16
Lbb. =bV
ina
+1 bb - E bV + vo - 2b- +v
aa
16
b
seu yaqo -aa +  quad +v + b - vb qui valor
4
potest substitui in aeq 6. et ita restabunt solum V et 
Sed videmur breviori calculo aed idem pervenire posse.
Nempe quaeramus differentiales aequationum 3 et 5 tam y. X et Y.
quam v. Z. S. considerando ut duplices.
Ex aqu. 3 fiet:
9
ZdZ - Zdx- xd xdx aqu sas
i
Et aequ. 4 fiet: adque. Et punctu quia du aequ t ex aeque
vdv + vdy +ydvrydu
adque = adx aequ vdy + ydv +2y dy + bdy + b dv sbaequ. 2
1o
Et ex in his aequ. G et co. pro dy ponendo yib ax: a sex 9 et co fcet
(11)
vdvt vydx: a + vb dxia + ydo + yy dx. a F rb dx. a FZ dz Zdx xZ xdae
adZ = +t ego vYdr: a + vbdc. a t ydv 1 2yy drra + 2yb dx:a
Et in aequ. 9 et 10 pro dx ponendo ex aequ. 2.) dya: g+b fiet
(11)
sas
var +vdy +ydv +ydy +ZdZ - Z dya: 7tb - xdz +Xdya: 7 + b aegu sas
adze- aa du: ytb aequ ady + y dx +2y dy + bdy + bdv. quas
12).
quationes jungendo fiet: ex aequ. 1c. dus aego sds- vav tyav +Zd2 + XaZ: v +y
(13
a+Z+X a: y+b. et ex aequ. 12 fiet dy aequ. adz. ydv - b dv: aa: y +b 1v t2y +b
on
(141L
qui duo valores ipsius dypossunt inter se aequari, sed dividantur prius per d do
et pro d dz: do ponatur per 8 et 9 valor y+ b:a. et pro gs ds: do
e
lz
dz: du + i seu  quad ytb +aa: a et
ita ex junctis aegu. 13. 14. fiet:
Quia differentiae
Seu y aequ
differentialis.
de
qutat C4, Si quad ytbraa: ∞- v + y B
d stem
+ Z+X y+b: a,:
v+y - Ztxa: gtb aequ (V +b - y - b): aa: y rb +v + 2y + b.
65
e
L
c
(15
seu fiet  O: D aequ 80: Q seu fiet:  O0 aequ 0D. unde
1G
sequitur vel O vel 8 vel D esse o. et si  est o vel po tanr rarsus
vel poteunte verum aliunde constat jam l ex aeque.7. quo f aequ.o