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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 58r, page id 00068198:0115
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it y = v + Z. Ergo ex aequ. dala ft dy: dx =  yy+XX, :aa
du fiet do + dZ dx, : ex = vv + 20Z +ZZ + xX,: aa
seu du: dx = vv+ 20Z + ZZ + Xx - d Z aa ): aa
ubi si vellemus facere, ZZ + XX = dZ aa = a dz: dx, haec
aqualio non nihulo facilior est ipsa data
sit jam Z=
2+31a
209+21a
et X = 1041aY.
208+ 21a
et dque = (209+ 21a) 3o des = (308 + 31a) 20d8 0
qu (20 +21a)
et  du - d Zdx
= 2e8. 30 l
20g+ 2a) 1odes (09 tuu rod92
- vot F R oqu. (208 +21 a)
Ergo Z7 + xx- dque na dabit qu 3.
Labit qu (30c5 + 31a) 2 + qu (109 +ua) 2 F  qu (20g + 21 a) 
dZ = dz-dx
ita ascendetur a ad D3, et sunt quatuor termini quos puto
tolli posse per 6 literas 3 10, 11, 30, 31, 20, 24.
X2
quid si sic y v + vy tiet Cg. 3. L L
bu XL ax=
+ e
 fiereti XX =
gagis
et dx = Zdy+ ydz. Ergo dy: dx seu ady:, 2dy + ydz =
Xx
si esset
e
2s
s +2Zyy: a
et fiet a dy = a aayyzdy + au Byydy + aa y a + 247 d2
dana
0a ((aa +ZZ) y3
a
seu dy: d, -
aZ)gy
:a. 
00
ita obtinnimus desidenatum et fiet et poncindo -dy: dz =  1y+ ryyr 13y,:
845
et   20 rey +229y, et c. et  30 + 31 y + dgy+ 33y
+34 y p E = D ii ut sit 
 AC20
L.1, 31 = 20 d 31 y quia L1 = 0 Bhit 3I constans a. -
stans
 ad, b
tandem Porro 1. 13. 3117 3. 13.92 + 3. 11. 33(= 20 d, 33) ubi ad huc suspendo
pdiciam. Rursus, L. 1 ∞31 + 2. 13. 32 + 3. 12. 33 + 4. 11. 3A = Eod3 A + 21d33+ cy 2t
+. 82c
 1 3L FZ 1X Y 3,13. 33+4. 12. 3475. 1135 =20d35 + 2d34 + ud 33. uro hibetu
no ponamus 31  extare et esse constantem, quia ergo extat 13, habetur et 
sed aeq. g. eaanescit posito 32 esse 0, quia 1E, H, 3Z, 32, 12, 11  21
sunt 0, et 34 pit esse 0. Et in q sed incaesp. _ quaerendum invenietur 35
4. 13, 34 + 5. 12. 35 +6. 11. 36 = 20 d36+ 21d35 + 22 d34, ubi omnia
evanescunt. ide 12. 25 20 d27 +21 264+ 223C si velunus, posscony
lora
tamen conservando 36, habere 4. 1334 = 20 436 + 22d34 et mo x
B. (3. 35 = 2od39C + 22d35
(t 7. 13. 9  20. d39 + 22 d 3)
113. 31.
220 d 33t uly 213
2. 13. 32= 20 d34t uly 
3. 13. 33=
20 d35+22d33
et 6. 3. 36 = 20.39+ 22d36
a
a
no
n + ab B.
habetur quaesitum per. 1B. 3 22d3) seu
s
13t 131, =. H(19L. ∞) ex subi curum 20 non
hit ergo aequatio- dy: dx =  139:  40 +gy t fiet si recte processinus
4. 13, 34 4 20436 +2d34
al
30 +gnum. s13dx. 22 fiet 
cd
Num _co h. et
dte= h du = numco deo
et fiet y13: 22) dx num s13ax. 12 + num du num 5 13dx: 22. seu y (13: 22) dx + dy
seu dy : dx = y. 13: 22 = 13y., 204229y res non succedit. Ergo enor in calculo
quid se jungamu aequationem 1 et 2 et per ponendo 23 = 0, 32, 34, 35, etc esse o
conservemus 31, et 33, (x aequ. 3 fiet a33: 35 seu log. 33, = 3) ax. 13: 2E
ergo sumitur 20 pro 0, quod est falsu
equ. t seu, 33 = log X num. 3 fdx. 13: 22. Et ex aeg. 1. fiet 13. 31 = 20. 13(33. 24) + 273)
et prodit quaesitum Et fiet   2b+ 31H+33y3=0 s b esset 6,
hurbo in infrnitum puditisnori gensseriei infunite
resmma
m