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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 373r, page id 00068196:0741
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L2
() 2
Aye = dx aa + bXx:, aa + exx est aequatio in qua du est element
curvae Elliptuae vel Hyperbolicae. fiet aa du + exxdus aad x - bx de
sit y = 10 + 1X + 2 X + 13 X +14X et C et dy = 11 + 2 12X + 3. 13X + 4. 14X etC
fiet audy = aa, + 1. 1. 1. II + 21. 2. 11. 12 X + 2. 1. 3, 11. 13X 4 2. 1. 4. 1. 14+ X f 2. 1. 5. 11. 15X
12. 2.12.12 2123. 12. 13 2.2.4. 12. 14
3, 3. 13
2. 1. 3. 1
J. 1. 11. 11
2. 1. 2. 11. 12
Cxxdu = C,
da
+BXX s
naa
Et inquirendo in destractitias, fit 12L _ 1H - f+.
1. 11. 11 aa = aa =0 seu 11 = +1, et 2, 1. 2. 11. 12=0 seu 12 =0 Et fit
B3 (7) - b - C, : 6
et 1920 ex termino X. videndum an non
et ex termino X fiat 16 =0 nam is ita stabil 2. 1. 6. 11. 16 + 2. 2.5. 12. 15 + 2. 3. 4. 13. 14
ndios
+ 2. 1. 4. 11. 14 +. 2. 2.3. 12.13b ubi patet omnia ubique esse teni
(11)
pares, alioqui omnibus reliquis destructis destrui et 16 seu esse 16 = 0. Rem
ergo reassumamus: dy = 1. 11 + 3.13X + 5. 15X + 7. 17 X etC. Et fiet
+aa dis = a4, 5H. H. 1. + 3. 1. 3. 11. 13 X + 2. 1. 5. 11. 15X 4 2. 1. 7. 11. 17X  + 2. 1.9. 11.19Y
ca
+ 3. 3. 13. B3 2.3.7. 13.15 2. 3.8.13. 17
.... ..... ......-..
.-.-
 -- - -  DH. II. 11
..-. -. 5: 5. 15 15
2. 1. 3. I1. 13
2. 1. 5, I1. 15
3rai ...............  3. 3. 13.13
AbX EX = (1qua + EaV Lo maatiCL thaathaC2  = 31 + BX +3AX ere
0
u
=a
.
ana
 ygRX
114)  ti n 34+ 3 19+C94 130
Est bitu  Hinc quia y = uut 13X + 15X + 17X ete. ideo incipiendo
at X quia a 15 X, quia in aequationis 13 termino 15 continente nempe x incipiunt
omnia procedere uniformiter, fiat 15X3 + 17X + 19X etc = v. Et  ex 
Et fiet y = 11X + 13X + v seu v = y = 11X = 13X3
Assimatur jam alia
aequatio aa dco + Cxx deo- aa dx0 quae nihil differt a priore, nisi quod b = 0
et fial cd = 21X + 23X3 + 25X  + 27 X etc. Constat Dari relationem
inter x et co ex suppositis quad quadraturis Conicis. sit autem 
118)
(181)
25 X + 27X + 29X C = e fietque eo = 21X + 23 X + e seu e = c0 - 21X - 23X
6
ob datas auteri quadraturas Conicas, datur  ex c ex X ergo datur et e ex x.
porro 21 = 1 et25 et 23E0, si absit b. fiet C = co - x et notandum
etia 13, 17, 21, 25 ete. fore = 0 seu debere evanescere, si absit b. quia
quia abest b. Ex his quidem patet e eodem modo deficiri ex a invenim
ex X, a, et 0, ut V invenitur ex X, a, et b. sed ita ex data e per X eto
 non deo indeniri v, quia non apparet quomodo pssit o ingrediatur calculum, id
enim fieri ab infinitis modis, neque adeo apparet quod proo substitui debeat . b.
illud interim si contra data fuisset V ex x, a, b habita fuisset potius e ex
X et a; pro b substituendo 0. nisi forte contingat, ut ora tunc evanescant
illud si sit b = 0. proditum evanescere etiam 23, 27,  etc. et fore
Et
W = WKX +25 X + 29X etc
 uXX
Cd = 21 X 4 25 X + 29 X etc.
ut yx = et ut Y Axt = F ut y - 1X = 13X + 15 X et c. videamus an constans
quaedam lex haberi possit, secundum quam 13 15, etc eodem modo habeantur, quam 25, 29 et
ac
 hoc posito haberetur semsi veluti si 13, 15, etc eodem modo haberentur ex a et b
quo 25, 29 etc. haberentur ex a, et  3a. Jane 13 = b:, 2. 1. 30, 11 (15 = 3C. 1. 1. 11. 1.- 3.3,
3: 2.1. 5. 11a4 et 17 = et et 19 e.
. 1.g. Ina sed video id uta ecedere
sed 25 = fC, 8. =C. 1.t. 11. 11,., 2. 1. 5. 1 au 2  29 = 2E 1. 3 b Bu S l sis
2. 2.