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# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 5
# Folio 85r, page id 00068207:0169
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C
Aequatio ad curvam (onicam neralis est  voce = p
_ H. v= fiat Z = 31X + 32y + 30t et  v = 49X + 4 y +40 b
EZ
aq. (4)
2. 40. 42y
= = 313 XX + 35 31. 32 Xy + 2. 30. 31XX + 30. 30HY
Z-
F32.37 97
12. 303rfy 4.
400. 31 YX + 3or t
00. 3L 8y
seu transferendo omnia membra in unum latus totumque aequando nihilo
5
=
fiale Z=LXL  3K + 329 F30N. Et substituendo valores iat
Et substituendo 41. 41 XX + 2. 41. 42Xy + 2. 4D. H1 fX +40. 40 f
VV = 42. 42. 9y
I
+X 31. 31XF + 732. 31 yy + 2Y3132 Xy + 2. 30. 31Y X +2 3032Y y +30. 3ort
-41. 41 - 42. 42 = 2. 91. 42 ..
= 2.40. 41t = 2 40421 - 40. 40 H
+ 1. 00. 31 Y +1. 00. 3t Y,  4 00. 30 rt
iden fificetur iatae aequationi multiplicatae per 50
soL NXX + rgu ta 13Xy + 00. gitx +eoprty +50. 10tt
identificatoriarum
Harum artlrarum Gex aequationum aps in seniamus 31, 32, 30, 41, 42A0. et erit
Et opo
ni fallor aliqua super numeparia 50.
si sit Rursus ex aegq. 2 et 3, inveniamus X et y per Z et V)
X = 00Z = 32y - 30t, : 31 = 00V - 42y - 40t,: 41
00. 41Z = 4 32. 41y - 30. a1F = 00. 31V - 31. 429 - 31.40t, et firt y
Fiet y = 00. 31V - 00. 41Z + 30. 41 t, :, 131. 4L. permutam 0 3. et 4. item Z et V
_ manet idem
- 32. 41
= 31. 40
Nam eodem modo Y = 00. 41Z = 00. 31V. + AV. 31 t 3:, +41. 32 quod est sindicium
41. 30
= 42. 31 Calcili probi
Hiac pari jure  per mutando. 1 ut 62
ex valore ipsius y, fiet valor ipsius X = 00. 32b - 00. 42 Z + 30. 42t,: 132. 41
2 32. 40. - 31. 42
(sol
Hinc pro. N, Et duoe valores ipsius ipsorum X et y, habent uundem denominatites signo disserentes
vel accipiunt
seu habent eundem denominatorem, signis numeratoris etdenominatoris in alterutro mutatis
Hinc si in valoribus X et Y pro 30, 31, 32, 40. 41. 42 substituamus valores
im inventos ex aequationibus sex identificatoriis, A
Habebitur modus datam aequationem generalem localem secundi gradus seu ad
Conicam reducendi ad formam aequationis 1.
superest ergo tantum ut sex illas aequationes absolvam exequamur.
sint binae aequationes 1AXX + 19yy + 15Xy + 12 ax +13aG + 10aa = 0
Locales ad Conicat
24XX + 29yy + 25 xy + 22 ax + 23 ay +20aa
Videamus an X et y sic explicare possimus, ut _trobiue tollantur L,  et xy Xy A et X, et y
Hoc succedit in omnibus p ex Conilis eacoppta pprabola
sit _ _ X = 31X + 32 + 30a et y 41X + 42 +40 a
a Hincaou
Excepo. 1. fit 14Xx = 1. 31. 31. XX + 2.1431. 32X+ 2. 14. 30. 31af + 14. 3u. 3uaa Hinc fit 3 3 pro tollendo Hb aZ
1. 32. 33
Ct + 2. 14. 30 32 a)
199y = 19. 41. X17 F +2. 19. 4. 42  + 2. 19. 40. 41 ax + 19. 40. 40aa
I9. 42M1
2. 19. 40. 42a
15Xy= 15, 31. 9122 + 15. 31. 42+ 15. 31. 40 ax + 15 340ay
1532. 42 W 15. 32. 41
12 AX C
12 ax =
ay =
20aa =
15. 30. 41 ax 15. 20. 92 ay 
15. 32. 40a) 15. 30.404a
15. 30. 42 a
12. 00. 31 aX + 12. 00, quaa
c2. c0. 32 av
13. 00. 41 aZ +13. 0v. 4u aa
13 00. 4247
o 00 ua 10. 00. 00aa
pt 2. 14. 30. 314 15.31. 30 + 12. 0b. G  =c
2.19. 40. 91 15.37. 41 13,. 0. 41)
protollan
. 14.3031 + 1732. 10 + 12 0032
2. 19. 40. 42 15. 30. 12, 13, 60. 12s
pro tollendo XV
2.19. 31.32 4 15. 31. 42
219. 41142 + 1G. 32. 41
Eadem ad aequ. 2
per mutando tantum l. et7.
Autg, 2 et 3
anenta
a
aqus
infertm a 
s
a resisim.
G3
1
5