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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 297r, page id 00068196:0589
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(8)
et fit D = 2. 61 4050 -20. 60 et O = _61 , -10. 50- 20. 60 + 2. 40. 50 -2. 20. 60
et Pob. aequo. fit (9050 - 20. 60) = - 10. 50C 20. 60) + (2, 40. 50 - 2. 20. 60
seu 60:50= 4+20 40 - 10: 20
Verum in eo jam subesse iideo incommodum quol quod 61.
non inmeditur velores  et 6, et ita rursus prva prodit
valor 60: 50, quod non est conveniens; opateret enim ipsam
datam princ praetransformare Ilai sic malim
65
Sit X = 507Z , et y = b 50ZV, requ et fiet
(16
(4)
fit ed - e et 9- et porro 2. 30. 50.50  5 et 270. 40. 50 + 2. 40. 50. 30 - 20. 30. 9 
et debet esse (3ol50.  (2. 30. 50. 50 + 2. 40. 50, 90-20. 8080 = (6, 30. 5050 et ita
(1)
habetur quaesitum. Calculum reapse faciamus
dx  dx: dy = 10X + 20y + 121:, 30X + 40y + 341. sit X= 502Z y 2 30ZV
. Et ex aeq. 1. per 2, 34,5. fret
ais
fiet dx = 2. 50. Zd.  dys 8Z epsim
retsm.
2.50. Zd9: 807d p 
 1050 22 + 20. 80ZV + 121:, 30. 50 27+40. 802V + 34)
et per cintem maltiplicando fiet:
1t
2.30. 5050 Z dq + 2. 40. 50. 5ZZdqe + 2.341.59742 C5.
= 10. 502 ete (ut in 2) + 20. 6077 et (ut in 3) + 121 :, 30. 50  ese (ut i 2) + 40. 6027ete (aln.) + 3u 2. 3050.502 d + 16240 50803 vd 1 2 341 50. l 810 50. 802 d
et
Ets
vdx + 2.40. 50. 80 230 dZ +2. 341. 50247 -10. 50. 802y -121. 807du
52. 30. 50277 + 2.30 50, fret
et
et s.
= 20. 80. 80
. 4
 209080
ceff  prodterens
esse e (coefficiens ipsius ZZ0d ) = 36 ( triplo coefficienti ipsius e av.
cerellut
cunue dum  con  2. 40- Q. 10 seu 49. - te - 10
etstod esi o exp et , e in g. 44
 per X et y sic ut fiat dx: dus = 10X + 20y + 121, : 9 30X - 20 y+ 34)
x ex hoc patet semper posse resolvi problema  per communem
geometriam, ce nam oeg.  est summabilis, et dabit:
30  4 230. 50. 507+ 4 10 50. 30
110)
-20. 80. 80
posito Z = Y ZoX et v = y: 80rFo
atque ita resoluta est aequatio 
ex5q tunc ex aq. 8. fiet c. Z
uet
et d fit  = 10: 20
et compendo causa ponendo - 1050 -20.80 =0 seu 80 = - 10. 50: 20 fiet aequatio
C
Et poterit summari aequatio 7 si modo ponatur
=1056. 80
quad sn effiteruu
et
et
22VX e si prique ed et  in ory. de: dcba. +.. cd +... 51+. co+. explicuissemus
60,70, 51, 72, 61,82, = 0 efiet fit O = 0, et D =o ergo BD= C secundaeqto
- yX = 
+341X + 341 yy - 121. y =0
1X
2. 30 XX + 2. 30y 4 2. 3091
si velium tamen calculam nostrum sufficere sine atra traas formatione, sic
x
10:20
10: 20
procedemus: Ex: dy = 10X + 207 + 121,: 30x +497 +341 sit X = 502Z et ot y =60 22+ 802V
412
o
XX
fiat Ax: dus 2 2. 5eL2. 58Z+Z :, 260 21Z + 8074B= 10. 50 37 + 20. 6027+20. 80225., 30. 52, + 40. 6a971 408
tq
2.40 10. 6
O= 2. 10.50.60
 t 2.40. 1050 22∞dy +2, 4050b02
1) +240.5060
2. 20. 60.60
G.3d
-2.20.60807 31- 20. 6080)
(8.
-2. 10.50. 69
21
8. 8
2090. 80
1. 40. 50. 8672
- 2. 20. 6080
et
seu 2. 40.50 +3, 10.50 + 20.60 =0 adeoque 60:50
oso sa dy ueB
L. 2.400-3.10,:20. Quo posito
summabilis est aequatio 6. Ac proinde generaliter possumus resolvere aequationem
differentialem qualis est . Unde etiam intelligimus alias altiores non
posse semper explicando ad hanc reduci, qua non semper sunt. absolute
resolubiles
6.51. 60