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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 24r, page id 00068196:0047
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Possum semper rem eo reducere
 d
tu e eletio data
affectiones
aequatione tangentiali, ut habeatur du  per solas functiones ipsius X.
posito, ipsam du esse constantem. a evloam unde semper separari possunt
indeterminatae. Sed et differentiando hunc valorem ipsius du habetur aequatio
in qua solum exprimuntur X, dx, dax, dx seu habetur relatio
later quatuor terminos X, (X), (X) C
(X)
IX)
sit (X) =VX, fiet
_ (V) (X) = (V) (V (V) VX et ((X)) = (V) (V) vX sit rursus
W V et ((V)) = (WV) W V e fietque X = vX, et (XD = WDVX
et (XHX = (W) WV vWvNx = (W)oWVX sit (10) = PW. et fiet
0) =
XN = 81Vx datur ergo relatio inter X, V, W et  sed mul
videamus an quia ide eies in infinitum prodire licet in ipsis differen
inde, quia semper aliae atque aliae prodeunt
His, possimus componere valorem Ubi dus ipsius dus multiplicati
ex valoribus aliquod membris in quorum
quo libet differentialis multiplicetur per sulm calegectam terminum
respondente venit
per factum _ ex Fyia,
ergo in mentem, ut habemus constantem a, et deo, quaerendam
per factum ex siu terimino et constante
jam et constantem ades seu constantem tertii gradus, quae quaeritur
a, dco, et
hac
quomodo ex datis habeatur. Sed video jam video haberi, si
di8 suit in progressione Geometrica seu dd8 = deodco: a
ergo arte fortasse poterit obtineri illa resolutio in membra qua
drabilia cum descendendum I ad _ ad gradus inferiores.
dd8ddt: deo, seu deo: dua = deo: a
a
considerandum praeterea quaedam quod Xddx = d (Xdx) - dxdx
Aladus = XX + yy, dx sit du constans fit 2X dxdx + 2ydy dx + (XX + yy) ddx = 0
p y.e
d0
seu 2X d_ + 2ydy dxdx + aa dus ddx = 0 seu - y = 2xdx tandydax; 2 dydx dx
est yy = 4XXdx + 4aa xdylp ddx + a dydy ddxddx,: 4 dydydxt = aady-Xxdx: 
  unde habetur du adeoque et dydus, et du, etc. per solas functiones
aftectiones ipsius. jam descendendum est ad hujus ipsius aequationis differentrationem
an sic et videndum an liceat eam resolvere
+ dX (ddx; dydyia) = 0 toltendo
ubi descendetur ad dd d.X
+d ddx (dx; dus)
alticma differem
ations, etthabebitur aequatio identica sed scothuere re atimes incogulas
Lunto L ynde d tollettur ax oporet aequ fi
n partes tales Ax (X; a)
aa
ifficile