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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 25
# Folio 14r, page id 00068043:0027
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pt aequatuo quaecuaque differentialis ex.g. ex data relatione inter DC et AB
fiet
invenire relationem BC ad ABC. E sit PC aequ p. jam
PCseu p: BC seuy..  ax +dy adx.
b: gy =: dx + du: dx. seu pp: yu aequ 1 + a
siet
pp ax aeq. yy dx F yydu. Ponamus jam sedus aeque yobe
ret: P
ax aequ ee dy dx + e dy
pp dx aequ yy dx + yc
aequ
reC.
t
habebitur
ita observatur lex romogenecrum
V nempe y + L ax Vy + 1
seu yy + dx
eb
e
ax aequ:
+C
 Vdx +ec
2ec
ergo valor ipsius
4 + ax pP
de
dx dx + 4Cepp seu y aequi d
ree
du
op
ree
qui valor ipsius y debet esse progressionis Geometricae posita
constanti seu aequ aco posita co infinite parva constanti
saltem autem hac methodo hubemus valorem ipsius y pure. Veum
alioqui parum lucramur, quique adhuc ignoramus qualis assumende sit X
in qua invorvntur difse rentiales ipsius X.
sed fortasse res meliu praecedit in illis aequationibus differentialibus semplicibus
quae mihi prodeunt in carculo illo compatatioo Teltra gousicog enerali
1.
si detur aequatio vde + v Z aequ haque ubi suppono
et h haberi. et adeo quaeritur soludi valor ipsius V, nec refert aus
et dz in eum in gredhantur ponamus ergo do aequ. ve. Ssed video rea
eodem redire quando L data
proinde nondum video quod hoc prosit
per X est explicanda ut et h