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# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 2
# Folio 8v, page id 00068074:0016
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NM reductignet. differentiales quadiaturas adumta nova
e lit videturiric eseom
sit C try. x
ossibas lonction
tialium ad quadraturas
sre folmoravali
12
sit dy: dx = (f X. y quaeritur FC (f.2) X. 9 = 0. fiat
(1
fietei et ut habeatur
XG (f. 3) X.y. D =0
relatio ipsius v ad X. y satem detragonistica, ponatur:
aliqua
d due dx. (f. 4) X. quaeritur aeq. 3.
ita enim debitur per 3 et 4 dabitur ex 2. saltem tetra
gonistice. Hoc ita fiet Ex aeq. 3. quaeratur differen
f. 5) dx. dy. X. 9. V
tialis. nempe de=  Aglx
Ex aeq. 4 et 5 fit tollendo du, fiet dy. dx = (f. 6) X. y. V
Ergo per 1 et 6 tollendo dy: dx habebitur (f. 7) X. 9. D =0
quae duae aequationes 3, et 7. debent coincidere. Id es
 debent ead vel eaedem esse in terminis vel saltem
habere divisorem communem. jam ipsa quidem
X. 9. V potest intelligi assumta qualis est, indivisi-
bilis. Nam fingumus eam dari; si jam substituatur
in aeq. 3. omnis hactenus institutus culculus in ta succedet.
S
ita intelligi potest arg. 3. indivisibilis. Fieri tamen
potest at aeq. 7. sit divisibilis. Itaque tantum opus
est aeq. Z. multiplicari per (f. 8Y. X. y. V. debent
coincidere ut fiat (f. 9) X. g. v = 0 et ita debent
coincidere aeq8. et 4g.7 formnqs et to formula-
et forgmula g. Et habetur quaesitum. In hac
methodo illud est elegans quod ipsam v. tolli non
necesse. Sed tantum dx. poterat etiam assum
V non ex X sed ex y. vel assumi poterant literae duae
est
locidaequ 1 Salinleg4
una Y exx, altera Z ex y, imo et tertia co ex xetus
verb. gr.  resumto calculo sit  duodu X. G.
ex
)u
dy: dx = (fr. 1.) Xug.  quaeritur (fr. 2) X. y = 0. fial
litera quadratorie data ita, ut tamen e
oller conecesse nu st. plemis plures quam
+. formula
vet er. formu