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# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 9
# Folio - , page id 00067968:0136
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se
yy = ax
sit Egnus = gax
ab sint abscossae
XX ay
dy - axtax seu Cyyt 2ydyydy (ax, tady
Assumatur hova abscissa novuque ordinata, sit
++ du = a yt dy seu (HH 2Xdo (+ dudod = (at adi
s
M
ne
ee
ad adus
Assumatur jam abscissa et ordinata nova sintque abscissarum
fit 2gdu
differentiae aequales, fiet x +2dx a y+ 2dy+ adque seu fret
XX +4Xdx + 4dx dx = ay+ 2ady+ addu
Hinc videtur inferri
= addue rejiciendo XX = ay et qxax = radyue, sed
falsa est haec aequatio 4axdx= aguus. quod sic ostendo. Habuimus
dx dx
A
Ergo sit
adque. Ergo fit 2 axdx addis
2Xdx
quare sequitur su aeg. princ elidenda esse incomparabilia, quam
i t
aquividetur dicendum
aequalia. sed si hoc verum esset etiam in aeq. V. prius oporteret
2Xdx et adque, quam xx =ay, unde non inveniretur aequatio
Exde = adque dicendum ergo. ia esse elidenda quae sunt gradus
elidi
uterioris. Cumsqe  aequ.  non sit habita nisi per primam differentiationem
elidendie tunt in ea doerentiationes secunde