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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 271v, page id 00068196:0538
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e ()
X
a
 V
2
a-5
Ergo e x. Ax = a V. dy
 dividento aequ. 2 per aeq. 1. fit.
seu e Saxix 4) ay:
C. _ax : X = a. dy: y.. ryse
Ergo e: a = (dy: y: (dx: X
Si de sint progressionis arithmeticae, erunt
dx: x progressionis Geonetricae Nam
Si X sint progressionis Geometricae erunt dx: X
progressionis Arithmeticae nacu si X est progressionis
Geometricae, erit dx ejusdem propositionis Geometricae
ergo dx: X est constans, ergo (dxix est
progressionis Arithmeticae. Eodem modo ostentitur
etiam X: ex dore, Arithmetriae progressionis si X
est Geometricae. Aee e8 Eodem argumento si
X sit progressionis Geoucetrie a dx:  est reciprocae
psius X, et dx: X est ut 1: XX et ita porro
Si X+a sit. progressionis Geometricae, etiam sdx: xa
erit Arthmeticae
si _ X +a Et progressionis
Gegmetrica, erit sex Lx: nera progressionis
Arihunticae
Oc .
e
. simuliter pollumus pocedere nnn tollendae serimum
ad sed cun quaerendo aequalione  exprimendi
secundum X et a reliquis literis sub generalibus coefficientia, dissimulatis
s
(+ X
inde assumemus aliam vl aquationem etiam continentem X
et a et quidem talem s ejus pe loco aegr.2.
differentiatem 3) ope 2 et 3 tollemque tom X quam ex
ex aeq: 1 restabit sola a cum liters  factitiis quarum
opes torcenda; sed puto viam praecedentis pagrnae eesse
imblitem faclius engu initit tolilu a, quam X
N
sed quando a er ifficalius tollitur licebit collere plius X
habemus cuum electionem