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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 103r, page id 00068200:0207
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29 Abventus
1679C
quaeddam observata circa modum d. d. dy. dus. ddus.
dx. dx. ddx ex se invicem inveniendi item
mne problema Taugentium re einversum, in quo non
habentur non aliae literae indeterminatae quam  y. de dus.
reducitur ad quadratutam. sit enim i  non
aliae x infinite parvae, quam dx. du. sine ipsarum
potentiis, reducitur ad quadraturam, et vet nulla ex ipsis
sit aequatio a+ bd 1btus t c Xdx c2 dus 4 cy dx + cy ty 1
indefinite parvis, vel alterutra galtem, non vero utraque
assurgit ad aliquam potentiam, tunc problema reducitur
ad quad raturam.
sit aequatio a + b xA btus + C dus +cd.
 ina cy  ayrgal hys etc du
sit aequatio a + b dx + bdus +  cX dx + ex ly + fy det gas dythll
h x dx + Kx Ydu + lX ax + im X u + n yt x + p y dus. 10
Ponatur y A Fy. seu ponantur d esse progussionis Geometricae
fiet VB do ry et Y x et ita porro
fiet: arbdu + b = 7β+ erc fy +x + g 97B
a + bx + cy + Cxy +5~ +g5  h Xy 1 k y la+ mos 0
Orun
quandocunque in aequatione differentiali unaquaeque indeterminata
non nisi a suis aut suarum indeterminatarum disfe differentus
aut primi secundi alte cujuscunque eae sint gradus afficitur
problema reducitur ad quadraturam
sit Nam omnium Xd x l item:
a+ bx+ xe 
br aliterque summa
( e +fX+GN ete
haben potest.
haberi potet idemque est etsi ponatur de. vel 3
ponendo enim  progressionis arithmetiaae aequantur fit dx d  
e) constantires eodem redit
ee
Hinc si sit aequatio: a + ba + ex + ex dc + Y. x
V. X. . ... x
. n. y + V.. G+ Yuits
Suyt suoy
problema reductum est ad quadraturam duarum harum
figurarum. Quod si fuisset utrebique di tus. E an
debemus extraher ad (nam ubique debet utobique eadem esse potentia
indeterminatae) possumus utrique extrahere radicem quam opus est,
et habetur aequatio in qua hinc solum ex illinc solum dus
quanquam exculiendum an hac extactione opus, nam ut supra)
dix. hac summa hujus seei talium ordinatarum ae du haber potet
oC
eodem mo
.. x0 4 haberi potest perinde ac si esset dx.
sed hoc discitiendum. Idem est si habeatur dix et ddque t ita porro