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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 78r, page id 00068198:0155
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Mias homoq Etsi heterogenca rni sceru non possint
tamen corum logarillum possunt quia loganhum homoge-
differentialium seu eementarium homogeneisunt aliorum
Logarthnis cum semper sint rumeri. Ergi logus - log dx
non est contraria legi homogercorum posrae
Vidto  si videa ne nisi aliae adhuc artes accedant, nihil hinc
duei posse. Ex. gr. dus  dy = de Ncta-xD asit y progressionis Geometricae
c
ptologa
fiet log y =  log dy, adesque logy = 2leg (aa- xX) + 10g dx Y primum in gentem
venit talem aequationem posse utilem esse in casu, quo dx =0, seu ubi ordinata y est
maxima, ibi enim eoanescere logodx. Sed postea vii re melius considerata) vidi cum
dx est infinile parva, logaritimum ejus non evanescere, sed fieri infinitum. Es
tum demum evaniscere log. dx, cum dx = deo constanti. Est  seu ipsi
itaque quando dx = ady: y fiet logy = 2 loq (aa - XX), seu fiet
E casu dynds dyndx qua  Y (aa ) qua sed hoc video per se jam
ady: Y
patere, nam quo casu y: a = dy. dx fiet utique gr  cum semper
sit dy: dx = saa - xx): a, fiet g: a = Vsaa - Xx): a seu log_ y = = log (aa = XX)
itaque ut aliquid hinc duci possit, pot oportebit rett aliquam aliam
literam invenori ut Z, cujqus etiam relatio quadnatoria detur ad y
autem relationem inter X et y ita ut dx: dqe =  ixe
sa habito y logy= loqe X _ Ilog dque, pro t fiat logdque log dx- logtqe V loya
sed hic
ita ut fiat  alogu dz = v log dZ. et detur V per X vel Z
casus difficilis obtentu
dari