- #1

qxcdz

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The geist of it is this: [tex]\mathrm d[/tex] and [tex]\int[/tex] are actually operators, with [tex]\mathrm d[/tex] being an operator that creates an infinitesimal from a variable, and [tex]\int[/tex] being a special kind of summation operator. So, whereas now, we'd recognise [tex]\int \mathrm dx[/tex] as being the same as [tex]\int 1 \mathrm dx[/tex], Leibniz would have seen it as applying an infinitesimal operation to a variable, and then it's inverse.

So, when Leibniz wrote things like [tex]\frac{\mathrm dy}{\mathrm dx}=\frac{\mathrm dy}{\mathrm dt}\cdot \frac{\mathrm dt}{\mathrm dx}[/tex], he saw it as literally cancelling down fractions, not as a trick with limits that just resembles cancelling down fractions.

Is this really what the notation meant? Is it still valid?