The first ever calculus textbook

O primeiro livro de ensino do Cálculo

episodic thoughts

The first ever calculus textbook, according to wikipedia, appears to have been published in 1696 (that’s 318 years ago) by Guillaume de l’Hôpital (following lectures given to him by Leibnitz) under the name Analyse des Infiniment Petits pour l’Intelligence des Lignes Courbes.

Handily, it’s available on Gallica. It is explicitely stated at the outset that letters from the start of the alphabet are taken for constants, while the end of the alphabet is reserved for variables. Then on page 4 there’s the very modern-looking statement

La différence de $latex xy$ est $latex ydx+xdy$.

One would say la différentielle nowadays, but otherwise the notation was in nice final form.

Already on page 9 some computations appear that might be demanding for first year students nowadays:

diff_hop1

And while the first few graphs are just what one would expect:

diff_hop_fig1

it does become quite intricate beyond that:

diff_hop_fig2

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Sobre Américo Tavares

eng. electrotécnico reformado / retired electrical engineer
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