How would Johann Bernoulli have tutored Euler?

Question

Early in Euler's life (when he was still a child/teenager), the Euler family friend Johann Bernoulli would tutor Euler in mathematics.

Do we know how Johann Bernoulli would have tutored the young Euler in mathematics? What concepts would Bernoulli have focused on developing in Euler? What standard would Bernoulli use to determine that his pupil was gifted?

Are there interesting pedagogical notes we can draw out of this history?

Answer 1

The story seems a bit different, with Euler visiting Basel University at age 14:

Leonhard Euler's father was Paul Euler. Paul Euler had studied theology at the University of Basel and had attended Jacob Bernoulli's lectures there. In fact Paul Euler and Johann Bernoulli had both lived in Jacob Bernoulli's house while undergraduates at Basel. (..)

Leonhard was sent to school in Basel (..) Euler learnt no mathematics at all from the school. However his interest in mathematics had certainly been sparked by his father's teaching, and he read mathematics texts on his own and took some private lessons. Euler's father wanted his son to follow him into the church and sent him to the University of Basel (..) He entered the University in 1720, at the age of 14 (..) Johann Bernoulli soon discovered Euler's great potential for mathematics in private tuition that Euler himself engineered. Euler's own account given in his unpublished autobiographical writings, see [1], is as follows:

... I soon found an opportunity to be introduced to a famous professor Johann Bernoulli. ... True, he was very busy and so refused flatly to give me private lessons; but he gave me much more valuable advice to start reading more difficult mathematical books on my own and to study them as diligently as I could; if I came across some obstacle or difficulty, I was given permission to visit him freely every Sunday afternoon and he kindly explained to me everything I could not understand ...

[1] A P Youschkevitch, Biography in Dictionary of Scientific Biography (New York 1970-1990).

From Full MacTutor biography Leonhard Euler