Hüseyin Tevfik Pasha

Upon the death of his teacher, Tevfik took over his classes and began to instruct students in algebra, analytic geometry, calculus, mechanics and astronomy.

He continued in diplomatic and military service: According to Sinan Kuneralp, Tawfik was "A mathematician of great talent, he assembled during his long stay a valuable library of scientific works and regularly lectured on a variety of subjects in clubs and institutes on the East coast".

[3]: 102  Tevfik was also offended by what he considered to be excess liberty and license among the lower classes in the United States.

Tevfik's book refers on page 11 to Introduction to Quaternions by Kelland and Tait which came out with a second edition in 1882.

Chapter four describes equations of geometric figures: line, plane, circle, sphere.

Chapter five, "Some additional applications" introduces the instantaneous velocity of a point moving along a curve as a limit, a reference to calculus.