Hüseyin Tevfik Pasha

Hüseyin Tevfik Pasha (1832 in Vidin, Ottoman Empire (now in Bulgaria) – 16 June 1901 in Constantinople (now Istanbul)) was a mathematician, author, and government official from the Ottoman Empire He served as military adjutant and Envoy of the Ottoman Empire to the United States, and served as Ottoman Minister of Finance from January – July 1881, and October 1897 – August 1898.

He is remembered for his Linear Algebra (1882, 1892) which outlined some vector algebra including a "special perpendicular" (cross product) and properties of curves. The book title was precocious since the early vector algebra was generalized in vector space, and this concept later produced linear algebra. He is known as Tawfiq Pasha of Vidin or as Vidinli Huseyin, Tawfiq Pasha in Turkish literature.

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". Tevfik was also offended by what he considered to be excess liberty and license among the lower classes in the United States. But complex numbers and quaternions are missing. Rather a three-dimensional treatment of geometry uses vectors extensively. A space algebra is introduced (page 16) with Products are given: :

Chapter three treats the cross product of vectors, calling it the "special perpendicular" and writing for the cross product of α and β. The special perpendicular is employed to compute the volume of a pyramid (p 35), an equation on skew lines that reduces to zero when they are coplanar, a property of a spherical triangle, and the coincidence of the perpendiculars in a tetrahedron.

Chapter four describes equations of geometric figures: line, plane, circle, sphere. The definition of a conic section is taken from Kelland and Tait: "the locus of a point which move so that its distance from a fixed point bears a constant ratio to its distance from a fixed straight line." Ellipse, hyperbola, and parabola are then illustrated.

Chapter five, "Some additional applications" introduces the instantaneous velocity of a point moving along a curve as a limit, a reference to calculus. The second rate of change is related to the reciprocal of the radius of curvature of the curve (p. 59)