68.
Arabian algebra: *
Although Al-Khwarizmi is the dominant figure, other Islamic scholars also made contributions. The Egyptian mathematician Abū Kāmil Shujā ibn Aslam (c. 850–930) first to accept irrational numbers as solutions to quadratic equations or as coefficients in an equation & first to solve 3 non-linear simultaneous equations with 3 unknown variables. Al-Karaji (953–1029) first to free algebra from geometrical operation & produced the greatest Arabic studies on algebra. He systematically studied the algebra of exponents & was the first to realize that the sequence x, x^2, x^3,... could be extended indefinitely. He was the first to operate with higher roots and to solve equations in the form of x^2n + ax^n=b. His work on algebra & polynomials gave the rules for arithmetic operations to manipulate polynomials. Omar Khayyám (1050- 1123 AD) considered equations of the 3rd degree, & provided both arithmetic & geometric solutions for quadratic equations. Sharaf al-Dīn al-Tūsī (1135–1213) dealt with 8 types of cubic equations with positive solutions & 5 types of cubic equations which may not have positive solutions.
Algebraic notation also advanced. Al-Hassār (Morocco) 12th century developed the modern symbolic mathematical notation for fractions (numerator & denominator separated by horizontal bar). Abū al-Hasan ibn Alī al-Qalasādī (1412–1486) introduced algebraic symbolism by using letters in place of numbers & by using initial letters, as mathematical symbols.
69.
Classical mechanics: *
Aristotle saw a distinction between "natural motion" and "forced motion", and he believed that in a hypothetical vacuum, there would be no reason for a body to move naturally toward one point rather than any other, and so he concluded a body in a vacuum must either stay at rest or else move indefinitely fast. He was the first to approach something similar to the law of inertia; he believed a vacuum would be impossible because the surrounding air would rush in to fill it immediately. He also believed that an object would stop moving in an unnatural direction once the applied forces were removed. In 260 BC Archimedes worked out the principle of the lever & connected buoyancy to weight. In 60 AD Hero of Alexandria wrote about the lifting of heavy objects and machines working on pressure; in 350 AD Themistius studied static friction & kinetic friction.
70.
art of the gems: *
Youth Adjusting His Sandal Strap, Greek, about 500 B.C., attributed to Epimenes. Cornelian scarab intaglio; 5/8 inch high, 3/8 inch wide, 5/16 inch in diameter.
