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In Archimedes' Book of Lemmas (ca 250), he introduces a figure that, due to its shape, has historically been known as "the shoemaker's knife" or arbelos.

What is the perpendicular height of a cloud when its angles of elevation were 35 degrees and 64 degrees as taken by two observers at the same time...

There are a number of wonderful mathematics websites that readers of Convergence should be aware of. We describe some of them here.

A comprehensive history of trigonometry from ancient times to the Renaissance.

A general formed his men into a square, that is, an equal number in rank and file, and he found that he had an excess of 59 men.

Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.

A man entered an orchard through 7 gates, and there took a certain number of apples. When he left the orchard, he gave the first guard half the apples he had and 1 apple more.

A historically minded textbook designed to teach real analysis by considering some of the problems faced by 19th century mathematicians.

Having been given the perimeter and perpendicular of a right angled triangle, it is required to find the triangle.

The cavity of our chimney is an upright parallelepiped, the diagonal of whose base is 60"; and the height of the lower side of the lintel above the plane of the floor is 40".

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