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Convergence articles

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In a rectangle, given the diagonal and perimeter, find the sides

This is the title page of the Nova Scientia (1537) of Niccolo Tartaglia (1499-1557). In this work, Tartaglia discussed the mathematics of artillery and developed methods for determining the range of a cannon.

If 40 oranges are worth 60 apples, and 75 apples are worth 7 dozen peaches, and 100 peaches are worth 1 box of grapes and three boxes of grapes are worth 40 pounds of pecans, how many pounds of pecans can be bought for 100 oranges?

Apollonius found how to draw normals to an ellipse from points in the ellipse by using hyperbolas. A modern version is presented here.

Three equal circles with radii 12 feet are tangent to each other. Compute the area enclosed between them.

A fox, a raccoon, and a hound pass through customs and together pay 111 coins.
One says that 10 is divided into three parts and if the small part is multiplied by itself and added to the middle one multiplied by itself the result is the large one multiplied by itself...
If in a circle ABDC, circumscribe an equilateral triangle ABC; the straight line AD is equal to the sum of the two straight lines BD and DC: required a demonstration.

A sketch of the history of topology, beginning with the polyhedron formula, but continuing up to the present.

Three vertical posts along a straight canal, each rising to the same height above the surface of the water. By looking at the line of vision, determine, to the nearest mile, the radius of the earth.