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Problems from Another Time

Individual problems from throughout mathematics history, as well as articles that include problem sets for students.

'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript - Acceptance of Negative Solutions
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
An Inscribed Ellipse
Given right triangle ABC where C is the right angle, ellipse O (a,b) is inscribed in it, with its major axis parallel to BC. Calculate the semi-major axis, a, in terms of AC, BC and b.
Viete: Triangle II
In a right triangle, the hypotenuse is 13 and the sum of the sides around the right angle is 17. Find the lengths of the sides around the right angle.
Travelling Steamers
The steamer, Katie, leaves the wharf at New Orleans and runs an average speed of 15 mph. When Katie had gone 25 miles, the steamer R.E. Lee leaves the wharf and runs the average speed of 18 mph. How far will the Lee go before she overtakes the Katie?
Bicyclists on a Track
Two bicyclists travel in opposite directions around a quarter-mile track and meet every 22 seconds. When they travel in the same direction on this track, the faster passes the slower once every 3 minutes and 40 seconds. Find the rate of each rider
To Each His Due
A man has four creditors. To the first he owes 624 ducats; to the second, 546; to the third, 492; and to the fourth 368.
Three Vertical Posts
Three vertical posts along a straight canal, each rising to the same height above the surface of the water. By using measurments of the posts, determine, to the nearest mile, the radius of the earth.
A Circular Problem
Determine the dimensions of the least isosceles triangle ACD that can circumscribe a given circle.
Ladder Day Question
A ladder is placed perpendicular to the plane of the horizon, and in coincidence with the plane of an upright wall.
Walk Around the World
Suppose a person whose height is 5 feet 7 inches travels 10000 miles in the arc of a great circle. How much further will the person's head have gone compared to their feet, the circumference of the Earth being 21600 miles?

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