Problems from Another Time

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

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?

Reverse the Digits

The sum of the two digits of a 2-digit number is 9. If 45 is subtracted from the number, the result will be expressed by the digits in reverse order. Find the number.

A Clothes Call

A man went to a draper and bought a length of cloth 35 braccia long to make a suit of clothes.

10 Into 3 Parts

Make of 10 three parts such that one part multiplied by 3 makes as much as the other multiplied by 4 and as the other multiplied by 5.

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?

Faster Than a Speeding Horse

A horse, halving its speed each day, travels 700 miles in 7 days. How far does it travel each day?