# Convergence articles

Displaying 151 - 160 of 665

A bibliographical reference to mathematics books printed in the new world before 1700.

There are two numbers which are to each other as 5 and 6 and the sum of their squares is 2196. What are the numbers?
Prove that the area of a regular polygon can be given by the product of its perimeter and half the radius of the inscribed circle.

An introduction to the prime numbers in many of their aspects.

Now there are 100 deers [being distributed] in a city. If one household has one deer there is a remainder...Find the number of households in the city.
Thirty flasks-10 full, 10 half-empty, and 10 completely empty- are to be divided among 3 sons so that flasks and contents should be shared equally. How may this be done?
Having been given the perimeter and perpendicular of a right angled triangle, it is required to find the triangle.
A method for extracting square roots used in Italy through the 18th century was introduced in a manuscript by the 12th century mathematician al-Hassar.
The incircle O(r) of triangle ABC touches AB at D, BC at E and AC at F. Find r in terms of AD, BE and CF.

Chuquet claimed that if given positive numbers a, b, c, d then (a + b) / (c + d) lies between a/c and b/d. Is he correct? Prove your answer