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Convergence articles

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

Our reviewer praises the selection of excerpts, the use of facsimiles rather than transcriptions, and the commentary and English translation in this collection.

A set of four congruent circles whose centers form a square is inscribed in a right triangle ABC where C is the right angle and serves as one corner of the square. Find their radius in terms of the sides; a,b,c, of the triangle.
This is the title page of the Treatise of Algebra (1685), by John Wallis. This is probably the first attempt at a history of the subject of algebra, presented in the context of a text on the subject. Among the most famous parts of this treatise is Wallis's discussion of the work of Thomas Harriot, especially his contention that Rene Descartes plagiarized Harriot's symbolization procedure in algebra.
Given a semicircle, Prove that if O is the circle's center, DO=OE.
The purchase price for an apple and an orange is 100 yen. When n oranges and n + 3 apples are bought the price is 520 yen. Find the number n of oranges and the price of one orange.
The radius of a circle is 3.20 meters. Compute to within .001m the areas of the inscribed and circumscribed equilateral triangles.
There is a circle from within which a square is cut, the remaining portion having an area of 47.6255 square units.
The highest point of the Andes is about 4 miles above sea level.

Images of the first printed edition of Euclid's Elements