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If a nonnegative quantity was so small that it is smaller than any given one, then it certainly could not be anything but zero. To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be. These supposed mysteries have rendered the calculus of the infinitely small quite suspect to many people. Those doubts that remain we shall thoroughly remove in the following pages, where we shall explain this calculus.
Loci: Convergence
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Mathematical Treasures
Isaac Barrow's edition of Euclid's Elements
This is the title page of Isaac Barrow’s (1630-1677) Euclide's Elements, 1660 edition. Barrow was self-taught in geometry. He originally published this book in 1655 as a simplified version of the Elements. It became very popular, and for the next half century was the standard English language text on the subject.
Below are pages 10 and 11 of Barrow’s Euclide's Elements. The illustration on page 11 presents Euclid's proof of Proposition I.5 (The base angles of an isosceles triangle are equal). This is the Pons Asinorum [Bridge of Asses] of medieval geometry. If one could prove this proposition, he or she was considered a competent mathematician.
