Euclid's Elements of geometry, the first six, the eleventh and twelfth books

by Euclid

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1752 ...did aright to give this rather than a worse. See Dr. Barrow's full and learned desence of this definition of Euclid, in his 21st and 2zd Mathematical Lectures; at the end of the latter whereof the Dr. concludes in these Tb(re is nothing extant in the nuhole ivori of the EL mi uts of Euclid more subtilely ini-entcd, mart solidly established, or mere accurately handled, than the decisive of proportionality. Some have given other definitions of proportion.-.l magnitudes, as Borcllus, in his Euciides ref1itutus; Taquet, in his Eu to to have a greater ratio to the second, than the third has to the fourth'. 8. Proportion is a similitude of ratios. did; and Malcolm, in his Arithmetic. But, as I have already faid, Euclid's is. the best of them all. I have sometimes thought that the doctrine of proportionality, in all quantities whatsoever, might be easily derived from the following positions, and Euclid's seventh book. 1. That those quantities that differ from one another by magnitudes less than any assignable magnitude! may be taken for equals, or represent one another. 2. That any four proposed magnitudes may either be accurately expressed in numbers, or else sour magnitudes that differ from teem by magnitudes less than any ajjignable ones may; and taerefore 3. Any four magnitudes may be taktn for proportionals, the first to the second, and the third to the fourths ivhen the produil of the multiplication of the numbers representing or measuring the first and fourth is equal to the product of the multiplication of the numbers represent1ng dr measuring the second and third magnitudes; and accordingly 4-Whatever properties of proportionality are deduced and demonstrated from the definition of proport1onal numbers, or fro/11 Euclid in his seventh book, nlill h...

130 pages, Paperback

First published January 1, 1957

About the author

Euclid (Ancient Greek: Εὐκλείδης Eukleidēs -- "Good Glory", ca. 365-275 BC) also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I (323–283 BC). His Stoicheia (Elements) is a 13-volume exploration all corners of mathematics, based on the works of, inter alia, Aristotle, Eudoxus of Cnidus, Plato, Pythagoras. It is one of the most influential works in the history of mathematics, presenting the mathematical theorems and problems with great clarity, and showing their solutions concisely and logically. Thus, it came to serve as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century. In the Elements, Euclid deduced the principles of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory and rigor. He is sometimes credited with one original theory, a method of exhaustion through which the area of a circle and volume of a sphere can be calculated, but he left a much greater mark as a teacher.