Elements of geometry, containing the first six books of Euclid

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. 1826 ...right PROPOSITION XXII. Theorem. which are les. Let ABDc be a circle, and Abdc a quadrilateral figure in it. Then any two opposite angles of »S2.1. it are equal" to two right angles; join Ad, Bc. Therefore because the three angles of every triangle are equal to two right angles, the angles Cab, Abc, Cba, are equal to two right angles. But the '. t1. 3. angle Abc is equalb to the angle Adb, for they are in the same segment, Abdc. And the angle Acb will De equal to the angle Adb, because they are in the same segment, therefore the whole angle Bdc is equal to the angles Abc, Acb. Take away the angle Bac, which is the angles Bac, Abc, Acb, are equal to the angles Bac, Bdc. But the angles Bac, Abc, Acb, are equal to two right wherefore also the angles Bac, Bdc, are equal to two right angles. In like manner we can demonstrate that the angles Abd, Acd, are also equal to two right angles. Therefore the opposite angles, &c. Q. E. D. Deduction. If two opposite angles of any trapezium be equal to two right angles, the other two angles are equal to two right angles, and a circle may be described about it. PROPOSITION XXIII. Theorem. Upon the same straight line, and on the same side of it, two similar segments of circles cannot be described which do not coincide with each other. For, if it be possible, on the same right line, Ab, let two similar segments of circles, Acb, Adb, be de scribed, which do not coincide with each other. Let the circum-ferences Acb, Adb, meet one ano-ther at the points1 A, B, and they, „ havea no other points common ex-A--»B » 10.3. cept A, B. But between A, B, one will be interior, and the other exterior. In the interior take any point c, and join A c, which, produced, will meet the ext...

Genres: Mathematics, Science, Nonfiction, History, Classics, Ancient

60 pages, Paperback

First published January 26, 2013

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.