 | Benjamin Peirce - Geometry - 1837 - 216 pages
...; for it has for its measure the half of an arc greater than a semicircumference. 111. Theorem. In the same circle, or in equal circles, equal arcs are subtended by equal chords. Demonstration. Let the arc AB (fig. 52) be equal to ihe arc BC. ' Join AC; and, in the triangle ABC,... | |
 | Adrien Marie Legendre - Geometry - 1837 - 376 pages
...same straight line, winch is impossible (Book I. Prop. XV. C«r. 2.). PROPOSITION IV. THEOREM. In ihe same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs Note. When reference is made from one proposition to another,... | |
 | James Bates Thomson - Geometry - 1844 - 268 pages
...which is impossible. (Prop. 15. 1. Cor. 2.) Hence, A straight line, $c. PROPOSITION IV. THEOREM. In the same circle, or in equal circles, equal arcs are subtended by equal chords; and, conversely, equal chords subtend equal arcs. If the radii AC, EO Dx-TP-v ^ are equal, and the arcs... | |
 | Nathan Scholfield - 1845 - 894 pages
...the same right line, which is impossible, (Prop. XVII. Cor. 2. B. II.) PROPOSITION IV. THEOREM. In the same circle or in equal circles, equal arcs are subtended by equal chords ; and conversely equal chords subtend equal arcs. If the radii AC, EO, are equal, and the arcs AMD, ENG;... | |
 | Benjamin Peirce - Geometry - 1847 - 204 pages
...; for it has for its measure the half of an arc greater than a semicircumference. 112. Theorem. In the same circle, or in equal circles, equal arcs are subtended by equal chords. Proof. Let the arc AB (fig. 52) be equal to the arc BC. Join AC ; and, in the triangle ABC, the angles... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...the same straight line, wmch is impossible (Book I. Prop. XV. Cor. 2.). PROPOSITION IV. THEOREM. In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs. Note. When reference is made from one proposition to another,... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...same straight line, which is impossible (B. L, P. 15, c. 2). GEOMETKY. PROPOSITION IV. THEOEEM. In the same circle, or in equal circles, equal arcs are subtended by equal chords : and conversely, equal chords subtend equal arcs. Let 0 and 0 be the centres of two equal circles, and suppose... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...1n a d1fferent Book, the number of the Book 1s also g1ven. 60 GEOMETRY. PROPOSITION IV. THEOREH. In the same circle, or in equal circles, equal arcs are subtended by equal chords : and conversely, equal chords subtend equal arcs. Let C and O be the centres of two equal circles, and suppose... | |
 | Jaime Luciano Balmes - Philosophy - 1856 - 568 pages
...the essential relations of things involves the condition that they exist. Thus, when we say that in the same circle or in equal circles equal arcs are subtended by equal chords, we suppose impliedly this condition, "if a circle exists." 48. Since this manner of explaining the... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...Proposition is found in a d1fferent Book, the number of the Book ia also given. PROPOSITION IV. THEOREM. In the same circle, or in equal circles, equal arcs are subtended by equal d1ords : and. conversely, equal chords subtend equal arcs. Let C and 0 be the centres of two equal... | |
| |
In the same circle, or in equal circles, equal arcs are subtended by equal chords : and conversely, equal chords subtend equal arcs. 
