 | 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
...given ; out when the 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... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...impossible (Prop. XVII., Cor. 2, Book I.). Therefore, a straight line, &c. PROPOSITION HI. THEOREM. • In equal circles, equal arcs are subtended by equal...and, conversely, equal chords subtend equal arcs. Let ADB, EHF be equal circles, and let the arcs AID, EMH also be equal ; then will the chord AD be... | |
 | Elias Loomis - Conic sections - 1860 - 246 pages
...impossible (Prop. XVII., Cor. 2, Book I.). fore, a straight line, &c. PROPOSITION HI. THEOREM. ThereIn equal circles, equal arcs are subtended by equal chords...and, conversely, equal chords subtend equal arcs. , Let ADB, EHF be equal circles, and let the arcs AID, EMH also be equal ; then will the chord AD be... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...straight line, which is impossible (Prop. XIV. Cor. 2, Bk. I.). PROPOSITION III. — THEOREM. 173. In the same circle, or in equal circles, equal arcs are...chords; and, conversely, equal chords subtend equal arm. BOOK III. For, since the diameters AB, EF are equal, the semicircle ADB may be applied to the... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...XIV. Cor. 2, Bk. I.). PROPOSITION III. — THEOREM. 173. In, the same circle, or in equal circfes, equal arcs are subtended by equal chords; and, conversely, equal chords subtend equal arcs. BOOK III. For, since the diameters AB, EF are equal, the semicircle ADB may be applied to the semicircle... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...straight line, which is impossible (Prop. XIV. Cor. 2, Bk. I.). PROPOSITION III. — THEOREM. 173. In the same circle, or in equal circles, equal arcs are...and, conversely, equal chords subtend equal arcs. BOOK III. For, since the diameters AB, EF are equal, the semicircle AF~~ r IB E ADB may be applied... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...cannot meet the circumference in more than two points ; which was to be proved. PROPOSITION IV. THEOREM. In equal circles^ equal arcs are subtended by equal...; and conversely, equal chords subtend equal arcs. 1°. In the equal cirMes ADB and EGF, let the arcs AMD and ENG- be equal : then will the chords AD... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...straight line, which is impossible (Prop. XIY. Cor. 2, Bk. I.). \ PROPOSITION III. — THEOREM. 173. In the same circle, or in equal circles, equal arcs are...and, conversely, equal chords subtend equal arcs. For, since the diameters AB, EF are equal, the semicircle Af ADB may be applied to the semicircle EGF... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...cannot meet the circumference in more than two points ; which was to be proved. PROPOSITION IV. THEOREM. In equal circles, equal arcs are subtended by equal...,' and conversely, equal chords subtend equal arcs. 1°. In the equal circles ADB and EGF, let the arcs AMD and ENG be equal : then will the chords AD... | |
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In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs. 
