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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. "
Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ... - Page 56
by Nathan Scholfield - 1845
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1895 - 450 pages
...straight line, which is impossible (BI, Pr. 17, Cor. 2*). Therefore a straight line, etc. PROPOSITION III. THEOREM. In the same circle or in equal circles, equal...are subtended by equal chords, and conversely equal chorda subtend equal arcs. Let ADB, EHF be equal circles, and let the arcs AI D, EMU also be equal;...
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Elements of Geometry: Plane and Solid

John Macnie - Geometry - 1895 - 386 pages
...shortest, distance from a point within a circle to its circumference. PROPOSITION V. THEOREM. 174. In the same circle, or in equal circles, equal arcs are subtended by equal chords; and conversely. 1°. Given: In equal circles ADB, A'D'B', AB, A'B', chords of equal arcs ACB, A'C'B' ; To Prove: Chord...
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Concrete Geometry for Beginners

Adelia Roberts Hornbrook - Geometry - 1895 - 224 pages
...each arc by a chord. Superpose and show the truth of the following principle : PRINCIPLE 11. — In the same circle or in equal circles equal arcs are subtended by equal chords. 84. Given the angle ABC 40° ; how many degrees has the angle formed by prolonging CB to D? By prolong-...
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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1899 - 246 pages
...equal central angles ; and of two unequal arcs the greater subtends the greater central angle. 241. In the same circle or in equal circles, equal arcs are subtended by equal chords ; and of two unequal arcs the greater is subtended by the greater chord. 249. In the same circle or in equal...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 496 pages
...no proof like that given in the text is required to establish it. PROPOSITION III. THEOREM. 241. In the same circle or in equal circles, equal arcs are subtended by equal chords; and of two unequal arcs the greater is subtended by the greater chord. In the equal circles whose centres...
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Plane Geometry

George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...no proof like that given in the text is required to establish it. PROPOSITION III. THEOREM. 241. In the same circle or in equal circles, equal arcs are subtended by equal chords; and of two unequal arcs the greater is subtended by the greater chord. In the equal circles whose centres...
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The Elements of Plane Geometry

Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...A ABE = A CDE. (?) .-. ZAEB = Z CED. (?) .-. arc AB = arc CD. (?) Proposition 99. Theorem. 132. In the same circle, or in equal circles, equal arcs are subtended by equal chords. Proposition 1OO. Theorem. 133. In the same circle, or in equal circles, if two chords are unequal,...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...then said to be circumscribed about the polygon. PROPOSITION II. THEOREM 177. In the same circle, or equal circles, equal arcs are subtended by equal chords;...and, conversely, equal chords subtend equal arcs. Hyp. In equal ©, O and O', arc AB = arc A'B'. To prove AB = A'B'. Proof. Draw radii, OA, OB, O'A',...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...then said to be circumscribed about the polygon. PROPOSITION II. THEOREM 177. In the same circle, or equal circles, equal arcs are subtended by equal chords...and, conversely, equal chords subtend equal arcs. Hyp. In equal ©, O and O', 76 THE CIRCLE Proof. Draw radii, OA, OB, O'A', O'B'. (equal arcs subtend...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...then said to be circumscribed about the polygon. PROPOSITION II. THEOREM 177. In the same circle, or equal circles, equal arcs are subtended by equal chords;...and, conversely, equal chords subtend equal arcs. Hyp. In equal ©, O and O', Proof. Draw radii, OA, OB, O'A', O'B'. Z AOB = Z A'O'B', (equal arcs subtend...
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