| Association for the Improvement of Geometrical Teaching - Euclid's Elements - 1888 - 208 pages
...A chord of a circle is the straight line joining any two points on the circumference. THEOR. 6. In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and of two unequal minor arcs the greater is subtended by the greater chord. In the equal circles DEF,... | |
| George Albert Wentworth - Arithmetic - 1888 - 378 pages
...not cease to coincide with the circumference when the sector is made to turn about its centre. 366. THEOREM. In the same circle, or in equal circles, equal arcs are subtended Iry equal chords. Let the arcs AMB and CND be equal (Fig. 17). Turn the arc AMB about the centre O... | |
| George Albert Wentworth - 1889 - 276 pages
...other chord. 78. Theorem. Circles having equal radii or equal diameters are equal; and conversely. 79. Theorem. In the same circle, or in equal circles,...arcs are subtended by equal chords; and conversely. 80. Theorem. The radius perpendicular to a chord bisects the chord and the arcs subtended by the chord.... | |
| George Albert Wentworth - 1889 - 264 pages
...other chord. 78. Theorem. Circles having equal radii or equal diameters are equal; and conversely. 79. Theorem. In the same circle, or in equal circles,...arcs are subtended by equal chords; and conversely. 80. Theorem. The radius perpendicular to a chord bisects the chord and the arcs subtended by the chord.... | |
| George Anthony Hill - Geometry - 1889 - 200 pages
.../^'£~^>P c / What is the conclusion ? PROOF. Apply No. 1, p. 70, and No. 15, p. 96. } , FIG. 100. 19. Theorem. — In the same circle, or in equal circles, equal arcs are subtended by equal chords (Fig. 100). What is the hypothesis ? What is the conclusion ? PROOF. Apply No. 16, p. 96, and No. 14,... | |
| James Wallace MacDonald - Geometry - 1889 - 80 pages
...Book I., Proposition XVI., Corollary. Proposition III. A Theorem. Proposition IV. A Theorem. 167. In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and conversely, if the chords are equal, the arcs also are equal. Proposition V. A Theorem. 168. In the same circle,... | |
| James Wallace MacDonald - Geometry - 1894 - 76 pages
...III. A Theorem. 166. The diameter is longer than any other chord. Proposition IV. A Theorem. 167. In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and conversely, if the chords are equal, the arcs also are equal. Proposition V. A Theorem. 168. In the same circle,... | |
| George Anthony Hill - 1891 - 206 pages
...the hypothesis? What is the conclusion ? PROOF. Apply No. 1, p. 70, and No. 15, p. 96. Fio. 100. 19. Theorem. — In the same circle, or in equal circles, equal arcs are subtended by equal chords (Fig. 100). What is the hypothesis ? What is the conclusion ? PROOF. Apply No. 16, p. 96, and No. 14,... | |
| 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;... | |
| 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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