 | Henry Elmer Moseley - Universities and colleges - 1884 - 214 pages
...opposite these angles are unequal, and the greater side is opposite the greater angle. 5. Prove that in the same circle, or in equal circles, equal arcs are subtended by equal chords. 6. Prove that the square of a side of a triangle opposite an acute angle is equal to the sum of the... | |
 | George Bruce Halsted - Geometry - 1885 - 389 pages
...the greater has the greater arc and the greater angle. THEOREM XV. 373. In the same or equal circles, of two unequal minor arcs, the greater is subtended by the greater chord ; of two unequal major arcs, the greater is subtended by the lesser chord. HYPOTHESIS. Minor arc AB... | |
 | George Albert Wentworth - Arithmetic - 1886 - 392 pages
...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 by equal chords. Let the arcs AMB and CND be equal (Fig. 17). Turn the arc AMB about the centre 0 until it coincides... | |
 | George Bruce Halsted - Geometry - 1886 - 394 pages
...the greater has the greater arc and the greater angle. THEOREM XV. 373. In the same or equal circles, of two unequal minor arcs, the greater is subtended by the greater chord ; of two unequal major arcs, the greater is subtended by the lesser chord. JL o HYPOTHESIS. Minor arc... | |
 | 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...arcs the greater is subtended by the greater chord. In the equal circles DEF, HKL let the arc DE be equal to the arc HK • then shall the chord DE be... | |
 | George Albert Wentworth - 1889 - 276 pages
...78. Theorem. Circles having equal radii or equal diameters are equal; and conversely. 79. Theorem. In the same circle, or in equal circles, equal arcs are subtended by equal chords; and conversely. 80. Theorem. The radius perpendicular to a chord bisects the chord and the arcs subtended... | |
 | George Albert Wentworth - 1889 - 264 pages
...78. Theorem. Circles having equal radii or equal diameters are equal; and conversely. 79. Theorem. In the same circle, or in equal circles, equal arcs are subtended by equal chords; and conversely. 80. Theorem. The radius perpendicular to a chord bisects the chord and the arcs subtended... | |
 | 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... | |
 | 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... | |
 | George Anthony Hill - Geometry - 1889 - 200 pages
...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,... | |
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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. 
