 | 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,... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...; and of two unequal arcs the greater subtends the greater angle at the centre. §§ 159, 160. (c) Equal arcs are subtended by equal chords ; and of...arcs, the greater is subtended by the greater chord. §§ 161, 162. (<Z) Equal chords subtend equal arcs ; and of two unequal chords, the greater subtends... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...the same circle or in equal circles two arcs are equal, the chords subtending them, are also equal; and of two unequal minor arcs, the greater is subtended by the greater chord. Let the pupil give a particular enunciation of the theorem, applying it to the diagram. Suggestions... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...the angle COD will coincide with the angle C'O'D'. Therefore, etc. PROPOSITION VI. — THEOREM. In the same circle, or in equal circles, equal arcs are subtended by equal clwrds; and, CONVERSELY, equal chords subtend equal arcs. Given. — In the two equal circles whose... | |
 | George Albert Wentworth - Geometry, Solid - 1902 - 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 circles, equal... | |
 | Education - 1902 - 880 pages
...figure is a parallelogram. 3 Prove that two mutually equiangular triangles are similar. 4 Prove that in the same circle or in equal circles equal arcs are subtended by equal chords. State th*e converse of this theorem. 5 Complete and demonstrate the following: the area of a regular... | |
 | Education - 1902 - 780 pages
...figure is a parallelogram. 3 Prove that two mutually equiangular triangles are similar. 4 Prove that in the same circle or in equal circles equal arcs are subtended by equal chords. State the converse of this theorem. 5 Complete a.nd demonstrate the following: the area of a, regular... | |
 | George Albert Wentworth - Geometry - 1904 - 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 are O and O',... | |
 | Isaac Newton Failor - Geometry - 1904 - 100 pages
...triangle. 328. Circumscribe a circle about an equilateral triangle. 329. Show by superposition that in the same circle or in equal circles equal arcs are subtended by equal chords. 330. Mark a point P within a circle and draw through it the longest and the shortest possible chords... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...part of it that is both a segment and a sector. BOOK II. PLANE GEOMETRY PEOPOSITIOK V. THEOREM 219. In the same circle, or in equal circles, equal arcs are subtended by equal chords. B" Given the equal circles 0 and 0', and arc AB = arc A'B'. To prove chord AB = chord A'B'. Proof.... | |
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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. 
