 In the same circle or in equal circles, equal chords subtend equal arcs; and of two unequal chords the greater subtends the greater arc. In the equal circles whose centres are 0 and 0', let the chords AB and A'B' be equal, and the chord AF greater than...  An Elementary Treatise on Plane and Solid Geometry - Page 31by Benjamin Peirce - 1873 - 150 pagesFull view - About this book
 | Benjamin Peirce - Geometry - 1847 - 204 pages
...halves of the equal arcs BC and AB. The triangle ABC is therefore isosceles, by § 58, and the chords AB and BC are equal. 113. Theorem. Conversely, in the...the arcs AB and BC, which are double their measures. 114. Theorem. In the same circle, or in equal circles, if the sum of two arcs be less than a circumference,... | |
 | George Anthony Hill - Geometry - 1889 - 200 pages
...is said "to be subtended by" the chord AB. To subtend means to stretch across. 18. Theorem. — In the same circle, or in equal circles, equal chords subtend equal arcs. What is the hypothesis? What is the conclusion ? PROOF. Apply No. 1, p. 70, and No. 15, p. 96. Fio.... | |
 | George Anthony Hill - 1891 - 206 pages
...is said "to be subtended by" the chord AB. To subtend means to stretch across. 18. Theorem. — In the same circle, or in equal circles, equal chords subtend equal arcs. "What is the hypothesis? What is the conclusion ? PROOF. Apply No. 1, p. 70, and No. 15, p. 96. Fio.... | |
 | George D. Pettee - Geometry, Modern - 1896 - 272 pages
...of = 'S 1 ] coincident extremities [common vertex, coincident sides] PROPOSITION II 146. Theorem. In the same circle, or in equal circles, equal chords subtend equal arcs, and, conversely, equal arcs are subtended by equal chords. Appl. Let m represent the n " " AB=12. Prove... | |
 | George Washington Hull - Geometry - 1897 - 408 pages
...concave arc is the line which passes through the centre of the circle. PROPOSITION VI. THEOREM. 155. In the same circle, or in equal circles, equal chords subtend equal arcs. D Given—AC and MN equal chords in the equal circles A CD and MNP. To Prove— arc AC= arc MN. Dem.—Draw... | |
 | George Albert Wentworth - Geometry - 1899 - 496 pages
...subtends the greater £). .-. chord AF > chord A'B'. § 154 Q. £. D. PROPOSITION IV. THEOREM. 243. CONVERSELY: In the same circle or in equal circles, equal chords subtend equal arcs; and of two unequal chords the greater subtends the greater arc. In the equal circles whose centres... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...unequal arcs subtends the greater Z). .-. chord AF > chord A'B'. § 154 QED PROPOSITION IV. THEOREM. 243. CONVERSELY: In the same circle or in equal circles, equal chords subtend equal arcs; and of two unequal chords the greater subtends the greater arc. In the equal circles whose centres... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...arcs are unequal, the greater arc subtends the greater central angle. Proposition 98. Theorem. 131. In the same circle, or in equal circles, equal chords subtend equal arcs. Hypothesis. In the OABD, of which E is the centre, chord AB = chord CD. Conclusion. Arc AB = arc CD.... | |
 | William James Milne - Geometry - 1899 - 404 pages
...circle. Which chord subtends the larger arc ? Which arc is subtended by the less chord ? Theorem. In the same circle, or in equal circles, equal chords subtend equal arcs; conversely, equal arcs have equal chords. Data : The equal circles whose centers are O and P, and any... | |
 | William James Milne - Geometry, Modern - 1899 - 258 pages
...circle. Which chord subtends the larger arc? Which arc is subtended by the less chord? Theorem. In the same circle, or in equal circles, equal chords subtend equal arcs; conversely, equal arcs have equal chords. Data : The equal circles whose centers are 0 and P, and any... | |
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