 | Adrien Marie Legendre - Geometry - 1828 - 346 pages
...points, they must have the same centre, and form one and the same circumference. THEOREM. 109. Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre. First. Suppose the chord AB= DE. Bisect those chords... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...three points ; which has been shown by the proposition to be impossible. PROPOSITION VIII. THEOREM. Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre. 'First. Suppose the chord AB — DE. Bisect these... | |
 | Education - 1849 - 682 pages
...greater side. 2. In every triangle the sum of the three angles is equal to two right angles. 3. Two equal chords are equally distant from the centre ; and of two unequal chord«, the less is at the greater distance from the centre. 4. A straight line perpendicular to a... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...points ; which has been shown, by the proposition, to be impossible. PROPOSITION VIII. THEOEEM. Two equal chords are equally distant from the centre; and of two unequal chords, the less is at the greater distance from the centre. Suppose the chord AB to be equal to the chord DE.... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...has been shown, by the proposition, to be impossible. 64 GEOMETRY. * PROPOSITION VIII. THEOREM. Two equal chords are equally distant from the centre; and of two unequal chords, the less is at the greater distance from the centre, Suppose the chord AB to be equal to the chord DE.... | |
 | Horatio Nelson Robinson - Conic sections - 1865 - 474 pages
...triangles, ACE, and ECB, are equal in all respects, and AE = EB. Hence the theorem. THEOREM III. In the same circle, or in equal circles, equal chords are equally distant from the center. Let AB and EF be equal chords, and C the center of the circle. From C, draw CG and CH, perpendicular... | |
 | James Maurice Wilson - Geometry - 1868 - 150 pages
...straight line 8 THEOREM 4. Equal chords of a circle are equally distant from the centre, and conversely ; and of two unequal chords the greater is nearer to the centre than the less, and conversely 9 SECTION II. ANGLES IN SEGMENTS OF THE CIRCLE. PAGE THEOREM 5. The angle subtended... | |
 | Trinity College (Hartford, Conn.) - 1870 - 1008 pages
...angles on the same side together equal to two right angles, the two lines are parallel. 3. Prove that in the same circle or in equal circles, equal chords are equally distant from the center; and of two unequal chords, the less is the more remote from the center. 4. Prove that if a... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...parallel chords is the diameter perpendicular to these chords. PROPOSITION VIII.— THEOREM. 18. In the same circle, or in equal circles, equal chords...distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre. 1st. Let AB, CD, be equal chords ; OE, OF, the perpendiculars... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...parallel chords is the diameter perpendicular to these chords. PROPOSITION VIII.— THEOREM. 18. In the same circle, or in equal circles, equal chords...distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre. 1st. Let AB, CD, be equal chords ; OE, OF, the perpendiculars... | |
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In the same circle, or in equal circles, equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre. 
