 In the same or in equal circles, of two unequal chords, the less is at the greater distance from the centre. DEM. — Let CE < AB, then is the perpendicular OD, which measures the distance of CE from the centre, greater than OD' •which measures the...  A Treatise on Special Or Elementary Geometry - Page 81by Edward Olney - 1872 - 1 pagesFull view - About this book
 | Adrien Marie Legendre - Geometry - 1819 - 574 pages
...still stronger reason CF^> CI. But CF = CO, since the chords AB, DE, are equal. Therefore CG > CI, and of two unequal chords the less is at the greater distance from the centre. THEOREM. 110. The perpendicular BD (fig. 54), at the extremity of the Fig. 54. radius AC, is a tangent... | |
 | Adrien Marie Legendre - Geometry - 1825 - 276 pages
...still stronger reason CF > CI. But CF = CG, since the chords AB, DE, are equal. Therefore CG > CI, and of two unequal chords the less is at the greater distance from the centre. THEOREM. 110. The perpendicular BD (fig. 54), at the extremity of the Fig. radius AC, is a tangent... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...still stronger reason CF> CI. But CF = C3, since the chords AB, DE, are equal. Therefore CG > CI, and of two unequal chords the less is at the greater distance from the centre, THEOREM. 110. The perpendicular BD (fig. 54), at the extremity of the Fij. 54," radius AC, is a tangent... | |
 | Adrien Marie Legendre - Geometry - 1828 - 346 pages
...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 by the perpendiculars CF, CG, and draw the radii... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...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 chords by the perpendiculars CF, CG, and draw the... | |
 | Adrien Marie Legendre - Geometry - 1838 - 382 pages
...III. 47 PROPOSITION VIII. THEOREM. Two equal chords are equally distant from the centre ; andoftwo unequal chords, the less is at the greater distance from the centre. First. Suppose the chard AB = DE. Bisect these chords by the perpendiculars CF, CG, and draw the radii... | |
 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...still stronger reason, CF^> CL But CF= CG, since the chords AB, DE, are equal. Therefore CG'^> CI, and of two unequal chords, the less is at the greater distance from the centre. THEOREM. 110. The perpendicular BD (fig. 54), at the extremity of the Fig. 54. radius AC, is a tangent... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...points. PROPOSITION VIII. THEOREM. Two equal chords are equally distant from the centre ; andoftioo unequal chords, the less is at the greater distance from the centre. First. Suppose the chord AB = DE. Bisect these chords by the perpendiculars CF, CG, and draw the radii... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...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. From C the centre of the circle, draw CF, and CG... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...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. From C the centre of the circle, draw CF, and CG... | |
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