 | 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, John Farrar - Geometry - 1825 - 280 pages
...circumference can pass through three given points. THEOREM. o 109. Two equal chords are at the same distance from the centre, and of two unequal chords the less is at the greater distance from the centre. Demonstration 1. Let the chord AB = DE (fig. 53). Bisect Fig. 53. these chords by the perpendicular... | |
 | Adrien Marie Legendre - 1825 - 570 pages
...would make one and the same circumference. THEOREM. 109. Two equal chords are at the same distance from the centre, and of two unequal chords the less is at the greater distance from the centre. Demonstration 1. Let the chord AB = DE (fig. 53). Bisect Fig. 53. these chords by the perpendicular... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...circumference can pass through three given points. THEOREM. 109. Two equal chords are at the same distance from the centre, and of two unequal chords the less is at the greater distance from the centre. Demonstration 1. Let the chord AB = DE (Jig. 53). Bisect Fig. 33: these chords by the perpendicular... | |
 | 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 - 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 ;...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
...three points ; which has been shown by the proposition to be impossible. PROPOSITION VIII. THEOREM. Two equal chords are equally distant from the centre ;...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
...would make one and the same circumference. THEOREM. 1 09. Two equal chords are at the same distance from the centre ; and, of two unequal chords, the less is at the greater distance from the centre. Demonstration 1. Let the chord AB — DE (fig. 53). Bisect Fig. 53. these chords by the perpendiculars... | |
 | 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... | |
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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. 
