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" Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre. "
Elements of Geometry - Page 29
by Adrien Marie Legendre - 1841 - 235 pages
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 208 pages
...CFis evidently greater than CO, and CO than C/(52) ; for a still stronger reason CF^> CI. But CF = CO, since the chords AB, DE, are equal. Therefore CG >...only the point A in common with the circumference ; there BD is a tangent (97). 111. Scholium. We can draw through a given point A only one tangent AD...
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Elements of Geometry

Adrien Marie Legendre - 1825 - 570 pages
...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...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 280 pages
...one and the same circumference. . • 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. these chords by the perpendicular CF,...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...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...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 346 pages
...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 by the perpendiculars CF, CG, and draw the radii...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...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 chords by the perpendiculars CF, CG, and draw the...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1838 - 386 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...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 384 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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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...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. From C the centre of the circle, draw CF, and CG...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...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. From C the centre of the circle, draw CF, and CG...
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