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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 and Trigonometry from the Works of A.M. Legendre ... - Page 64
by Charles Davies - 1854 - 432 pages
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 208 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...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 224 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...
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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
...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...
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Elements of Geometry

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...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 280 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...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 346 pages
...common 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...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...circumferences passing through the same three points ; which has been shown by the proposition to be impossible. PROPOSITION VIII. THEOREM. Two equal chords are equally...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 - 1837 - 359 pages
...circumferences passing through the same three points ; which has been shown by the proposition to be impossible. PROPOSITION VIII. THEOREM. Two equal chords are equally distant from the centre ; andofttno unequal chords, the less is at the greater distance from tfi* wntre First. Suppose 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

Adrien Marie Legendre - Geometry - 1839 - 372 pages
...three points; which has been shown by the proposition to be impossible. PROPO8ITION VIII. THEOREM. 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 radii...
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