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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. "
Syllabus of Propositions in Geometry: Intended for Use in Preparing Students ... - Σελίδα 7
των Harvard University - 1899 - 31 σελίδες
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Elements of Geometry

Adrien Marie Legendre - 1819 - 574 σελίδες
...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...

Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 1825 - 280 σελίδες
...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...

Elements of Geometry

Adrien Marie Legendre - 1825 - 570 σελίδες
...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...

Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 1825 - 294 σελίδες
...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...

Elements of Geometry

Adrien Marie Legendre - 1825 - 276 σελίδες
...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...

Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - 1828 - 346 σελίδες
...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...

Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1836 - 394 σελίδες
...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...

Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1838 - 382 σελίδες
...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...

Elements of Geometry

Adrien Marie Legendre - 1841 - 288 σελίδες
...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...

Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - 1849 - 372 σελίδες
...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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