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 29by Adrien Marie Legendre - 1841 - 235 pagesFull view - About this book
| 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... | |
| 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... | |
| 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,... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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