| 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... | |
| 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... | |
| 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 - 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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