 | Adrien Marie Legendre, Charles Davies - 1857 - 442 σελίδες
...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 tf1e centre, Suppose the chord AB to be equal to the chord DE. From C the centre of the circle, draw... | |
 | William Chauvenet - 1871 - 380 σελίδες
...THEOREM. 18. 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. 1st. Let AB, CD, be equal chords ; OE, OF, the perpendiculars which measure their distances from the... | |
 | Charles Davies - 1872 - 464 σελίδες
...impossible. PROPOSITION VIII. THEOREM. In equal circles, equal chords are equally distant from tht centres,' and of two unequal chords, the less is at the greater distance from the centre. For, let the circle KLG be placed upon ACIf, so that the centre _K shall fall upon the centre 0, and... | |
 | William Chauvenet - 1872 - 382 σελίδες
...THEOREM. 18. 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. 1st. Let AB, CD, be equal chords ; OE, OF, the perpendiculars which measure their distances from the... | |
 | Edward Olney - 1872 - 270 σελίδες
...greater than arc CnD, it must be less. PROPOSITION VI. 167. Theorem.—In the same or in equal circles, of two unequal chords, the less is at the greater distance from the centre. DEM.—Let CE < AB, then is the perpendicular OD, which measures tlm distance of CE from the centre,... | |
 | Adrien Marie Legendre - 1874 - 500 σελίδες
...impossible. PROPOSITION VTII. THEOREM. In equal circles, equal chords are equally distant from the centres / and of two unequal chords, the less is at the greater distance from the centre. 1°. In the equal circles ACH and KLG, let the chords AC and KL be equal : then will they be equally... | |
 | George Albert Wentworth - 1877 - 416 σελίδες
...THEOREM. 185. IIi the same circle, or 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. In the circle ABE С let the chord AB equal the chord CF, and the chord CE be less than the chord CF.... | |
 | Edward Olney - 1877 - 272 σελίδες
...greater than arc CwD, it must be less. PROPOSITION VL 167. TJieorem.—In the same or in equal circles, of two unequal chords, the less is at the greater distance from the centre. DEM.—Let CE < AB, then is the perpendicular OD, which measures the distance of CE from the centre,... | |
 | George Albert Wentworth - 1881 - 266 σελίδες
...THEOREM. 185. In the same circle, or 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. E In the circle AB EC let the chord AB equal the chord С f, and the chord CE be less than the chord... | |
 | Edward Olney - 1883 - 352 σελίδες
...contrary to the hypothesis. PROPOSITION IX. 153. Theorem.—In, the same circle, or in equal cir, cies, of two unequal chords, the less is at the greater distance from the centre; and, conversely, of two chords which are unequally distant from the centre, that which is at the greater... | |
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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. 
