 | Horatio Nelson Robinson - 1865 - 474 σελίδες
...triangles, ACE, and ECB, are equal in all respects, and AE = EB. Hence the theorem. THEOREM III. In the same circle, or in equal circles, equal chords are equally distant from the center. Let AB and EF be equal chords, and C the center of the circle. From C, draw CG and CH, perpendicular... | |
 | Trinity College (Hartford, Conn.) - 1870 - 1008 σελίδες
...angles on the same side together equal to two right angles, the two lines are parallel. 3. Prove that in the same circle or in equal circles, equal chords are equally distant from the center; and of two unequal chords, the less is the more remote from the center. 4. Prove that if a line is... | |
 | William Chauvenet - 1871 - 380 σελίδες
...parallel chords is the diameter perpendicular to these chords. PROPOSITION VIII.— 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,... | |
 | William Chauvenet - 1872 - 382 σελίδες
...parallel chords is the diameter perpendicular to these chords. PROPOSITION VIII.— 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,... | |
 | Association for the improvement of geometrical teaching - 1876 - 66 σελίδες
...than two straight lines drawn to the circumference are equal, that point is the centre, THEOR. n. In the same circle, or in equal circles, equal chords are equally distant from the centre; and of two, unequal chords the greater is nearer to the centre than the less. [First part by... | |
 | Elias Loomis - 1877 - 458 σελίδες
...lines bisecting the three sides of a triangle at right angles meet in the same point. PROPOSITION VIII. THEOREM.. In the same circle or in equal circles, equal chords are equally distant from the centre; and of two unequal chords, the less is the more remote from the centre. Let the chords AB,... | |
 | James Maurice Wilson - 1878 - 450 σελίδες
...the centre of the circled. * Euclid, in. 10. t Euclid, III. 9. 130 ELEMENTARY GEOMETRY. THEOREM n. In the same circle, or in equal circles, equal chords are equally distant from the centre; and of two unequal chords the greater is nearer to the centre than the less*. First. Part.... | |
 | Elias Loomis - 1880 - 456 σελίδες
...the three sides of a triangle at right angles meet in the same point. PROPOSITION vui. TIIROREM. In the same circle or in equal circles, equal chords are equally distant from the centre ; and of two unequal chords, the less is the more remote from the centre. Let the chords AB,... | |
 | 1881 - 504 σελίδες
...rectangle contained by their sum and difference. 5. Senior Paper, No. 2. 6. Senior Paper, No. 4. 7. In the same circle, or in equal circles equal chords are equally distant from the centre ; and of two unequal chords the greater is nearer to the centre than the less. 8. The angle... | |
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In the same circle, or in equal circles, equal chords are equally distant from the center; and, conversely, chords equally distant from the center are equal. 
