 | Horatio Nelson Robinson - Conic sections - 1865 - 474 pages
...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 pages
...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... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...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, CD,... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...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, CD,... | |
 | Edward Olney - 1872 - 270 pages
...point to a line is always meant the shortest distance. PROPOSITION III. 164. Theorem.—In the same or in equal circles, equal chords are equally distant from the centre. DEM.—Let O and O' be two equal circles, and chord EF= chord GH; then are the perpendiculars LO and... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...point to a line is always meant the shortest distance. PROPOSITION III. 164. Theorem. — In the same or in equal circles, equal chords are equally distant from the centre. DEM. — Let 0 and O' he two equal circles, and chord EF = chord GH ; then are the perpendiculars LO... | |
 | Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...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 Theor,... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...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, DE, in the... | |
 | James Maurice Wilson - 1878 - 450 pages
...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. En. Let... | |
 | Education, Higher - 1881 - 504 pages
...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 at the... | |
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In the same circle or in equal circles, equal chords are equally distant from the center; and conversely. 
