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" If two chords intersect in a circle, the difference of their squares is equal to the difference of the squares of the difference of the segments. "
The Principles of Analytical Geometry ... - Page 79
by Henry Parr Hamilton - 1826 - 326 pages
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Elementary Illustrations of the Celestial Mechanics of Laplace ..., Part 1

Pierre Simon marquis de Laplace, Thomas Young - Astronomy - 1821 - 388 pages
...sides. The segments of the base being a' and a", the difference of their squares is a'2 — a"2; but the difference of their squares is equal to the difference of the squares of the two sides, since the perpendicular is the same for both the right angled triangles formed by the division...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 194 pages
...circumferences, the chords of the intercepted arches will be parallel. 73. If two chords intersect, the difference of their squares is equal to the difference of the squares of the differences of their segments. (Pr. 35.) 74. If equal arches be assumed from the extremities of the...
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Geometrical Propositions Demonstrated, Or, a Supplement to Euclid: Being a ...

William Desborough Cooley - Geometry - 1840 - 106 pages
...alternate angles, and consequently DB and AC are parallel (i. Prop. 27). If two chords (AB, CD) intersect, the difference of their squares is equal to the difference of the squares of the differences of their segments. If the chord AB be bisected, then the rectangle under the unequal segments...
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A collection of examples in pure and mixed mathematics, with hints and ...

Alfred Wrigley, William Henry Johnstone - Mathematics - 1845 - 222 pages
...intercepted arcs will be parallel. (Euclid, iii. 32. Cape, ii. 48.) 35. If two chords intersect in a circle, the difference of their squares is equal to the difference of the squares of the difference of the segments. (Euclid, ii. 8, and iii. 35. Cape, iii. 61, 77.) 36. If two chords be drawn...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...AP and AQ are together double of the square of the radius. 6. If two chords intersect in a circle, the difference of their squares is equal to the difference of the squares of the difference of the segments. 7. Two parallel chords in a circle are respectively six and eight inches...
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National Society's Monthly Paper

1856
...is equal to the sum ofthe squares of the diagonals. 2. If two straight lines intersect in a circle, the difference of their squares is equal to the difference of the squares of the difference of their segments. 3. Deseribe a circle in that part of a segment of a circle which is cut...
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The English Journal of Education, Volumes 11-13

Education - 1857 - 1266 pages
...equal to twice as many right angles as the polygon has sides. 4. If two chords intersect in a circle, the difference of their squares is equal to the difference of the squares of the differences of the segmente. SECTION II. 1. Prove the rule for finding the square root of a binomial,...
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The Educational record, with the proceedings at large of the ..., Volumes 3-4

British and foreign school society - 1857 - 544 pages
...equal to twice as many right angles as the polygon has sides. 4. If two chords intersect in a circle, the difference of their squares is equal to the difference of the separes of the differences of the segments. 1. Prove the rule for finding the square root of a binomial,...
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Elements of algebra

Philip Kelland - 1860
...sum by the latter is the number or fraction itself 55. Prove that if 1 be divided into any two parts, the difference of their squares is equal to the difference of the parts themselves. 56. Prove that if 2 be divided into any two parts the difference of their squares...
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Collection of Examples and Problems in Pure and Mixed Mathematics: With ...

Alfred Wrigley - Mathematics - 1862 - 330 pages
...circumferences, the chords of the intercepted arcs will be parallel. 42. If two chords intersect in a circle, the difference of their squares is equal to the difference of the squares of the difference of the segments. 43. If two chords be drawn from any point of a circle, and upon these chords,...
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