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" Given the vertical angle, the difference of the two sides containing it, and the difference of the segments of the base made by a perpendicular from the vertex ; construct the triangle. "
Geometrical Problems Deducible from the First Six Books of Euclid: Arranged ... - Page 281
by Miles Bland - 1827 - 377 pages
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Technical arithmetic and mensuration

Charles Watkins Merrifield - Arithmetic - 1873 - 120 pages
...8 1 in. Ans. Again: 251^ @ 2s. 6d = 7546^. = £& 8í. 10|</. Ans. 2. If AB = 28, BC = 45, CA = 53, the difference of the segments of the base made by a perpendicular from A on BC = (CA + AB)(CA-AB)-7-BC = 81 x 254-45 = 45 = BC ; Л ABC is a right angle, and the area = £(45...
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Pure mathematics, Volume 1

Edward Atkins - 1874 - 428 pages
...base is a circle. 31. Given the vertical angle, the difference of the two sides containing it, and the difference of the segments of the base made by a perpendicular from the vertex, to construct the triangle. 32. Show that the locus of the middle point of a straight line, which moves...
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Elements of Euclid Adapted to Modern Methods in Geometry

Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...the difference of the squares on the sides of a triangle is equal to the difference of the squares on the segments of the base, made by a perpendicular from the vertex (I. 37, cor. 3), it follows from Cor. 1 to this Proposition, that the rectangle under the sum and difference...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry - 1876 - 446 pages
...given straight line. 130. Given the vertical angle, the difference of the two sides containing it, and the difference of the segments of the base made by a perpendicular from the vertex ; construct the triangle. 131. Given the vertical angle, and the lengths of two lines drawn from the...
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Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 130 pages
...figures. 20. The base of a triangle is 63 ft., and the sides 25 ft. and 52 ft. respectively. Show that the segments of the base, made by a perpendicular from the vertex, are 15 ft. and 48 ft. respectively, and that the area of the triangle is 630 sq. ft. 21. In the same...
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An Elementary Geometry: Plane, Solid, and Spherical : with Numerous ...

William Frothingham Bradbury - Geometry - 1877 - 262 pages
...angle to the opposite side, and the perpendicular given, to construct the triangle. 124. Two sides and the difference of the segments of the base made by a perpendicular from the vertical angle to the base given, to construct the triangle. Is there any ambiguity in this Problem...
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Exercises Contained in Wentworth's Geometry: With Key, Followed by a ...

George Albert Wentworth - 1879 - 196 pages
...produced: EA C is the A. Ex. 46. Given the vertical angle, the difference of the sides containing it, and the difference of the segments of the base made by a perpendicular from the vertex: construct the triangle. Take AB = difference of base segments; make £ABC — | given Z, and draw AC...
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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...angle to the opposite side, and the perpendicular given, to construct the triangle. 124. Two sides and the difference of the segments of the base made by a perpendicular from the vertical angle to the base given, to construct the triangle. Is there any ambiguity in this Problem...
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The Field Engineer: A Handy Book of Practice in the Survey, Location, and ...

William Findlay Shunk - Railroad engineering - 1880 - 362 pages
...plane triangle, as the base is to the sum of the other two sides, so is the difference of those sides to the difference of the segments of the base made by a perpendicular let fall from the vertical angle. 6. In any plane triangle, as twice the rectangle under any two sides...
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382 exercises, solved, upon the 3rd, 4th, 5th, and 6th books of Euclid

Patrick M. Egan - 1883 - 212 pages
...required triangle. EXERCISE 102. Given the vertical angle, tlie difference of the sides containing it, and the difference of the segments of the base made by a perpendicular from the vertex: to construct the triangle. (Fig. 102, Plate VII.)—Let AD equal the difference of the segments of...
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