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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 305
by Miles Bland - 1819 - 377 pages
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A complete treatise on Practical Land-Surveying, etc

Thomas Holliday - Electronic book - 1838 - 80 pages
...Rule.—As the base or greatest side is to the sum of the other two sides, so is the difference of the sides to the difference of the segments of the base made by a perpendicular, let fall from the greater angle upon the base. Then half this difference being added to half the base,...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841
...construct the triangle. 61. 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. 62. Given the three distances of a point within a square from three angular...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Robert Potts - 1845
...given straight line. 61. 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. 62. On a given straight line to describe a triangle having its vertical angle...
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A system of practical mathematics; being no.xvi. of a new series of school-books

1845
...from (arts. 36 and 59), and (Alg. 69). 7. Prove that the difference of the sides of a triangle, is to the difference of the segments of the base made by a perpendicular upon it from the vertex, as the cosine of half the sum of the angles at the base, is to the cosine...
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The first six and the eleventh and twelfth books of Euclid's Elements; with ...

James Thomson - Geometry - 1845 - 358 pages
...is, sin j (A — B) :sinJ(A + B) :: a— b : c. PROP. V. THEOR. — In any plane triangle, the sum of the segments of the base made by a perpendicular from the vertex, is to the sum of the other sides, as the difference of those sides to the difference of the segments....
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...AB.AF + AD.AH=AC.AG. 100. 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. BOOK IV, DEFINITIONS. i. A RECTILINEAL figure is said to be inscribed in...
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - Geometry - 1846 - 138 pages
...QED . 5 Th. The base of a triangle is to the sum of both the sides, as the difference of the sides is to the difference of the segments of the base, made by a perpendicular falling upon it from the vertex, or to the sum of the segments, when the base must be produced to meet...
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The Elements of Analytical Geometry: Comprehending the Doctrine of the Conic ...

John Radford Young - Geometry, Analytic - 1848 - 288 pages
...Given one side, the difference between the square of the other side, and the square of the base, and the difference of the segments of the base, made by a perpendicular from the vertical angle, of a plain triangle, to determine the triangle. Put a = the given sides 62 = the difference...
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclides - 1849
...the greatest angle ? 37. 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. THEOREMS. 1. If two circles cut each other, the straight line joining...
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THE ELEMENTS OF ANALYTICAL GEOMETRY; COMPREHENDING THE DOCTORINE OF THE ...

J.R. YOUNG - 1850
...Given one side, the difference between the square of the other side, and the square of the base, and the difference of the segments of the base, made by a perpendicular from the vertical angle, of a plain triangle, to determine the triangle. Put a = the given sides Z?2 = the difference...
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