Geometrical Analysis: Or the Construction and Solution of Various Geometrical Problems from Analysis, by Geometry, Algebra, and the Differential Calculus; Also, the Geometrical Construction of Algebraic Equations, and a Mode of Constructing Curves of the Higher Order by Means of Points

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J. B. Lippincott & Company, 1872 - 279 páginas

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Página 210 - PROP. X. THEOR. IF a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.
Página 210 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced...
Página 139 - In a triangle, having given the base, the sum of the other two sides, and the length of a line drawn from the vertical angle to the middle of the base, to find the sides of the triangle.
Página 10 - ... algebra, or the modern analysis, from the mechanical facility of its operations, has contributed, especially on the Continent, to vitiate the taste and destroy the proper relish for the strictness and purity so conspicuous in the ancient method of demonstration. The study of geometrical analysis appears admirably fitted to improve the intellect, by training it to habits of precision, arrangement, and close application. If, the taste thus acquired be not allowed to obtain undue ascendancy, it...
Página 101 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Página 98 - Describe a circle which shall pass through two given points, and have its centre in a given line.
Página 25 - To trisect a right angle. 37. To divide a triangle into two parts by a line drawn parallel to a side, so that these parts shall be to each other as two given straight lines. 38. To divide a triangle into two parts by a line drawn perpendicular to the base, so that these parts shall...
Página 140 - In any 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.
Página 30 - The lengths of three lines drawn from the three angles of a plane triangle to the middle of the opposite sides, being 18, 24, and 30, respectively ; it is required to find the sides.
Página 149 - PROBLEM XVII. IN a Right-angled Triangle, having given the Perimeter or Sum of all the Sides, and the Perpendicular let fall from the Right Angle on the Hypothenuse ; to determine the Triangle, that is, its Sides. PROBLEM XVIII.

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