A Treatise on Elementary Geometry: With Appendices Containing a Collection of Exercises for Students and an Introduction to Modern Geometry

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J.B. Lippincott, 1898 - Geometry - 368 pages
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Page 19 - The perpendicular is the shortest line that can be drawn from a point to a straight line.
Page 79 - At a given point in a given straight line, to construct an angle equal to a given angle. Let A be the given point in the straight line AB, and 0 the given angle.
Page 216 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Page 348 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 217 - The volume of the frustum of any pyramid is equal to the sum of the volumes of three pyramids whose common altitude is the altitude of the frustum, and whose bases are the lower base, the upper base, and a mean proportional between the bases of the frustum.
Page 117 - The sum of the squares of the sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals.
Page 263 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180 and less than 540. (gr). If A'B'C' is the polar triangle of ABC...
Page 40 - If two sides of a quadrilateral are equal and parallel, the figure is a parallelogram.
Page 127 - Any two rectangles are to each other as the products of their bases by their altitudes. Let _R and R' be two rectangles, k and k...
Page 29 - Any side of a triangle is less than the sum of the other two sides...

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