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 & Company, 1871 - Geometry - 368 pages
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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 115 - X PB'; that is, if through a fixed point without a circle a tangent to the circle is drawn, and also any secant, the tangent is a mean proportional between the whole secant and its external segment.
Page 46 - The three perpendiculars from the vertices of a triangle to the opposite sides meet in the same point.
Page 127 - The areas of two rectangles are to each other as the products of their bases by their altitudes.
Page 129 - The area of a parallelogram is equal to the product of its base and altitude. Let...
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 219 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section.
Page 261 - Any side of a spherical triangle is less than the sum of the other two.
Page 95 - If four quantities are in proportion, they are in proportion by composition, ie the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.
Page 132 - Two triangles having 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.

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