### Popular passages

Page 48 - Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the other.
Page 185 - If four quantities are in proportion, they are in proportion by Inversion; that is, the second term is to the first as the fourth term is to the third.
Page 397 - If the first of three quantities is greater than the second, and the second is greater than the third, then the first is greater than the third.
Page 290 - The areas of two circles are to each other as the squares of their radii, or as the squares of their diameters. S TrR2 R* If1' = ~R^ = "cT* = -D'*
Page 275 - The areas of two regular polygons of the same number of sides are to each other as the squares of their radii, or as the squares of their apothems.
Page 186 - In any proportion the terms are in proportion by Composition; that is, the sum of the first two terms is to the first term, as the sum of the last two terms is to the third ter.n.
Page 93 - The line which joins the mid-points of two sides of a triangle is parallel to the third side and equal to one half of it.
Page 386 - We assume that but one straight line can be drawn through a given point parallel to a given straight line.
Page 382 - The formula states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the base and altitude.
Page 256 - 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.