Elements of Plane Geometry: For the Use of Schools

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Lewis & Sampson, 1844 - Geometry, Plane - 96 pages
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Page 31 - A circle is a plane figure bounded by a curved line, every point of which is equally distant from a point within called the center.
Page 71 - 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 53 - In any proportion, the product of the means is equal to the product of the extremes.
Page 89 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 59 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 16 - Conversely, if two angles of a triangle are equal, the sides opposite them are also equal, and the triangle is isosceles.
Page 84 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Page 72 - If a perpendicular is drawn from the vertex of the right angle to the hypotenuse of a right triangle : 1st.
Page 72 - Two triangles, which have an angle in the one equal to an angle in the other, are to each other as the rectangles of the sides Fig.
Page 20 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...

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