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 63 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
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 54 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Page 83 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 59 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 61 - From this proposition it is evident, that the square described on the difference of two lines is equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines.
Page 84 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.

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