Plane Geometry

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C.E. Merrill, 1917 - Geometry, Plane - 318 pages

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Page 275 - Euclid's, and show by construction that its truth was known to us ; to demonstrate, for example, that the angles at the base of an isosceles triangle are equal...
Page 278 - Two triangles are equal if two sides and the included angle of one are equal respectively to two sides and the included angle of the other...
Page 178 - If the product of two quantities is equal to the product of two others, one pair may be made the extremes, and the other pair the means, of a proportion.
Page 68 - 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 182 - 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 79 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.
Page 255 - 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 71 - If two triangles have two sides of one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side. 132- If two triangles have two sides of...
Page 278 - ... equals the sum of the squares on the other two sides. The latter is called
Page 281 - ... is equal to the sum of the areas of two circles whose diameters are 1 and 2 inches respectively.

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