Plane and Solid Geometry

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D. C. Heath, 1916 - Geometry - 467 pages
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Page 166 - The sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.
Page 207 - The areas of two similar triangles are to each other as the squares of any two homologous sides.
Page 166 - The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
Page 83 - If two sides of a triangle are unequal, the angles opposite are unequal, and the greater angle is opposite the greater side.
Page 30 - If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the triangles are equal.
Page 105 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Page 209 - 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. B' ADC A' D' C' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove = — • A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Page 299 - An equiangular polygon inscribed in a circle is regular if the number of its sides is odd. PROPOSITION VIII. THEOREM 405. Regular polygons of the same number of sides are similar. E Hyp. ABCDE and A'B'C'D'E' are regular polygons of n sides.
Page 204 - 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 13 - To express fractional parts of the unit, the degree is divided into sixty equal parts called minutes, and the minute into sixty equal parts, called seconds. Degrees, minutes, and seconds are represented by the symbols, . ', ", respectively. Thus, 43 22' 37" represents an angle of 43 degrees, 22 minutes, and 37 seconds.

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