Entrance Examinations in Mathematics, 1884 to 1898 [with Supplements to 1900]

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Page 175 - Two triangles having 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.
Page 4 - The sum of any two face angles of a trihedral angle is greater than the third face angle.
Page 113 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Page 173 - The area of a circle is equal to one-half the product of its circumference and radius.
Page 33 - If two sides of a triangle are unequal, the angles opposite are unequal, and the greater angle is opposite the greater side.
Page 35 - In two polar triangles each angle of the one is the supplement of the opposite side in the other. Let ABC, A'B'C
Page 125 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Page 188 - It follows that the ratio of the circumference of a circle to its diameter is the same for all circles.
Page 147 - An oblique prism is equivalent to a right prism whose base is a right section of the oblique prism, and whose altitude is equal to a lateral edge of the oblique prism. Hyp. OM is a right section of oblique prism AD', and OM ' a right prism whose altitude is equal to a lateral edge of AD'. To prove AD' =0= GM' . Proof. The lateral edges of GM
Page 5 - CD be intersected by the parallel planes MN, PQ, RS, in the points A, E, B, and C, F, D.

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