Yale University Entrance Examinations in Mathematics: 1884 to 1898

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Boardman School Press, 1898 - Mathematics - 208 pages

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Page 173 - 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 190 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it.
Page 125 - The bisector of an angle of a triangle divides the opposite side into segments which are proportional to the adjacent sides.
Page 115 - 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 171 - The area of a circle is equal to one-half the product of its circumference and radius.
Page 35 - If two sides of a triangle are unequal, the angles opposite are unequal, and the greater angle is opposite the greater side.
Page 37 - 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 186 - It follows that the ratio of the circumference of a circle to its diameter is the same for all circles.

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