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Page 17 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 17 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Page 13 - Prove that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the sides containing the right angle.
Page 13 - ... distance h from the vertex, where h is the height of the water barometer. If the bell be lowered so that its vertex is at a depth 5A/2 below the surface of the water, find how high the water will rise in the bell.
Page 19 - Any two sides of a triangle are together greater than the third side.
Page 7 - Show that the perimeter p of a regular polygon of n sides inscribed in a circle of radius R...
Page 1 - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments. If two chords of a circle intersect either inside or outside the circle the rectangle contained by the parts of the one is equal to the rectangle contained by the parts of the other.
Page 5 - The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.