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Page 15 - 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 15 - 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 11 - 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 11 - ... 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 17 - Any two sides of a triangle are together greater than the third side.
Page 5 - Show that the perimeter p of a regular polygon of n sides inscribed in a circle of radius R...
Page 3 - The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.
Page 11 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another...

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