Numerical Problems in Plane Geometry: With Metric and Logarithmic Tables

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Longmans, Green, and Company, 1896 - 161 pages
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Page 80 - Similar triangles are to each other as the squares of their homologous sides.
Page 101 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 69 - 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 diminished by twice the product of one of those sides and the projection of the other upon that side.
Page 79 - If four quantities are in proportion, they are in proportion by composition, ie the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.
Page 93 - 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 101 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Page 74 - The bisector of an angle of a triangle divides the opposite side into segments which are proportional to the adjacent sides.
Page 101 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Page 68 - Prove that, if from a point without a circle a secant and a tangent be drawn, the tangent is a mean proportional between the whole secant and the part without the circle.
Page 74 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...

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