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 79 - Similar triangles are to each other as the squares of their homologous sides.
Page 100 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 78 - 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 92 - 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 100 - 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 64 - OA will be 13 inches. 3. Prove that an angle formed by a tangent and a chord drawn through its point of contact is the supplement of any angle inscribed in the segment cut off by the chord. What is the locus of the centre of a circumference of given radius which cuts at right angles a given circumference? 4. Show that the areas of similar triangles are to each other as the squares of the homologous sides. 5. Prove that the square described upon the altitude of an equilateral triangle has an area...
Page 67 - 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 73 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Page 87 - The exterior angles of a polygon, made by producing each of its sides in succession, are together equal to four right angles.
Page 50 - The sum of two opposite angles of a quadrilateral inscribed in a circle is equal to the sum of the other two angles, and is equal to two right angles.

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