Numerical Problems in Plane Geometry: With Metric and Logarithmic Tables
Longmans, Green, and Company, 1896 - 161 pages
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A B C acres adjacent altitude answer base bisect bisector BOOK centre characteristic chord circle circumference circumscribed College COMMON LOGARITHMS Construct decimal Define described diagonals diameter difference distance divided drawn equal equivalent exterior external extreme feet figure Find the area find the length Find the number Find the radius Find the side foot formed four GEOMETRY Give given given point greater half Harvard hexagon homologous sides HOURS hypotenuse inches included increase inscribed intercepted interior intersect isosceles June less line joining logarithm LOGARITHMS OF NUMBERS mantissa meet metres middle points miles one-half opposite sides parallel parallelogram pentagon perimeter perpendicular problems Prove quadrilateral radii radius ratio rectangle regular hexagon regular polygon respectively right angles scribed secant segments Show square square feet straight line subtended tangent third side trapezoid triangle units University vertex vertices yards
Page 77 - Similar triangles are to each other as the squares of their homologous sides.
Page 98 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 76 - 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 90 - 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 98 - 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 62 - 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 65 - 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 71 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Page 85 - The exterior angles of a polygon, made by producing each of its sides in succession, are together equal to four right angles.
Page 48 - 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.