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15 feet acres adjacent sides altitude angle is equal apothem arc intercepted arc subtended bisect bisector centre chord circum circumscribed cologarithm COMMON LOGARITHMS construct a triangle decagon diagonals divided dodecagon equiangular polygon equilateral triangle escribed exterior extreme and mean figure Find the area find the length Find the number Find the radius Find the side GEOMETRY given line given point homologous sides hypotenuse intercepted arcs interior angles intersect isosceles triangle joining the middle June legs line joining LOGARITHMS OF NUMBERS mantissa mean proportional metres middle points miles opposite sides parallelogram perimeter perpendicular PLANE GEOMETRY problems Prove quadrilateral radii rectangle regular hexagon regular inscribed regular polygon respectively rhombus right angles right triangle scribed secant Show similar triangles square equivalent square feet straight line tangent terior third side trapezoid triangle A B C triangle is equal vertex vertices yards
Page 77 - Similar triangles are to each other as the squares of their homologous sides.
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.