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ABCD adjacent altitude apply base bisect called centre chord circle circumference coincide common conceive consequently construct corresponding curve DEM.-Let demonstration described diagonals diameter diedral difference direction distance dividers draw drawn edge equal equiangular equivalent extremities faces fact fall feet figure four Geometry given given line greater Hence homologous inches included inscribed intersect joining latter length less manner mark mean measured meet move oblique opposite parallel parallelogram pass path perpendicular plane polygon position prism produced PROP proportional PROPOSITION pyramid quadrilateral radii radius ratio reason rectangle regular remains represent respectively revolve right angles sides similar solid sphere spherical square straight line student supplement Suppose surface tangent Theorem.-The third triangle triedral vertex vertices volume whence
Page 104 - The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
Page 139 - Theorem. — The area of a trapezoid is equal to the product of its altitude...
Page 128 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other.
Page 31 - Can you make a triangle so that one of its sides shall be less than the difference between the other two, or equal to the difference ? Ex. 5. If you have two triangles with only one side and one angle in the one equal to one side and one angle in the other, can you apply one as a pattern and make it fit on the other ? Cut out two such triangles and try it Ex. 6. If you have two triangles with only two sides of one respectively equal to two sides of the other, can you make one fit as a pattern on...
Page xii - LEMMA 4. — A common divisor of two numbers is a divisor of their sum and also of their difference.
Page 156 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 147 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Page 196 - Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases.