Elements of Geometry and Trigonometry |
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Page 16
... taken in the same order , are equal , each to each . 23. A DIAGONAL of a polygon is a straight line joining the vertices of two angles , not consecutive . 24. A BASE of a polygon is any one of its sides on which the polygon is supposed ...
... taken in the same order , are equal , each to each . 23. A DIAGONAL of a polygon is a straight line joining the vertices of two angles , not consecutive . 24. A BASE of a polygon is any one of its sides on which the polygon is supposed ...
Page 45
... taken as many times as the polygon has sides , less two . Let ABCDE be any polygon : tnen will the sum of its interior angles A , B , C , D , and E , be equal to two right angles taken as many times as the polygon has sides , less two ...
... taken as many times as the polygon has sides , less two . Let ABCDE be any polygon : tnen will the sum of its interior angles A , B , C , D , and E , be equal to two right angles taken as many times as the polygon has sides , less two ...
Page 46
... taken twice ; that is , to four right angles . If the angles of a quadrilateral are equal , each will be a right angle . Cor . 2. The sum of the interior angles of a pentagon is equal to two right angles taken three times ; that is , to ...
... taken twice ; that is , to four right angles . If the angles of a quadrilateral are equal , each will be a right angle . Cor . 2. The sum of the interior angles of a pentagon is equal to two right angles taken three times ; that is , to ...
Page 47
... taken as many times as the polygon has sides , less two : hence , the sum of the exterior angles is equal to two right angles taken twice ; that is , equal to four right angles ; which was to be proved . PROPOSITION XXVIII . THEOREM ...
... taken as many times as the polygon has sides , less two : hence , the sum of the exterior angles is equal to two right angles taken twice ; that is , equal to four right angles ; which was to be proved . PROPOSITION XXVIII . THEOREM ...
Page 49
... taken at equal distances from a given straight line , and on the same side of it , the straight line joining them will be parallel to the given line . PROPOSITION XXXI . THEOREM . The diagonals of a parallelogram divide each other into ...
... taken at equal distances from a given straight line , and on the same side of it , the straight line joining them will be parallel to the given line . PROPOSITION XXXI . THEOREM . The diagonals of a parallelogram divide each other into ...
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Common terms and phrases
ABCD ACĀ² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence