Elements of Geometry and Trigonometry |
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Page 93
... placed in each , are called homologous . The corresponding angles are homologous angles , the corresponding sides are homologous sides , the corresponding diagonals are homologous diagonals , and so on . 3. SIMILAR ARCS , SECTORS , or ...
... placed in each , are called homologous . The corresponding angles are homologous angles , the corresponding sides are homologous sides , the corresponding diagonals are homologous diagonals , and so on . 3. SIMILAR ARCS , SECTORS , or ...
Page 94
... placed that their lower bases shall coincide ; then , because they have the same altitude , their upper bases will be in the same line DG , parallel to AB . C G H The triangles DAH and CBG , have the sides AD and BC equal , because they ...
... placed that their lower bases shall coincide ; then , because they have the same altitude , their upper bases will be in the same line DG , parallel to AB . C G H The triangles DAH and CBG , have the sides AD and BC equal , because they ...
Page 95
... placed that the base of D E F the triangle shall coin- cide with the lower base A of the parallelogram ; BA then , because they have equal altitudes , the vertex of the triangle will lie in the upper base of the parallelogram , or in ...
... placed that the base of D E F the triangle shall coin- cide with the lower base A of the parallelogram ; BA then , because they have equal altitudes , the vertex of the triangle will lie in the upper base of the parallelogram , or in ...
Page 124
... placed . Let ABCDE and FGHIK be two similar polygons , the angie A being equal to the angle F , B to G , C to H , and so on : then can they be divided into the same number of similar triangles , similarly placed . For , from A draw the ...
... placed . Let ABCDE and FGHIK be two similar polygons , the angie A being equal to the angle F , B to G , C to H , and so on : then can they be divided into the same number of similar triangles , similarly placed . For , from A draw the ...
Page 125
... placed , the polygons themselves will be similar . PROPOSITION XXVII . THEOREM . The perimeters of similar polygons are to each other as any two homologous sides ; and the polygons are to each other as the squares of any two homologous ...
... placed , the polygons themselves will be similar . PROPOSITION XXVII . THEOREM . The perimeters of similar polygons are to each other as any two homologous sides ; and the polygons are to each other as the squares of any two homologous ...
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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