Elements of Geometry and Trigonometry |
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Page 31
... polygons . Every convex polygon is such that a straight line , drawn at pleasure , cannot meet the contour of the polygon in more than two points . PROPOSITION XXVII . THEOREM . If the sides of any polygon be produced out , in the same ...
... polygons . Every convex polygon is such that a straight line , drawn at pleasure , cannot meet the contour of the polygon in more than two points . PROPOSITION XXVII . THEOREM . If the sides of any polygon be produced out , in the same ...
Page 32
... polygon has sides , and consequently , equal to the sum of the interior angles plus the exterior angles . Taking from each the sum of the interior angles , and there remains the exterior angles , equal to four right angles . PROPOSITION ...
... polygon has sides , and consequently , equal to the sum of the interior angles plus the exterior angles . Taking from each the sum of the interior angles , and there remains the exterior angles , equal to four right angles . PROPOSITION ...
Page 42
... polygon is circumscribed about a circle , when all its sides are tangents to the circumference : in the same case , the circle is said to be inscribed in the po- lygon . ос PROPOSITION I. THEOREM . Every diameter divides the circle and ...
... polygon is circumscribed about a circle , when all its sides are tangents to the circumference : in the same case , the circle is said to be inscribed in the po- lygon . ос PROPOSITION I. THEOREM . Every diameter divides the circle and ...
Page 91
... polygons are composed of the same number of tri- angles , similar each to each , and similarly situated . Let ABCDE , FGHIK , be two similar polygons . BOOK IV 91.
... polygons are composed of the same number of tri- angles , similar each to each , and similarly situated . Let ABCDE , FGHIK , be two similar polygons . BOOK IV 91.
Page 92
... polygon FGHIK , draw diagonals FH , FI to the other an- gles . 9 . H G F These polygons being similar , the angles ABC , FGH , which are homologous , must be equal , and the sides AB , BC , must also be proportional to FG , GH , that is ...
... polygon FGHIK , draw diagonals FH , FI to the other an- gles . 9 . H G F These polygons being similar , the angles ABC , FGH , which are homologous , must be equal , and the sides AB , BC , must also be proportional to FG , GH , that is ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex