Elements of Geometry and Trigonometry |
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Page 16
... BASE of a polygon is any one of its sides on which the polygon is supposed to stand . 25. Triangles may be classified with reference either to their sides , or their angles . When classified with reference to their sides , there are two ...
... BASE of a polygon is any one of its sides on which the polygon is supposed to stand . 25. Triangles may be classified with reference either to their sides , or their angles . When classified with reference to their sides , there are two ...
Page 31
... base equal to AC , by hypothesis , AD common , and BD equal to DC , by construction : hence , the triangles BAD ... base , bisects the angle at the vertex , and is perpendicular to the base . PROPOSITION XII . THEOREM . If two angles of ...
... base equal to AC , by hypothesis , AD common , and BD equal to DC , by construction : hence , the triangles BAD ... base , bisects the angle at the vertex , and is perpendicular to the base . PROPOSITION XII . THEOREM . If two angles of ...
Page 94
... base . I 6. The ALTITUDE OF A TRAPEZOID , is the perpendicular distance between its parallel sides . These sides are called bases ; one the upper , and the other , the lower base . 7. The AREA OF A SURFACE , is its numerical value ...
... base . I 6. The ALTITUDE OF A TRAPEZOID , is the perpendicular distance between its parallel sides . These sides are called bases ; one the upper , and the other , the lower base . 7. The AREA OF A SURFACE , is its numerical value ...
Page 95
... 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 the prolongation of that base . From A , draw AE parallel to BC , forming the ...
... 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 the prolongation of that base . From A , draw AE parallel to BC , forming the ...
Page 96
... bases . There may be two cases : the bases may be commensu- rable , or they may be incommensurable . 1o . Let ABCD and HEFK , be two rectangles whose altitudes AD and HK are equal , and whose bases AB and HE are commensurable : then ...
... bases . There may be two cases : the bases may be commensu- rable , or they may be incommensurable . 1o . Let ABCD and HEFK , be two rectangles whose altitudes AD and HK are equal , and whose bases AB and HE are commensurable : then ...
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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