Elements of Geometry and Trigonometry |
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Page 139
... S by any plane ABCDE ; from O , a point in that plane , draw to the several angles the straight lines AO , OB , OC , OD , OE . B S D The sum of the angles of the triangles ASB , BSC , & c . formed about the vertex S , is equal to the ...
... S by any plane ABCDE ; from O , a point in that plane , draw to the several angles the straight lines AO , OB , OC , OD , OE . B S D The sum of the angles of the triangles ASB , BSC , & c . formed about the vertex S , is equal to the ...
Page 143
... S , and terminating in the different sides of the same polygon ABCDE . The polygon ABCDE is called the base of the pyramid , the point S the vertex ; and the triangles ASB , BSC , CSD , & c . form its convex or lateral sur- face . 11 ...
... S , and terminating in the different sides of the same polygon ABCDE . The polygon ABCDE is called the base of the pyramid , the point S the vertex ; and the triangles ASB , BSC , CSD , & c . form its convex or lateral sur- face . 11 ...
Page 145
... S - ABCDE , of which SO is the altitude , be cut by the plane abcde ; then will Sa : SA :: So : SO , and the same for the other edges : and the polygon abcde , will be similar to the base ABCDE . First . Since the planes ABC , abc , are ...
... S - ABCDE , of which SO is the altitude , be cut by the plane abcde ; then will Sa : SA :: So : SO , and the same for the other edges : and the polygon abcde , will be similar to the base ABCDE . First . Since the planes ABC , abc , are ...
Page 146
Adrien Marie Legendre Charles Davies. Cor . 1. Let S - ABCDE , S - XYZ be two pyramids , hav- ing a common vertex and the same altitude , or having their bases situated in the same plane ; if these pyramids are cut by a plane parallel to ...
Adrien Marie Legendre Charles Davies. Cor . 1. Let S - ABCDE , S - XYZ be two pyramids , hav- ing a common vertex and the same altitude , or having their bases situated in the same plane ; if these pyramids are cut by a plane parallel to ...
Page 160
... ABC be a triangular yramid , ABC - DEF a triangular prism of the same base and the same altitude ; the pyramid will be equal to a third of the prism . Cut off the pyramid F - ABC from the ... S - ABCDE be a pyramid . Pass the 160 GEOMETRY .
... ABC be a triangular yramid , ABC - DEF a triangular prism of the same base and the same altitude ; the pyramid will be equal to a third of the prism . Cut off the pyramid F - ABC from the ... S - ABCDE be a pyramid . Pass the 160 GEOMETRY .
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Common terms and phrases
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface Cosine Cotang cylinder diagonal diameter dicular distance divided draw drawn equal angles equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex
Popular passages
Page 241 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page 19 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 232 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Page 168 - The radius of a sphere is a straight line drawn from the centre to any point of the surface ; the diameter or axis is a line passing through this centre, and terminated on both sides by the surface.
Page 18 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Page 169 - The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude, Fig.
Page 20 - In an isosceles triangle the angles opposite the equal sides are equal.
Page 86 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 225 - B) = cos A cos B — sin A sin B, (6a) cos (A — B) = cos A cos B + sin A sin B...
Page 168 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.