Elements of Geometry and Trigonometry |
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Page 151
... described with the same solid angle A , and the same edges AB , AD , AE . PROPOSITION VIII . THEOREM . If two parallelopipedons have a common base , and their upper bases in the same plane and between the same parallels , they will be ...
... described with the same solid angle A , and the same edges AB , AD , AE . PROPOSITION VIII . THEOREM . If two parallelopipedons have a common base , and their upper bases in the same plane and between the same parallels , they will be ...
Page 168
... describes a ᎠF solid , which is named a spherical sector . E C 10. 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 ...
... describes a ᎠF solid , which is named a spherical sector . E C 10. 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 ...
Page 178
... described by any portion of the perimeter of the inscribed polygon , as BC + CD , is equal to EH x circ . OF ( Prop ... solid described by the triangle will be a third of the cylinder described by the rectangle . of Let ACB be the ...
... described by any portion of the perimeter of the inscribed polygon , as BC + CD , is equal to EH x circ . OF ( Prop ... solid described by the triangle will be a third of the cylinder described by the rectangle . of Let ACB be the ...
Page 179
... solid described by ABC will , in that case , be the difference of the two cones described by ABD and ACD ; but at the same time , the cylinder de- scribed by BCEF will be the difference of the two cylinders described by AFBD and AECD ...
... solid described by ABC will , in that case , be the difference of the two cones described by ABD and ACD ; but at the same time , the cylinder de- scribed by BCEF will be the difference of the two cylinders described by AFBD and AECD ...
Page 180
... solid described by the triangle ABC is also measured by x ABC x IK , or which is the same thing , by ABC x circ . IK , circ . IK being equal to 27x IK . Hence the solid described by the C revolution of the triangle ABC , has P B MKN for ...
... solid described by the triangle ABC is also measured by x ABC x IK , or which is the same thing , by ABC x circ . IK , circ . IK being equal to 27x IK . Hence the solid described by the C revolution of the triangle ABC , has P B MKN for ...
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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 convex surface cosine cotangent 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 measured by half number of sides opposite 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