Elements of Geometry and Trigonometry: Translated from the French of A.M. Legendre by Daniel Brewster : Revised and Adapted to the Course of Mathematical Instruction in the United States |
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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
... solid terminated by a curved surface , all the points of which are equally ... described in this movement , by the curve DAE , will have all its points ... solid , which is named a spherical sector . E 10. The radius of a sphere is a ...
... solid terminated by a curved surface , all the points of which are equally ... described in this movement , by the curve DAE , will have all its points ... solid , which is named a spherical sector . E 10. The radius of a sphere is a ...
Page 178
... described by any portion X of the perimeter of the inscribed polygon , as BC + CD , is equal to EH × circ . OF ... solid described by the triangle will be a third of the cylinder described by the rectangle . Let ACB be the triangle , and ...
... described by any portion X of the perimeter of the inscribed polygon , as BC + CD , is equal to EH × circ . OF ... solid described by the triangle will be a third of the cylinder described by the rectangle . Let ACB be the triangle , and ...
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- B scribed by BCEF will be the difference E A C D of the two cylinders described by AFBD ...
... 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- B scribed by BCEF will be the difference E A C D of the two cylinders described by AFBD ...
Page 180
... solid described by the triangle ABC is also measured by ABCX IK , or which is the same thing , by ABC × circ . IK , circ . IK being equal to 2 ′′ × IK . Hence the solid described by the C revolution of the triangle ABC , has P I B MKN ...
... solid described by the triangle ABC is also measured by ABCX IK , or which is the same thing , by ABC × circ . IK , circ . IK being equal to 2 ′′ × IK . Hence the solid described by the C revolution of the triangle ABC , has P I B MKN ...
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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 hence homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron PROBLEM Prop 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