Elements of Geometry and Trigonometry |
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Page 46
... described from the centre O , with the radius OB , will pass through the three given points A , B , C. We have now shown that one circumference can always be made to pass through three given points , not in the same straight line we say ...
... described from the centre O , with the radius OB , will pass through the three given points A , B , C. We have now shown that one circumference can always be made to pass through three given points , not in the same straight line we say ...
Page 49
... . ) . And , whenever the triangle CAD can be constructed , it is plain D that the circles described from the centres C and D , will cut each other in A and B. 7 E PROPOSITION XIII . THEOREM . If the distance between the BOOK III .
... . ) . And , whenever the triangle CAD can be constructed , it is plain D that the circles described from the centres C and D , will cut each other in A and B. 7 E PROPOSITION XIII . THEOREM . If the distance between the BOOK III .
Page 52
... described from the vertices of the angles as centres with equal radii . Let ACB be the greater and ACD the less angle . Let the less angle be placed on the greater . If the propo- sition is not truc , the angle ACB will be to the angle ...
... described from the vertices of the angles as centres with equal radii . Let ACB be the greater and ACD the less angle . Let the less angle be placed on the greater . If the propo- sition is not truc , the angle ACB will be to the angle ...
Page 53
... described with equal radii , as is implied in all the foregoing propositions . Scholium 1. It appears most natural to measure a quantity by a quantity of the same species ; and upon this principle it would be convenient to refer all ...
... described with equal radii , as is implied in all the foregoing propositions . Scholium 1. It appears most natural to measure a quantity by a quantity of the same species ; and upon this principle it would be convenient to refer all ...
Page 62
... described from the centre E , with the radius EF - B , will cut the side DF in two points F and G , lying on the same side of D : hence there will be two triangles DEF , DEG , either of which will satisfy the conditions of the pro- blem ...
... described from the centre E , with the radius EF - B , will cut the side DF in two points F and G , lying on the same side of D : hence there will be two triangles DEF , DEG , either of which will satisfy the conditions of the pro- blem ...
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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.