Elements of Geometry and Trigonometry |
From inside the book
Results 6-10 of 83
Page 48
... radius CA ( Book I. Prop . XIV . Sch . ) ; hence in reference to this new tangent , the radius AC would be an oblique line , and the perpendicular let fall from the centre upon this tangent would be shorter than CA ; hence this supposed ...
... radius CA ( Book I. Prop . XIV . Sch . ) ; hence in reference to this new tangent , the radius AC would be an oblique line , and the perpendicular let fall from the centre upon this tangent would be shorter than CA ; hence this supposed ...
Page 49
... radius being at the same time less than the sum of the smaller and the distance between the centres , the two circumferences will cut each other . For , to make an intersection possible , the triangle CAD must be possible . Hence , not ...
... radius being at the same time less than the sum of the smaller and the distance between the centres , the two circumferences will cut each other . For , to make an intersection possible , the triangle CAD must be possible . Hence , not ...
Page 50
... radius AD must be less than the sum of the radius AC and the distanceCD between the centres ( Prop . XII . ) ; which is contrary to the supposition . Cor . Hence , if two circles touch each other , either exter nally or internally ...
... radius AD must be less than the sum of the radius AC and the distanceCD between the centres ( Prop . XII . ) ; which is contrary to the supposition . Cor . Hence , if two circles touch each other , either exter nally or internally ...
Page 57
... radius greater than the half of AB , describe two arcs cutting each other in D ; the point D will be equally distant from A and B. Find , in like manner , above or beneath the line AB , a second point E , equally distant from the points ...
... radius greater than the half of AB , describe two arcs cutting each other in D ; the point D will be equally distant from A and B. Find , in like manner , above or beneath the line AB , a second point E , equally distant from the points ...
Page 58
... radius greater than BA , describe two arcs intersecting each other in D ; draw AD : it will be the perpendicular required . For , the point D , being equally distant from B and C , must be in the perpendicular raised from the middle of ...
... radius greater than BA , describe two arcs intersecting each other in D ; draw AD : it will be the perpendicular required . For , the point D , being equally distant from B and C , must be in the perpendicular raised from the middle of ...
Other editions - View all
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.