Elements of Geometry and Trigonometry |
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Page 2
... Equations of the Point and Straight Line - of the Conic Sections of the Line and Plane in Space - also , the dis- cussion of the General Equation of the second degree , and of surfaces of the second order . DAVIES ' DESCRIPTIVE GEOMETRY ...
... Equations of the Point and Straight Line - of the Conic Sections of the Line and Plane in Space - also , the dis- cussion of the General Equation of the second degree , and of surfaces of the second order . DAVIES ' DESCRIPTIVE GEOMETRY ...
Page 38
... equation to , or subtract it from M.P , and we shall have , M.P ± N.P = M.P + M.Q ; or ( MN ) x P ( P + Q ) × M. But MN and P , may be considered the two extremes , and P + Q and M , the two means of a proportion : hence , M ± N : M ...
... equation to , or subtract it from M.P , and we shall have , M.P ± N.P = M.P + M.Q ; or ( MN ) x P ( P + Q ) × M. But MN and P , may be considered the two extremes , and P + Q and M , the two means of a proportion : hence , M ± N : M ...
Page 128
... equation from the second , and observing that the triangles APC , APB , which are both right angled at P , give AC2 - PC2 = AP2 , and AB2 - PB2 = AP2 ; we shall have AP2 + AP2 = 2AQ2 — 2PQ2 . Therefore , by taking the halves of both ...
... equation from the second , and observing that the triangles APC , APB , which are both right angled at P , give AC2 - PC2 = AP2 , and AB2 - PB2 = AP2 ; we shall have AP2 + AP2 = 2AQ2 — 2PQ2 . Therefore , by taking the halves of both ...
Page 207
... equations of the problem . The solu- tion of these equations , when so formed , gives the solution of the problem . No general rule can be given for forming the equations . The equations must be independent of each other , and their ...
... equations of the problem . The solu- tion of these equations , when so formed , gives the solution of the problem . No general rule can be given for forming the equations . The equations must be independent of each other , and their ...
Page 208
... equation or Hence , or x = s - y x2 - s2-2sy + y2 y2 — a2 — s2 + 2sy — y2 2y2—2sy = a2 — s2 or a2 - s2 y2 — sy = 2 By completing the square y2 — sy + 1s2 = 1a2 — 1s2 or Hence y = s ± √1a2 — 1s2 - 4 or 3 x = ! s = √√ } a2 — 1s2 = 3 or ...
... equation or Hence , or x = s - y x2 - s2-2sy + y2 y2 — a2 — s2 + 2sy — y2 2y2—2sy = a2 — s2 or a2 - s2 y2 — sy = 2 By completing the square y2 — sy + 1s2 = 1a2 — 1s2 or Hence y = s ± √1a2 — 1s2 - 4 or 3 x = ! s = √√ } a2 — 1s2 = 3 or ...
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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.