## Elements of Geometry and Trigonometry |

### From inside the book

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**EQUATIONS**OF THE POINT AND STRAIGHT LINE - of the CONIC SECTIONS of the LINE AND PLANE IN SPACE - also , the discussion of the GENERAL**EQUATION**of the second degree , and of SURFACES OF THE SECOND ORDER . DAVIES ' DESCRIPTIVE GEOMETRY ... Page 38

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**equation**to , or subtract it from M.P , and we shall have , M.P + N.P - M.P + M.Q ; or ( M ± N ) × P = ( P ± Q ) × M. But M ± N and P , may be considered the two extremes , and P + Q and M , the two means of a proportion : hence , M ± N ... Page 128

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**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

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**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

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**equation**x = s - y or Hence , or or x2 = s2 — 2sy + y2 y2 = a2 — s2 + 2sy — y2 2y2 - 2sy = a2- a2 - s ? y2 — sy— 2 By completing the square y2 — sy + 1s2 = 1a2 — ¡ s2 or Hence y = ‡ s ± √ + a2— + s2 = 4 or 3 x = { s = √ { a2 = + s2 ...### Other editions - View all

### Common terms and phrases

adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine cylinder diagonal diameter dicular distance divided draw drawn 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 parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall 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 Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex