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arch arithmetical progression axis bisected body centre co-efficients cone conic section constant quantity cosec cubic equation Cunliffe cycloid denote described determine diameter difference distance divided draw drawn ellipse elliptic functions equal equation Eratosthenes expression formula given by position given curve given point given ratio hence horizontal hyperbola integral intersection length Lowry Mathematical maximum Memoir motive force parabola parallel parallelogram perpendicular plane polygon problem Prop QUESTION R. M. College radius rational function rectangle reduced Required the demonstration resolved right angles right-angled triangle root Second Solution shew sides similar triangles sine square string substituted subtangent suppose surface Swale taking the fluxion tangent tion trigonometry velocity vertex vertical Wallace weight whence
Page 49 - It may be said of him, what can, perhaps, hardly be said of any other person, that whatever he has done has been perfect at the moment of its production. His processes were all of a finished nature. Executed by the hand of a master, they required no correction; and...
Page 49 - ... perfect at the moment of its production. His processes were all of a finished nature ; executed by the hand of a master, they required no correction ; and though many of them were performed in the very infancy of chemical philosophy, yet their accuracy and their beauty have remained unimpaired amidst the progress of discovery ; and their merits have been illustrated by discussion, and exalted by time.
Page 182 - If from one of the angles of a rectangle a perpendicular be drawn to its diagonal, and from their intersection lines be drawn perpendicular to the sides containing the opposite angle, then putting (P,p) for the last perpendiculars, and (D) for the diagonal, P*+/>* = D*.
Page 20 - If the force vary directly as the distance from the centre, shew that the velocity of a falling body, is to that in a circle at the same distance, as the right sine to the cosine of a circular arc, whose radius is the greatest distance, and versed sine the space through which the body has fallen.
Page 98 - A Treatise on the construction, properties and analogies of the three conic sections. Third edition. In-8".
Page 57 - The sum of all the angles of a polygon is equal to twice as many right angles as the polygon has sides, less two.
Page 62 - ... an angle with the tangent equal to that made by the tangent with the axis. Cor. 3. Now as V bisects TD and VB is, parallel to PD, the point .B bisects' TP. Draw FB, and that line bisects the base of an isosceles triangle, it is therefore perpendicular to the base. Hence, we have this general truth : If from the focus of a parabola a perpendicular be drawn to any tangent to the curve, it will meet the tangent on the axis of Y. Also, from the two similar right-angled triangles, FB V and FB T, we...
Page 84 - The earth acts on anybody with a gravitational force inversely proportional to the square of the distance of the body from the centre of the earth.
Page 43 - Since there are 60 seconds in a minute and 60 minutes in an hour, the value of both columns is 60*.