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الصفحة 231 - In whatever manner a number of bodies change their motions, if we suppose that the motion which each body would have in the following moment, if it were perfectly free, is decomposed into two others, one of which is the motion which it really takes in consequence of their mutual actions, then the other component will be such, that if each body were impressed by a force which would produce it alone, the whole system would be in equilibrium.
الصفحة 187 - E', the point in which any other line AN, making a given angle with AB, meets the curve, draw from N, the point in which it meets the circumference of the circle QER, NO, perpendicular to AB, so that AO may be the cosine of NAO, and from O toward A take OP = AB, then AP will be the cosine of the angle ABE' ; so to find BE' draw PQ perpendicular to AP, meeting the circle in Q ; join AQ, and draw BE' parallel to AQ, meeting AE' in E', the point E
الصفحة 260 - Elementa Sphaericae Doctrinae. 4to. Basil. 16 — . [D. 20. 3.] PAMAN (Roger) The Harmony of the Ancient and Modern Geometry asserted. 4to. London, 1745. [C. 22. 27.] PARDIES (Ignatii Gaston) Elementa Geometriae. 12mo. Oxonii, 1694. [Dd. 4. 54.] PEACOCK (DM) A System of Conic Sections, adapted to the Study of Natural Philosophy. 8vo. London, 1810. [Dd. 1. 25.] Another Copy. 8vo. London, 1810. [C. 27. 30.] PLAYFAIR (John) Elements of Geometry ; containing the first Six Books of Euclid, with Elements...
الصفحة vi - A perfectly flexible chain is wound round a cylinder supported with its axis parallel to the horizon. Then, if the weight and dimensions of the cylinder be given, and also the length and weight of the chain ; it is required to determine the time in which the chain, impelled by the force of gravity, will unwind itself ; a given length being unwound at the commencement of the motion; Second Morning.
الصفحة 196 - A Reply to a Critical and Monthly Reviewer, in which is inserted Euler's Demonstration of the Binomial Theorem.
الصفحة v - Bacchus caught Silenus asleep by the side of a full cask, and seized the opportunity of drinking, which he continued for two-thirds of the time that Silenus would have taken to empty the whole cask. After that Silenus awoke, and drank what Bacchus had left. Had they...
الصفحة v - If the opposite sides of an irregular hexagon inscribed in a circle be produced till they meet ; the three points of intersection will be in the same straight line.
الصفحة 262 - ... g multiplied into the sum of all the products of each body into the space it has perpendicularly descended, will be equal to the sum of all the products of each body into the square of its velocity.
الصفحة 231 - In whatever manner several bodies change their actual motions, if we conceive that the motion which each body would have in the succeeding instant, if it were quite free, is decomposed into two others, of which one is the motion...
الصفحة 195 - ... a lunar distance is the observed distance of the moon from the sun, or from a particular star or planet, at any instant. The lunar theory is brought to such perfection, that the times of these phenomena, observed under any meridian, when compared 'with those computed for Greenwich in the Nautical Almanac, give the longitude of the observer within a few miles.