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A.cos Acad already analytical angles applied base becomes Bernoulli calculation called chord circle coefficient common computed consequently contain corresponding cosine curve deduced determined difference differential divided elements equal equation error Euler Example expression former formula function given gives greater Hence instance integral introduced involving Isoperimetrical latter less logarithms maximum means measure method multiply nearly object observed obtained operation opposite places plane preceding principle Prob problems Prop quantity radius reduced represent root rules sides similar similarly sine solution solved spherical triangle substitute suppose symbols Tables taken tangent third Treatise triangle Trigonometrical true variation vary whence
Page 193 - The surface of a spherical triangle is measured by the excess of the sum of its three angles above two right angles, multiplied by the tri-rectangular triangle.
Page viii - Lagrange indeed, whose power over symbols is so unbounded that the possession of it seems to have made him capricious, has treated the subject of Variations without the foreign notation; this he rejects altogether; and, which is strange, has employed the English notation, but not adopted its signification. Thus, with him, x is not the fluxion, but the variation of x: the fluxions or differentials of quantities are not 'expressed by him, but solely the fluxionary or differential coefficients ; thus,...
Page vii - ... examination of the works of the contemporaries of Newton; works once read and celebrated: yet the writings of the Bernoullis are not antiquated from loss of beauty, nor deserve neglect, either for obscurity, or clumsiness of calculation, or shallowness of research. Their processes indeed are occasionally somewhat long, and want the trim form of modern solution. They are not, however, therefore the less adapted to the student, who is solicitous for just and full views of science, rather than for...
Page 129 - The sum of the three sides of a spherical triangle is less than the circumference of a great circle. Let ABC be any spherical triangle; produce the sides AB, AU, till they meet again in D.
Page 144 - That is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles.
Page 127 - A sphere is a solid terminated by a curved surface, all the points of which are equally distant from a point within called the centre.
Page 140 - ... sun in the meridian. The arches being supposed semi-circular, it is required to find the curve terminating that part of the surface of the water which is illuminated by the sun's rays passing through any arch. 7- It is required to express the cosine of an angle of a spherical triangle in terms of the sines and cosines of the sides.