A Treatise on Plane and Spherical TrigonometryJ. Deighton & sons, 1819 - 264 pàgines |
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1+p² a+b+c ABDE Acad analytical arithmetical calculation Calculus of Variations chord circle circumference co-sec co-tan coefficient computed consequently cos.c curve cycloid deduced determined differential dx dx dx² equal equation Euclid Euler Example expression Fluxions formula of solution fVdx given Hence instance integral Isoperimetrical problems James Bernoulli John Bernoulli latter loga logarithms maxima and minima maximum multiple arcs multiply Naper's nearly Petrop plane principle Prob Prop quadrant quantity radius right angle root rules secant sides similar triangles similarly sin.³ sin.c sine sine and cosine solved spherical angle spherical excess spherical triangle substitute subtract supplemental triangle supposed symbols tangent Theorem Treatise Trigonometrical variation versed sine
Passatges populars
Pàgina 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.
Pàgina vi - 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,...
Pàgina v - ... 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...
Pàgina 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.
Pàgina 144 - That is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles.
Pàgina 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.
Pàgina 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.
Pàgina 136 - The measure of the surface of a spherical triangle is the difference between the sum of its three angles and two right angles.