# A Synopsis of Practical Mathematics: Containing Plain Trigonometry, Mensuration of Heights, Distances, Surfaces, and Solids; Surveying of Land, Gauging, Navigation, and Gunnery. With Tables of the Logarithms of Numbers, and of Sines and Tangents. For the Use of Schools and Men of Business

T. Cadell, jr. and W. Davies; and J. Fairbairn, at Edinburgh, 1799 - Logarithms - 328 pages

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Page 17 - The diameter of a circle is a right line drawn through the centre, and terminating in the circumference on each side, as AB.
Page 307 - Rule. Multiply the Logarithm of the given number by the Index of the proposed power, and the product will be the Logarithm, whose natural number is the power required.
Page 306 - And in division, subtract the logarithm of the divisor from the logarithm of the dividend, the remainder is the logarithm of the quotient.
Page 6 - In any continued geometrical progression, the product of the two extremes is equal to the product of any two means that are equally distant from them, or equal to the square of the middle term when there is an uneven number of terms.
Page 201 - RULE. Multiply the length by the breadth, and the product by the depth or...
Page 309 - Divide the logarithm of the given number by the index of the root ; and the quotient will be the logarithm of the required root (Art.
Page 17 - The sine of an arc is a line drawn from one end of the arc, perpendicular to the radius or diameter drawn through the other end : or, it is half the chord of double the arc ; thus HL is the sine of the arc HB.
Page 307 - Complement of a Logarithm. Begin at the left hand, and write down what each figure wants of 9, only what the laft fignificant figure wants of ю j fo the Сотр.
Page 243 - ... 9" with the meridian. And 3dly. That the differences of longitude on different rumbs, are to one another as the tangents of the angles of those rumbs with the meridian. Hence it follows, that the difference of the log. tangents of the half complements of the latitudes, is to the difference of longitude a ship makes...
Page 58 - IN a plain triangle, the fum of any two fides is to their difference, as the tangent of half the fum of the angles at the bafe, to the tangent of half their difference.