## Elements of Plane and Spherical Trigonometry: With Their Applications to Mensuration, Surveying, and Navigation |

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altitude angle base bearing bottom called characteristic circle Co-tangent column complement computed correction corresponding cosine course cubic decimal Degrees departure determine diameter difference difference of latitude direction distance divided draw east entire equal equator example feet field figures four fraction Geometry give given greater ground half height Hence horizontal hypothenuse inches latitude length less logarithm logarithmic sine longitude manner means measured meridian method middle miles minutes Multiply natural object observed obtain opposite parallel perpendicular places plane positive preceding Prob PROBLEM Prop proportional quadrant radius remaining represent Required right-angled triangle RULE sailing scale secant ship side sine solidity spherical triangle square station subtract surface Tangent Theorem third triangle ABC unity vertical yards

### Popular passages

Page 76 - ALSO THE AREA OF THE TRIANGLE FORMED BY THE CHORD OF THE SEGMENT AND THE RADII OF THE SECTOR. THEN...

Page vi - The characteristic of the logarithm of a number greater than unity is one less than the number of integral figures in the given number.

Page 78 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...

Page 40 - In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference.

Page 42 - The side opposite the given angle is to the side opposite the required angle, as the sine of the given angle is to the sine of the required angle.

Page 118 - Small errors of this kind are unavoidable ; but when the error does not exceed one link to a distance of three or four chains, it is customary to distribute the error among the sides by the following proportion : As the perimeter of the field, Is to the length of one of the sides, So is the error in latitude or departure, To the correction corresponding to that side. This correction, when applied to a column in which the sum of the numbers is too small, is to be added; but if the sum of the numbers...

Page 91 - To find the surface of a cone. • RULE, Multiply the circumference of the base by half the side for the convex surface ; to which add the area of the base when the entire surface is required.

Page 75 - As 360 is to the number of degrees in the arc, so is the area of the circle to the area of the sector. This follows from Geometry, Prop. 14, Cor., B. III. Ex. 1. What is the area of a sector whose arc is 22°, in a circle whose diameter is 125 feet ? The length of the arc is found to be 23.998.

Page 18 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.

Page 44 - Given two sides and the included angle, to find the third side and the remaining angles. The sum of the required angles is found by subtracting the given angle from 180°.