An Easy Introduction to Plane Trigonometry: The Application of it to the Measuring of Heights, Distances & Land; & the Use of the Portable Case of Mathematical Instruments

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J. Eddowes, 1766 - Mathematical instruments - 80 pages
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Actually Introduction to Trigonometry.

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Page 2 - Sine of an arc is a line drawn from one end of the arc perpendicular to a radius drawn...
Page 2 - ... is a part. 17. The segment of a circle is a part of a circle cut off by a chord ; thus the space...
Page 80 - V through the centre c to the other side of the dial, for the like hours of the morning ; which done, lay the ruler on the point a, and draw the last five hours in the forenoon through the dots 5, 4, 3, 2...
Page 80 - Because the hour-lines are less distant from each other about noon, than in any other part of the dial, it is best to have the centres of these quadrants at a little distance from the centre of the dial-plane, on the side opposite to XII, in order to enlarge the hour-distances thereabout under the same angles on the plane.
Page 4 - It is plain that the cosine of an arc is always equal to that part of the radius which is intercepted between the sine of that arc and the centre.
Page 79 - Th::; donei fetting one foot of the compafles in the beginning of the fcale at XII, and extending the other to each hour on the fcale, lay off thefe extents from...
Page 30 - To work the rule of three : for, fince the firft is to the fécond as the third is to the fourth...
Page 20 - ... to the point where the angle is to be made ; mark the point under the given degree, and draw the other iide thto
Page 26 - ... part thereof, becomes the transverse distance of the first term 2, then the transverse distance of the third term 10, taken from the same scale of equal parts, will give 30, the fourth proportional required. TO DIMINISH A LINE IN ANY ASSIGNED PROPORTION. Example. — Let it be required to diminish a line of 4 inches in the proportion of 8 to 7. Open the sector until the transverse distance of 8 is equal to the lateral distance of 7.
Page 64 - Being poorly prepared for the duties of a surveyor they used a long grape-vine for a measuring rod, it is said, cutting notches in it for the desired widths of the streets and alleys.

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