Thesaurarium mathematicae, or, The treasury of mathematicks containing variety of usefull practices in arithmetick, geometry, trigonometry, astronomy, geography, navigation and surveying ... to which is annexed a table of 10000 logarithms, log-sines, and log-tangents / by John Taylor.

PROP. III. How by the Semicircle to take an Inaccessible Dis∣tance at two Stations.

Admit A, and B, be the two Stations, from either of which it is required to find the distance unto the Church at C; placing your Instrument at B, the Index lying on the Diameter, and di∣rect your sights unto the Church at C, fasten your Instrument, and turn your sights about un∣till you see through your sights, your second Station at A, so will you find your Index to cut* 1.1 30° 00', which is the Quantity of the Angle ABC. Then measure the distance AB, which is found to be 250 Yards, then with your In∣strument at A, make the like Observation as before, and you will find the Angle BAC to contain 50° 00'. Now by the third Maxim of Plain Triangles §. 1. Chap. 5 you find also the Angle ACB, to be 100° 00': now to find the distance AC, and BC, you may by their oppo∣site proportion according to prop. 1. §. 3. chap. 5. find the distance of AC, thus.

As S. of V. at C 100° 00',

To Log. cr. AB 250 yards.

So is S. of V. B 30° 00',

To Log. cr. AC 127 yards. Which is the di∣stance of the Church from A.

Now to find the distance BC, say,

As S. of V. at A 100° 00',

To Log. cr. AB 250 yards.

So S. is of V. at A 50° 00',

To Log. cr. BC 194 4/10 yards, which is the di∣stance of the Station B, from the Church at C.

Notes

• * 1.1

  Fig. 62.