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. V. How by the Semicircle to take the Plot of a Field at two Stations, by measuring from each Station to the visible Angles: the Field being so Irregu∣lar that from no one Place thereof, all the Angles can be seen.

Admit A, B, C, D, E, F, G, H, I, K, to be the Figure of a Field, whose Plot is required: having made choice of your two Stations, viz. Q, and P, and placed Marks in all the Angles: Then place your Semicircle at Q, and there* 1.1 six it with the Needle hanging over the Meri∣dian of the Chart, represented by R, Q, X, and direct your sights unto all the visible Angles, viz.

A, B, C, D, E, and F, and note down the Quantity of each Angle in your Field-book: Then measure with your Chain from your Station Q, to the Angles A, B, C, D, E, and F, and their length so found, note down in your Field-book also.* 1.2

This done direct your sight unto your second Station P, and note down in your Field-book the degree of Declination, of your second-station P, from the Meridian. Then measure the Stationary Distance PQ with your Chain, and note it down in your Field-book also.

Then remove the Instrument unto P, your second-station, and there fix it with the Needle hanging over the Meridian line of the Chart re∣presented by TPB, then direct your sights to the several visible Angles at this second Station, viz. F, G, H, I, and K, in order one after ano∣ther, and note down the Quantity of each An∣gle in your Field-book: Then with your Chain measure from your Station P, to these several Angles G, H, I, and K, (in all respects as at the first station Q.) and their length so found note down in your Field-book likewise: So have you finished your Observation, and your work stan∣deth thus.* 1.3

The Observation taken at the first Station Q.

Angles.	D	M	C.	L
A	50	00	6	60
B	80	00	7	65* 1.4
C	140	12	12	00
D	220	07	11	10
E	270	05	12	60
F	330	00	6	00

The Declination of the Station P, from the Meridian R Q X, is 30° 00', and the Stationary distance Q P is 9 Chains.

The Observation taken at the second Station P.

Angles.	D	M	C	L
F	227	11	00	00
G	297	00	12	00
H	347	16	9	90
I	60	00	6	00
K	90	00	6	26* 1.5

☞ Note that the manner of taking the Plot of a large Champain Field, at many Stations, is almost the same with this Proposition; for he that can do the one, can also perform the o∣ther: therefore for brevity sake I here omit it as superfluous.

Notes

• * 1.1

  Fig. 55.
• * 1.2

  Fig. 55.
• * 1.3

  Fig. 55.
• * 1.4

  Fig. 55.
• * 1.5

  Fig. 55.