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. II. How by the Semicircle to take an Inaccessible Al∣titude, at two Stations.

Let AB be a Tower whose height is required; having placed your Instrument at E, as before direct your sights unto the Top of the Tower at B, and finding the Degree cut by the Index,* 1.1 to be 23° 43', I say it is the Quantity of the Angle at E: Now by reason of Water, or such like Impediment, you can approach no nearer the Base of the Tower, than D, Therefore measure ED, which is found to be 512 Feet, then at D, make the like Observation, and the Angle at D, appeareth to be 50° 00', whose Complement is the Angle DBA, 40° 00', and the Complement of the Angle E 23° 43', is the An∣gle EBA 66° 17': Now if the lesser Angle at B, be taken out of the greater, the remainder is 26° 17', the Angle EBD: Now first to find the side BD, of the Trangle EBD, say according to prop. 1. §. 3. chap. 5. thus.

As S. of V. EBD, 26° 17',

To Log. cr. ED 512 Feet.

So is S. of V. at E 23° 43',

To Log. cr. BD 465 2/10 Feet required.

Now to find the Height of the Tower AB, say according to prop. 2. §. 2. chap. 5. thus.

As Radius or S. 90°,

To Log. cr. DB 465 2/10 Feet found.

So is S. of V. BDA 50° 00',

To Log. cr. BA 356 3/10 Feet, which is the height* 1.2 of the Tower required.

☞ Note that in taking any manner of Alti∣tude the height of your Instrument must be added unto the height found, and that will give you the True Altitude required.

Notes

• * 1.1

  Fig. 61.
• * 1.2

  Fig. 61.