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.

PROPI. The Rumb, and Distance sailed thereon being gi∣ven,* 1.1 to find the Difference of Latitude, and the Departure from the Meridian.

Admit a Ship sails N. W. by N. 372' or Miles, or 124 Leagues, I demand her Difference of Latitude and departure from the Meridian?

〈1 page duplicate〉〈1 page duplicate〉

〈1 page duplicate〉〈1 page duplicate〉

In the Triangle ABC, the Hypothenuse AC representeth the distance sailed, or Rumb-line,* 1.2 BC the departure from the Meridian, and AB the difference of Latitude.

1. To find which say,

As Radius or S. 90°,

To Log. distance sailed 372'.

So is Sc. V. A of the Course 56° 15',

To Log. cr. AB 309 3/10 Minutes, which being divided by 60' giveth 5°. 9'. 18" for the Diffe∣rence of Latitude.

2. To find the Departure from the Meridian* 1.3 say,

As Radius or S 90°,

To Log. Rumb-line AC 372'.

So is S. of V. of the Course A 33° 45',

To Log. cr. BC 206 6/10 Minutes, the departure from the Meridian, which divided by 60 giveth 3°. 26'. 36" for the difference of Longitude.

Note that by this Proposition you may keep an Account how much you have sailed either East or West, North or South.

Notes

• * 1.1

  The Do∣ctrine of Rightli∣ned Trian∣gles, both Right, and Oblique∣Angled, applied to Propositi∣ons of Plain Sai∣ling.
• * 1.2

  Fig. 44.
• * 1.3

  Fig. 44.