Nine geometricall exercises, for young sea-men and others that are studious in mathematicall practices: containing IX particular treatises, whose contents follow in the next pages. All which exercises are geometrically performed, by a line of chords and equal parts, by waies not usually known or practised. Unto which the analogies or proportions are added, whereby they may be applied to the chiliads of logarithms, and canons of artificiall sines and tangents. By William Leybourn, philomath.

PROP. I. Two Places which differ onely in Latitude, to find their Distance.

IN this Proposition there are two Varieties.

1. If both the Places lie under one and the same Meridian, and on one and the same Side of the Aequinoctial, either on the North or South Side thereof, then substract the lesser Lati∣tude from the greater, and the Difference converred into Miles (by allowing 60 Miles to one Degree) shall give you the Distance.

Example. London and Ribadio lie both under one Meridian, namely of 20 degr. of Longitude; but they differ in Latitude, for London hath 51 d. 30 min. and Ribadio hath Latitude 43 d. both North; the difference of Latitude is 8 degr. 30 m. which being turned into Miles makes 510 miles.

2. If the two Places lie under one and the same Meridian,

but one on the North, and the other on the South-side of the Aequinoctial, adde both the Latitudes together, the Sum is the Distance.

[illustration] geometrical diagram

Example. London and the Island Tristan Dacunhu lie both under one Meridian; but London hath 51 degr. 30 min. North Latitude, and the Island hath 34 d. South Latitude: their Sum is 85 degr. 30 min. which converted into Miles (by dividing

the Degrees by 60. and allowing for every Minute one Mile) makes 5130 miles. And such is the distance of London and the Island Tristan Dacunhu.

To find the distance of these Places upon the Projection.

Seeing that they all lie under one Meridian, namely, N E G H S, find the Pole thereof at K; then lay a Ruler to K and E, it will cut the first Meridian in a; also a Ruler laid from K to G will cut the Meridian in b: the distance a b, measured upon the Line of Chords, will give 8 degr. 30 min. the Distance of London and Ribadio. Again, to find the Distance between London and the Island Tristan Dacunhu, lay a Ruler from K to E, it will cut the first Meridian in a, (as before) and laid from K to H, it will cut the first Meridian in c: the Distance a c, being mea∣sured upon the Line of Chords, will contain 85 degr. 30 m. the Distance between London and the Island, which in Miles is 5130.