Trigonometry as taught in schools and school books is mostly 
“analytical ” and takes years to master. For seamen, this is 
generally impossible. What they chiefly want is that part of 
the science dealing with the practical solution of triangles by 
which all problems in Navigation are worked. The following 
pages contain all that the seaman needs in this respect; and no 
man of ordinary intelligence, and otherwise fairly educated, 
should find any difficulty in learning their contents in a short 
time, and without a teacher. 

There are two distinct varieties of Trigonometry, viz., Plane 
and Spherical. In-Plane Trigonometry all sides of triangles are 
straight lines, and are expressed in lineal measure, such as miles, 
yards, feet, or inches. In Spherical Trigonometry widely different 
conditions prevail, for the sides are all portions of Great Circle 
arcs, and are expressed in angular measure—degrees, &c.
Plane Trigonometry is used in Navigation for all the Sailings 
except Great Circle, and Spherical for that and all astronomical 
problems involving triangles.