This section is from "The American Cyclopaedia", by George Ripley And Charles A. Dana. Also available from Amazon: The New American Cyclopędia. 16 volumes complete..
East (Anglo-Saxon, East; the corresponding word in many other languages having a similar etymological significance), the quarter in which the heavenly bodies rise. Due east is the direction toward the east precisely at right angles to each meridian line; the reverse direction is due west. An object is said to bear due east when it is seen exactly in this direction, but it is said to be due east when it is on the same parallel of latitude as the observer. An object that is due east will in northern latitudes bear N. of E., unless it be very near the observer, because a line perpendicular to a meridian in any latitude, if continued in one direction as a great circle, would depart from the parallel of latitude and intersect the equator at a distance of one fourth of a circle. A column of smoke, for example, over New York city, could it be seen at Nauvoo, would bear 5 3/4° N. of E., and smoke rising from Nauvoo would bear from New York 5 3/4° N. of W. The bearing is the direction in which a great circle from the observer through the object starts from the observer; while the course or actual direction is the direction of a line to the object cutting every meridian at the same angle.
 
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