TRACT 29.

DIVISION OF THE QUADRANT.

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never consist of more than four or five figures, viz, abouthalf the number of figures that are in the divisors mentionedin the preceding article,

20. Again, As the difference of the cosines :

to the sum of the cosines : :so tangent of half their difference :to cotangent of half their sum.

And thus the cotangents will be found, by dividing the sumof the cosines of two arcs, differing by 2, by their smalldifference.

21. Also, the secant of an arc, is equal to the sum of itstangent and the tangent of half its complement; and thecosecant of an arc, is equal to the sum of its cotangent andthe tangent of half the arc ; or half the sum of the tangentand cotangent, is equal to the cosecant of the double arc.Whence the secants and cosecants will be easily made.And thus we have pointed out methods, by which the wholetables may be readily constructed.