Full text: A treatise of algebra

242 OF f»LANK I III G ON 0 MET lit. 
6. The versed sine of an arch is the part of the dia 
meter intercepted between the arch and its sine : so AF 
is the versed sine of AB, and DF of DB. 
7. The co-sine of an arch is the part of the diameteT 
intercepted between the centre and the sine; and is equal 
to the sine of the complement of that arch. Thus CF is 
the co-sine of the arch AB, and is equal to BI, the sine 
of its complement HB. 
8. The tangent of an arch, is a right line touching 
the circle in one extremity of that arch, continued from 
thence to meet a line drawn from the centre through the 
other extremity; which line is called the secant of the 
same arch : thus AG is the tangent, and CG the secant 
of the arch A B. 
9. The co-tangent and co-secant of an arch are the 
tangent and secant of the complement of that arch; 
thus HK and CK. are the co-tangent and co-secant of 
the arch AB. 
10. A trigonometrical canon is a table exhibiting 
the length of the sine, tangent, See. to every degree 
and minute of the quadrant, with respect to the radius 
which is supposed unity, and conceived to be divided 
into 10000000 or more decimal parts. Upon this table 
the numerical solution of the several cases in trigono 
metry depend; it will therefore be proper to begin with 
its construction. 
mioposiTioN r* 
The number of degrees and minutes, Sc. in an arch 
being given; to find both its sine and co-sine. 
This problem is resolved, by having the ratio of the 
circumference to the diameter, and by means of the 
known series for the sine and co-sine (hereafter de 
monstrated). For, the semi-circumference of the circle, 
whose radius is unity, being 3,141592653589793 &c. 
it will therefore be, as the number of degrees or mi 
nutes in the whole semi-circle is to the degrees or 
minutes in the arch proposed, so is 3,14159265358 &c. 
to the length of the said arch; which let be denoted by 
a; then, by the series above quoted, it$ siue will be ex-
	        
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