368. Having collected these Elements or Requisites, the following part
of the work may be very much facilitated by means of a good Sector, with
the use of which the reader should be so well acquainted, as to know how
to open it to any given Radius, as far as it will go; and to take off
the Chord or Sine of any Arc of that Radius. This is done by first
taking the extent of the given Radius in your Compasses, and then
opening the Sector so as the distance cross-wise between the ends of the
lines of Sines or Chords at _S_ or _C_, from Leg to Leg of the Sector,
may be equal to that extent; then, without altering the Sector, take the
Sine or Chord of the given Arc with your Compasses extended cross-wise
from Leg to Leg of the Sector in these lines. But if the operator has
not a Sector, he must construct these lines to such different lengths as
he wants them in the projection. And lest this Treatise should fall into
the hands of any person who would wish to project the Figure of a solar
or lunar Eclipse, and has not a Sector to do it by, we shall shew how he
may make a line of Sines or Chords to any Radius.
[Sidenote: Fig. II.
How to make a line of Chords.