The Cross-Staff is an Artificial Quadrant, Geometrically projected into that Form as an Instrument of greatest ease and exactest use in Navigation, by which in any natural disturbance of weather (the Sun or Stars appearing) the Poles height may be known, when the Astrolaby or Quadrant are not to be used: Conveying the use of the Quadrant from the beame of the Sun, to the beams of the Eye: for whereas by the Quadrant the Sun beame perceiving the Dioptra sheweth his height, so by the Cross-Staff the beame of the Eye conveyed to the Sun or Star, doth likewise give their height. The Demonstration whereof is thus:
- Make a plain Square consisting of four right Angles, as is the Square, i.o.h.n.
- the angle i. shall be assigned to the Center of the Quadrant, then placing one foot of your Compasses, stretch the other foot to the Angle n. and therewith describe a quarter of a Circle, as is the Arc o.d.n.
- then from the Center i. to his opposite angle h. draw a right line, by which line the Quadrant o.d.n. is divided into two equal parts,
- from the point d. divide the Arc d.n. into 90 equal parts, drawing from the center i. lines through every of those divisions touching in the line n.h. as by this Figure appeareth:
- Then consider the length of your Transversary, and take half thereof, laying it upon the line i.o. in the point S.
- from that point S. draw a Parallel to the line i.n. as is the line S.y. and as that line doth intersect the divisions of the half Quadrant, so shall be the degrees of the Cross-Staff; and note that the sides of the Square, must be as long as the Staff that is graduated
- Because the Staff would be of unreasonable length to contain more than than 60 degrees, therefore to keep him in due form for the ease of his use, and that the complement of 90 deg. should be contained upon the staff, the other 30 are artificially projected upon the Transversary, as by this demonstration appeareth,
- and in this sort consider the length of your staff from that point S. to the last intersection which endeth in 30 deg. lay down the length of the line i.h. at the point of v
- from that point draw a right line, cutting the line i.h. to the right Angles as in the line v.a. being just the length of half the Transversary:
- then divide the ark o.d. into 45 equal parts, accounting from the point d to the point o. then from the Angle i. draw right lines to the first 15 of those parts, and as those lines do cut the line v.a. so must the Transversary be graduated on both his parts, where unto vanes being framed, your staff is finished to your use.