The Sector altered.
CHAP. I.
Of the Sector in general.
Amongst the many Writers that have been upon the Sector, Mr. Gunter hath done best, the Lines of his Instrument being most in number, and of the most formal contrivance, and the most largely Commented upon: yet some Inconveniences have been found in the Use of that Instrument: Partly because his Lines of Tangents, Secants, and Rumbs, or Meridional parts come not from the Center, and so could not in all cases with convenience admit of proportional Works; and partly because he had no Line of versed Sines, (of which in his Book there is good Use, and might have been much more) but instead thereof he is compelled to use the Line of right Sines, which is but half of the whole Scale of versed Sines, and besides the parts of it stand the contrary way, so that the fittings of the proportional terms whereby to work with half the Scale instead of the whole, and then the application of the parts from one end to the other, will be not a little Troublesome.
To remedy these and other like defects, I have altered the form of the Sector once more:
- By diminishing the number of the old Scales, for instead of two of each kind, there is but one.
- By taking the Meridian Line quite away; and supplying the Use thereof by other means.
- By bringing the Scales of Tangents and Secants to the Center.
- By adding a Line of Versed Sines, and some other Scales of good use.
- And by changing the form of working upon the Instrument: of all which things I shall give an account in this following Treatise: but first it will be requisite to describe the order and disposition of the Lines, how each of them is to be placed.
CHAP. II.
How the several Lines are disposed upon the Sector.
Whereas in other Sectors there are always two Lines of one kind, upon each Leg one, answering to the like Scale upon the other leg, in this there is but one Line of one kind, from whence it comes to pass, that one side or flat of this Sector holds all Scales that are drawn from the center, and do fill up both sides of the other, and by this means the other side is free for other Scales.
Upon the one Leg therefore of the first side are:
- A Line of equal parts.
- A Line of Solids, and between these two Scales and the edge, there are inserted two particular Scales more. Namely,
- Of Inscribed bodies.
- Of Equated bodies, with a Scale of Metals.
So again, upon the other Leg are:
- The Lines of Sines.
- The Lines of Superficies, and between them two Scales and the edge are inscribed two other particular Scales as:
- The Line of Quadrature. And,
- Segments.
All these Scales are drawn from the Center, and being measured from thence, are all of one length: and do lie at such Angles one from another, and to the edges of the Sector, will give them convenient distance. So that this one side of the Instrument doth now contain so many Lines of Scales, coming from the Center, as were before on both sides.
Upon the second side of the Sector are four Scales, two upon one Leg, and two upon the other. As namely upon one Leg,
- Versed Sines, with a Zodiack Line annexed to it.
- A Line of Tangents going up to 63 gr. 26 m.
- A Line of Secants going up to 60 gr.
- A Line of Chords going up to 90 gr.
All these are drawn from the Center, and all of one length with those on the other side of the Instrument. The Radius of the Versed Sines, Tangents, and Secant Lines are just half of the inscribed Lines, and so will be of very good use in the working of proportions, and in the projecting of the Sphere very commodious.
The descriptions of each Scale may be made by those Tables, and in that manner that Mr. Gunter hath directed.
Between these four Scales may be placed other Scales of good use, tending to wards (though not running up to) the center, as a Tangent of three hours of good use in Dialling, and other the like Lines.
Of the other Lines inscribed on the edges and spare places of the Sector.
If the Sector be made of wood, it will require some competent thickness, so that the edges will be large enough to receive some useful Scales also.
The Sector then being opened, and so made a straight Ruler; the outer edge hath inscribed upon it the three usual Scales of Logarithmeticall Numbers, Sines and Tangents. The inner edge hath two Scales upon each Leg, one pair of those Scales upon one Leg is to find the mean Diameter, and the one of them is divided into 14 equal parts, the other (of the same length with it) is divided into 20 equal parts, each of them subdivided decimally. The other pair of Scales upon the other Leg is also divided equally, one of them containing four parts, which are to represent feet, and the other bein of the same length is divided into 400 parts, representing Inches of the former Feet, and each of these representative, both feet and inches are subdivided decimally. And again, upon the two flat edges of the Sector thus opened (near the outer edge) are inscribed two peculiar Scales (upon one edge) of equal parts for Wine and Ale measure. Upon the other flat side are two Scales more, each equal to the other, both of a just foot length; one is divided into 12 inches, and each inch subdivided Decimally, the other is divided into 10 equal parts, and each of them again into 10. These two Scales serve for true inch and true foot measure.
In this manner are the Lines disposed, now follows,
CHAP. III.
The general use of the Sector, and the manner of working upon it.
