THE
DESCRIPTION and USE
OF AN
INSTRUMENT
called the
DOUBLE SCALE
OF
PROPORTION

By which Instrument, all Questions in

May be most accurately and speedily performed, without the assistance of either Pen or Compasses.

By Seth Partridge.

LONDON,
Printed for Hannah Sawbridge at the Bible on Ludgate Hill, 1685.

THE Double Scale of Proportion.
The Description and Use of an Instrument consisting of Doubled Scales.

Whereby all Conclusions Mathematical may be performed only by Application of Scales.

CHAP. I.

The Instrument described.

The Instrument whereof I treat in this Book, I call the Double Scale, for that the Scales, or Lines thereupon, are doubled; so & in such manner, that by applying the one to the other, they will of themselves resolve any question Mathematical, that may be done by the Pen, or by Tables of Sines, Tangents, and Logarithms. The Scales principally inscribed thereupon, are those most admirable Lines of Numbers, of Sines, and of Tangents, whose use hath been heretofore set forth, only to be wrought upon with a pair of Compasses, and no otherwise. But I have so contrived them double, upon an Instrument to move, or slide along one by the other, in such manner, that upon the same, without any assistance of Compasses, I can work all Conclusions Mathematical, that can be wrought by the single Lines, with the help of Compasses, both in Arithmetick, Geometry, Trigonometry, Astronomy, Geography, Navigation, Gaging of Vessels, Fortification, Gunnery, Dialling. Yea, and the Usurer too, may hereby also compute the true interest of his money. In all which, I shall give you some examples for your instruction, in the use of my Double Scale.

The body, or matter whereof the Instrument is made, may be either of Brass, or of very good and well seasoned Box. It consisteth of three pieces, or Rulers, each one about half an inch in breadth, & about a quarter of an inch in thickness, more or less, as the Maker and User of them pleaseth; and for their length, they may be made to what length you will, either one foot, two foot, three foot, or more or less, for they are not limited to any length, only the longer they are, the larger and more will be the divisions of the Scales, and so consequently the more exact in operation. These three Rulers, or pieces of this Scale, are to be all of one even length and thickness and by the edges so evenly joynted, that they may justly slide alone close one by the other, having at each end a little plate of Brass, or Wood fitted to hold them close together, and so fastened to the two out-fide pieces, that they may be kept steady, and the middle Ruler to slide to and fro between them.

The Lines, or Scales ingraven on this Instrument, are the ordinary lines of Numbers, of Sines, and of Tangents, only they are set on double, that is, once upon one Ruler, and once upon the other, upon one and the same joynt; as the line of Numbers is set both upon one of the out-fide pieces, & and on the middle piece, that is, on both sides the joynt, and numbered on both, and so set to the very edges of both Rulers, that both lines being joyned together, may appear to be but as one line of Numbers, & this line of Numbers is (as it were) twice repeated, or doubled in the length of the Ruler, that is, beginning with 1 at one end of the Ruler, which I call the lower end, and continued to 1 or 10 at the middle, and from thence begin again, and continued to 10 or 100 at the upper end. Also upon the other side of the Rulers, upon the same joynt, is in like manner set a like line of Numbers, and this line of Numbers is fitted to be used with the line of Tangents, as that on the other side is with the lines of Sines, without any turning of the Instrument. But you may omit on the line of Numbers upon one fide, only observing to turn the Instrument, when the work requireth to be done on several lines, as in the sequel it will appear.

The Scales, or Lines of Sines, are in like manner set on twice, that is, once upon the other edge of the middle piece, and also on the inside of the other out-fide piece, and they are to be set on, upon both sides the joynt, that they may appear as one line of Sines, being laid close together, and numbers set to the Divisions on both parts, and is in the lines of Numbers.

The lines of Tangents is set upon the other side of the Rulers, opposite to the lines of Sines upon the same joynt with them, and likewise so set upon both parts of the Instrument, that the parts being laid close together, the line may appear to be both as one line of Tangents, and numbered on both parts to 45 at the upper end, against 90 on the lines of Sines, and front 45 back again to 89 at the lower end, as is usually done in the lines ofTangents. This Instrument having those Scales, or (as it pleased their first Inventor to call them) Lines, thus ingraven or set on it, will work all conclusions, as may be wrought by Mr. Gunters Lines, or Mr. Wingates, by only applying the Lines one to another, without the use of Compasses, which must be always had and used with theirs; yet you may use Compasses with these Scales, if you please, and so try and examine your work by both ways, and when you have made such trial, use which way you like best, and that (for ought I know) may be my Double Scales.

To shew the making of the Scales of Numbers, Sines and Tangents, is a thing altogether needless, the making of them being already so sufficiently set forth by others, that for me to do it again, were but labour lost, both to me in writing, and to the Reader in reading. And those that are makers of Mathematical Instruments, do already well understand the making of them, and for a man to make one for his own use, is but vain, for that he may buy one at a cheaper rate than make it, I shall therefore proceed to the use: Wherein note, that for distiniction of the sides of the Scales, or Lines on the Rulers, I use the Terms of Firft and Second, as being as proper for the purpose as any other could have been: For evermore, that side of any Line, whereon the first term in the rule of Proportion is taken, I call the first side; and the other side of the Line, whereon the second term in the Rule is taken I call the second side. And then for the third term in the Rule, it is always taken on the same side that the first term is taken on: & for the fourth term, which is the term sought, it is evermore found on that same second side, whereon the second term is taken. As if the first term be taken on any Scale, upon the out side Ruler, then the second term is on the middle Ruler, and if the first term be taken on the middle Ruler, then the second term is on the same Scale upon an out-fide Ruler. And when the work is by several Lines, then the two out-side Rulers both bear the name of Firft, or Second.

Other scales may be added to this Instrument, and set on the sides and edges thereof, as a Scale of equal-parts, or a Line of inches, a Meridian-line, a Gage-line, a line of Chords, the lines of Board and Timber-measure, or any others, such as your Calling and Occasions have most use for.

Seth Partridge verweist zur Konstruktion der Skalen explizit auf die Anleitung von Edmund Gunter. Der ebenfalls erwähnte Edmund Wingate (1596-1656) führte 1628 die Gunter Scale in Frankreich ein und brachte 1658 eine englische Übersetzung (Construction and Use of the Line of Proportion) heraus. Sein Buch Construction and Use of the Rule of Proportion von 1648 enthält einige Verbesserungen gegenüber Gunters Entwurf.
(Nach: FLORIAN CAJORI: ON THE HISTORY OF GUNTER´S SCALE AND THE SLIDE RULE DURING THE SEVENTEENTH CENTURY. BERKELEY 1920.)