The English globe being a stabil and immobil one, performing what the ordinary globes do, and much more / invented and described by the Right Honorable, the Earl of Castlemaine ; and now publish't by Joseph Moxon ...

J. Moxon To the Reader.

HAving Courteous Reader engaged to show you the Pro∣blems and Operations on the Sector, which the Noble Au∣thor supposes every one (that studies the Geometrical way of Dialling) to know, I shall here begin.

I. Upon a Line given (AB) to erect (CD) a Perpen∣dicular.

[illustration]

IF there be a Point (as C) given in (AB) the Line on which the Perpendicular is to fall, Mark on both sides of the said Point (with your Compass) the equidistant Points M and N, then opening them at pleasure, put one foot on M and describe the blind Arch EF, and putting the other Foot in N, describe the blind Arch GH, and the fair line from (D) their Intersection to the Point C, will be the Perpen∣dicular requir'd. Now if you have no Point assign'd (in the said Line (AB) to terminate your Perpendicular by take two Points there at pleasure, as suppose M and N, and opening how you will your Compasses, describe the blind Arches EF and GH above your Line, and OP and QR below it, and the In∣tersections

of these Arches (to wit, D and S) will be two points to draw your Perpendicular by.

II. Upon (C) the end of (AC) a given Line, to draw (DC) a Perpendicular.

[illustration]

OPEN your Compasses at a convenient width, and putting one Foot on C, let the other (within reach of AC) mark any where, as at F: then touching or cut∣ting from thence the said AC (with the moving Foot of your Compasses) at, suppose, E, and describing on the other side of F the blind Arch GH, lay your Ruler on FE, and it will cut the said Arch, at, suppose D, so that DC will be the requir'd Perpendicular.

III. A Line (AB) being given how to draw (DG) a Pa∣rallel to it.

[illustration]

HAVING taken two points in the said Line, as suppose A and B, open your Compasses at what width you please, and putting one foot on A, describe the blind Arch CDE, and putting one foot on B describe the blind Arch FGH, then if you lay your Ruler on the highest part or greatest Extuberancy of the said Arches, to wit on the Points D and G, the Line so drawn will be the requir'd Parallel.

IV. To describe a true Square.

[illustration]

AB being a Line as long as the side of the Square you design, erect on the end A, the Perpendicular DA of the for∣mer length; then taking between your Compasses the said AB, put one foot on D, and describe the blind arch EF, and again putting one foot on B, describe the blind arch GH, to cut EF, and if from their Intersection C, you draw the fair lines CB and CD, you have a true Square.

V. To draw an Oblong, or (as they commonby call it) a Long Square.

[illustration]

AB being the longest side of this Square, erect on the end A, the Perpedicular DA, of the length of the shortest; then taking between your Compasses, the line AB, put one foot on D, and describe the blind arch EF: and taking between your Com∣passes the line AD, describe the blind arch GH, to cut the said EF, and if from their Intersection C, you draw the fair lines CB and CD, you have the Square you design.

VI. To Describe an equilateral Triangle, or an Isos∣celes.

[illustration]

OPEN your Compasses at AB, being the side of the Triangle you design, and putting one foot on A, describe the blind Arch EF, and again putting one foot on B, describe the blind Arch GH to cut the said EF, and if from their In∣tersection C, you draw the fair lines CA, and CB, you have a true equilateral Triangle; Nor is there any difference in the Description of the Isosceles ASB, for the only difference be∣tween them is, that the sides AS and BS of the Isosceles are longer (or if you please they may be shorter) than the Base AB, whenas all three sides are equal in the equilateral Triangle.

VII. To make a Triangle of three given Lines.

[illustration]

SUPPOSE the first line given be AB, the second AC, the third BC, and that you are to make a Triangle of them: let AB be the Base, and taking the given line AC between your Compasses, put one foot on the Base at A, and describe the Blind Arch EF, then taking the given line BC, between your compasses, put one foot on the Base at B, and describe the Blind Arch GH, to cut the said Arch EF, and if you draw lines, from their Intersection at C, to A and B, on the aforesaid Base, you have your intent.

VIII. To describe an Oval.

[illustration]

CROSS RP at right Angles with IM, and taking with your Compasses (on the said lines from the intersection O) equal distances, to wit, OA, OB, OC, and OD, and draw through the point C, the lines AK and BH, each equal to twice AC, as also throu' D the lines AN and BL, each equal to twice BC, then A and B being Centers, describe the Arches KPM, and HLR; in like manner C and D being Centers, describe the Arches HIK, and LMN, and the figure thus drawn will be a perfect Oval.

[illustration]

So much for the Geometrical Problems necessary for Dial∣ling, and as for the Instrumental ones, i. e. those performed by the Sector, they are, as I may say, of two sorts, some belonging to one side of it, and some to the other; for the side marked with L is divided into 100 equal parts, and called the LINE of LINES, and the side mark'd with S, the LINE of SINES. First then of the LINE of LINES, which by the way, tho' it be divided (as I said) but into 100 parts, may yet stand for 1000, if you fancy every 10 Divisions a Line of 100 parts, and in like manner it will stand for 10000 parts, if every division be deemed 100, therefore a Line (v. g.) of 75 equal parts, may be exprest by 75 of those Divisions, or by 7½ or by ¾.

Notes

• p. 71.
• Of the Sector.