Another method.

Another way is thus: Divide the side a. b. of the square into six equal parts & mark off the two extreme parts, one at either end, by the points f. and g.; then draw the inner and broader limb, with its point at e. as above; and to this, in an upward direction, a narrower one, so that between f. g. be left a vacant s.p.a.ce, and so more readily the letter slope forward. Then you are to draw the two lateral and vertical limbs--the near and slender, and the farther broad one--at the top, indeed, as in the first sketch, but at the bottom produce them to the two angles c. and d. and finally add projecting cusps, as you were instructed in the first M; but the projection below will pa.s.s beyond the square at the points c. and d. Or you shall make M at top with acute angles, in which case the lateral limbs will slope the more; or shear them off obtusely, and in this fashion (whichever pleases you best) make them as you see them depicted in the following diagrams.

[Ill.u.s.tration: M]

THE LETTER N.

Likewise the letter N you shall make in its square thus: First you are to draw two standards vertical and slender, so that at top & bottom they may touch the square, & that being produced, the nigh one at the bottom, and the farther at the top, they may touch the angles at c. and b. Now join these two by a broad oblique limb, running from the angle a. to the point e., by which is denoted the remote side of the farther limb, where you shall allow the acute angle to remain; but at the top, this limb, produced beyond the angle a., you are to round out to a fifth part of the length of a. b. This prolongation should incurve below, a fifteenth part of the distance a. b. projected on two arcs, the upper one the greater, the lower the less. For the lesser arc, therefore, you shall take as diameter of its circle, a line the fifth part of the distance a. b. and its centre is to be taken outside the square, so that the foot of the compa.s.s may touch the tip of the extension and the angle a.; then extend a little the feet of the compa.s.s, and shift its centre until the arc touch both the tip of the part produced, & the broad oblique limb, in the middle point between the side a. c. & the nearer of the two slender vertical limbs.

Or you may make the letter N in such fashion that its upper nigh extension shall remain within the square; or you may make from it an acute angle as shown overleaf.

[Ill.u.s.tration: N]

THE LETTER O.

Now O you shall make this way in its square. Set in the square the diameter c. b. and bisect it in the point e., so that e. may form a middle point between the two points f. and g. which are to be your two centres; and from each let a circle be described touching two sides of the square; & where the circles cut one another, there with your hand you must shape the slender outline of the letter to a juster proportion, as below is shown.

[Ill.u.s.tration: O]

THE LETTER P.

P you shall make in its square in this wise. Divide the square a. b. c. d. by the median horizontal line e. f.; then divide a. e. & b. f. equally by the line g. h. Next draw, first the broad vertical limb for this letter P, as you did a short while ago for K, and afterwards erect the line i. k. the distance of its own breadth to the right of your vertical limb; (here you must ever observe that in a lettered square we speak of the angle a. as the "hither" angle, that is, to the left; & the angle b. as the "farther" angle, that is, to the right).

Then where the line i. k. cuts g. h. call the point l., and next draw two slender horizontal limbs, the upper below a. b., the lower above e. f., from the broad vertical limb as far as the line i. k. Set one leg of the compa.s.s on the point l., extending the other to the lower side of the lower horizontal limb near k.; then describe an arc through the line g. h. as far as the other slender horizontal limb of this same P, & where it cuts the line g. h. set the point m. Next, on the far side of m. measure the width of the large limb of the letter, along the line g. h. to the point n. and let your compa.s.s be stretched so that with one foot it may touch the line a. b. and with the other the point n.; then set one foot of the compa.s.s on n. & the other on the line g. h. to the right, in the point o., in which this foot is to be left standing immovable, and with the other is to be described an arc, pa.s.sing through the point n. and touching the lines a. b. and e. f.

Or you may form the loop of this letter in the following manner. Set a leg of the compa.s.s under the transverse g. h. in the line i. k., in a place median between the line e. f. & the lower part of the upper transverse of the slender limb, in the point p. and describe an arc as before, pa.s.sing through m. so that the loop will be acute at the bottom, and its tip will end in the middle s.p.a.ce between the line i. k. and the broad vertical limb of the letter.

Or make this same P with a circular sweep, by shifting the compa.s.s upon the diameter, so that that sweep may be broader at the top (as though made with a pen) as will be shown in the diagram on the following page.

[Ill.u.s.tration: P]

THE LETTER Q.

Make your Q in its square in the self-same manner as was prescribed for O; but add to it its tail thus: Draw a diameter of the square, the line a. d., about which, starting from the curved outline, begin to draw a long tail, producing it through the angle d. in such fashion that d. may be in the middle of the thickest part of the tail; but where the tail begins let it be a little narrower than in the angle d., where it should attain its real thickness. Then let it be drawn out, beyond the angle d.

to the length of the entire diameter, and in a downward direction, yet so that it curves while it slopes, & that its tip shall not fall lower than a third of the side below the lowest side of the square, and shall tend, as it nears the point, to grow sharper little by little, and at length end in a very fine point indeed.

Or you shall give Q a shorter tail in this fashion, to wit: set your compa.s.ses to the length of the side c. d. and draw a tail from the bulge of the same letter, describing through the point d. its inner arc of the same length as c. d., taking care that the tail bend upwards until it again reach c. d. produced, in the point h.; then shift your compa.s.ses, & with the other leg again describe from the bulge of the letter an arc below d. & continue it until again it reach h., but in such fashion that the tail shall find its greatest thickness at the start, as in the following figure is doubly depicted.

[Ill.u.s.tration: Q]

THE LETTER R.

Moreover R you must make in its square just as was directed for P; but then erect a right line q. r. through the middle point of the square, & let it cut the exterior arc of the rounded limb in s., from which point, downwards towards the angle d., let there be drawn a broad tract, almost equal to that which you made above for the letter K., but this is to be somewhat bent in, and so shaped by your hand that its tip, well formed, may arrive directly on the angle d.

Or make R in such fashion that its rounded sweep, as though made with a pen, shall be above broader, & narrower below. To accomplish this, you must shift your compa.s.ses on the diameter q. e. & not allow the rounded limb to touch the vertical one, as was described in P. Besides, the oblique limb is to be deduced from the rounded one with a little more of a curve; just as I have drawn overleaf.

[Ill.u.s.tration: R]

THE LETTER S.

Next, the letter S you shall make as follows in its square, a. b. c. d.

First draw the horizontal line e. f. and the median & vertical one g. h.

and let them bisect one another in the point m. Then choose the main thickness of the letter, and set it in the line g. h. so that the point m. may divide it, having one-third of the thickness below it; next, set the lesser thickness, at the top beneath g., indicating it by the point i., and at bottom, above h. in the point k.; and the thickness of the letter indicate above by n. and below by l.

Next, set a leg of your compa.s.ses on the line g. h. in the mid-point between i. and n., and with the other describe a circle pa.s.sing through i. and n.; in like manner, upon the line g. h. set your compa.s.ses upon the mid-point of g. l. and describe a circle pa.s.sing through g. & l.

Then once more set your compa.s.s on the same line g. h. in the mid-point of n. h. and describe a circle through n. & h.; and lastly, in the mid-point of l. k. you must set one leg, & with the other is a circle to be described through these same points l. & k.; afterwards cut off by vertical section the upper portion of this letter, so that the part thus cut off may contain in its extremity the maximum thickness of the letter and a third part besides, & also that its tip may project downwards so far as to stand midway between the centre of the circle i. n. and the side b. d.; in other words, let the tip be distant on the right, from the circle i. n. the first third of the interval between the greater and lesser circles.

Next cut the lower limb of the letter to the left, by a vertical line through the mid-point between the two circles, & in such fashion that the part so cut off may be a fourth part wider & higher than the upper, and that its tip may rise to the height of the centre of the circle n. h.

Another method.

Yet another way may you make the letter S. In the square a. b. c. d.

bisect the horizontal line e. f. in the point m.; then set one leg of your compa.s.s upon the mid-point between g. and m. & with the other describe a segment of a circle in the direction of a. e. pa.s.sing through the points m. and g.; next, set your compa.s.s upon the mid-point between m. and h. and describe a segment of a circle through m. and h. in the direction of f. d. The two arcs will touch above, in front, and below, in the rear, the exterior curvatures of this same letter S.

Next, draw through m. the diameter c. b. and at its middle indicate the maximum thickness of the letter by the two points p. and q. from which let there be drawn two right lines, one up, & one down, to those two arcs; & next, from the two points p. & q. draw two curved parallels to the same arcs, regulating the distance between them, their elevation & depression from the centres of the same circles. Next, indicate below g.

and above h. the minimum thickness of the letter; and from these points you will with your hand fashion the inner shape of the letter, both above and below, & produce the limb of S, above towards b. Cut it off so that its lower tip may touch the segment, & that the part cut off upwards may contain a tenth part of a. b. and that the segment may still exceed the part cut off. Then construct a vertical line r. s. to the right of e. c. and distant from it a fifth part of c. d.; let it cut the diagonal c. b. in t. and to the angle just formed produce the extremity of the letter, making the part so cut off a third broader than the upper portion. Lastly, you will have to produce the tip ever so little beyond t.; as I have briefly indicated.

[Ill.u.s.tration: S]

THE LETTER T.