Stratarithmetrie

Stratarithmetrie is the skill (appertaining to war) by which a man can set in a figure, analogous to any geometric figure appointed, any certain number or sum of men: capable of such a figure (by reason of the usual spaces allowed between soldiers, and because no fractions can be made of men. Yet nevertheless he can order the given sum of men into the greatest such figure that can be ordered of them) and certify the surplus (if any) and the next certain sum which, with the surplus, will admit a figure exactly proportional to the assigned figure. By which skill also, of any army or company of men (the figure and sides of whose orderly standing or array is known), he is able to express the exact number of men contained within that figure: or (in order) able to be contained.

Note.

And this figure and its sides he is able to know: either being by and at hand, or far off. Thus far stretches the description and property of Stratarithmetrie: sufficient for this time and place.

The difference between Stratarithmetrie and Tacticie.

"It differs from the tactical feat of drawing up battle lines, because there it takes wisdom and foresight to what purpose he orders the men; and skillful ability also, for any occasion or purpose, to devise and use the fittest and most necessary order, array, and figure of his company and sum of men." By figure I mean such as a perfect square, triangle, circle, oval, long square (which the Greeks call Eteromekes), rhomb, rhomboid, crescent, ring, serpentine, and such other geometric figures: which in wars have been and are to be used for convenience, necessity, and advantage, etc. And he ought to have no small skill who can give a true report, or near the truth, of the numbers and sums of footmen or horsemen in the enemy's ordering. To make an estimate from afar, between close terms of more and less, is not a thing very common among those who would gladly do it.

I. D., friend, you will find it hard to carry out my description of this feat. But by chorography you can help yourself somewhat: where the figures known (in sides and angles) are not regular, and where a resolution into triangles can serve, etc. And yet you will find it strange to deal so generally with arithmetic figures, and that for battle array: their contents differ so much from like geometric figures.

Great policy may be used by the captains (at fitting times and in convenient places): as to use figures that make the greatest show of as many men as he has; and using the advantage of the three kinds of usual spaces (between footmen or horsemen) to take the largest; or when he would seem to have few, being many: and the contrary, in figure and space. The herald, pursuivant, sergeant royal, captain, or whoever is careful to come near the truth in this, besides the judgment of his expert eye, his skill of tactical ordering, and the help of his geometric instrument, ring or astronomical staff (conveniently framed for carrying and use), he may wonderfully help himself with perspective glasses. In which (I trust) our posterity will prove more skillful and expert, and for greater purposes, than in these days can almost be credited to be possible.

Thus I have lightly passed over the artificial feats depending chiefly upon common geometry, and commonly and generally reckoned under the name of geometry.

Stratarithmetrie is the skill, used in war, by which a man can set any set number or total of men into a figure like any given geometric figure, provided that figure can hold them. Two things limit it: the usual spaces allowed between soldiers, and the fact that men cannot be divided into fractions. Even so, he can arrange the given number of men into the largest figure they can fill, and report the surplus, if there is any. He can also report the next set number that, with the surplus, will make up a figure exactly like the figure assigned. The same skill works the other way. Given any army or company of men, whose figure and sides in orderly standing or array are known, he can state the exact number of men contained in that figure, or that could be contained in it in order.

He can also know this figure and its sides, whether he is near at hand or far off. That is as far as the description and the nature of Stratarithmetrie goes, enough for this time and place.

The difference between Stratarithmetrie and tactics.

"It differs from the art of tactics (drawing up battle lines), because there you need the wisdom and foresight to know what purpose you are ordering the men for, and the skilled ability to design and use, for any occasion or purpose, the fittest and most necessary order, array, and figure for your company and total of men." By figure I mean a square, triangle, circle, oval, rectangle (the Greeks call it Eteromekes), rhombus, rhomboid, crescent, ring, serpentine, and such other geometric figures, which have been and are to be used in war for convenience, necessity, and advantage, etc. He must have no small skill who would give a true report, or one near the truth, of the numbers and totals of foot soldiers or horsemen in the enemy's formation. To estimate from far off, down to close limits of more and less, is not common, even among those who would gladly do it.

I. D. — my friend, you will find it hard to carry out my description of this work. But by chorography you can help yourself somewhat, where the figures known by their sides and angles are not regular, and where resolving them into triangles can serve, etc. And yet you will find it strange to deal so generally with arithmetic figures, and for a battle array, since their contents differ so much from those of like geometric figures.

Captains can make good use of policy, at fitting times and in suitable places: using figures that make the greatest show of the number they have, and, taking advantage of the three usual kinds of space between foot soldiers or horsemen, taking the largest; or, when they want to seem few though they are many, doing the opposite in both figure and space. The herald, pursuivant, sergeant royal, captain, or anyone careful to come near the truth here, besides the judgment of his expert eye, his skill in tactical ordering, and the help of his geometric instrument — a ring or an astronomical staff, built conveniently for carrying and use — can wonderfully help himself with perspective glasses, in which, I trust, our descendants will prove more skillful and expert, and for greater purposes, than in these days can almost be credited as possible.

Thus I have quickly passed over the artificial feats that depend chiefly on common geometry, and that are usually and generally counted under the name of geometry.