Archemastrie

Now I end, with Archemastrie. The name is not so new as the art is rare; for another art, a degree below this in skill and power, had already been given this English name. And yet this will serve our purpose well enough for now. This art teaches how to bring to actual sensible experience all worthy conclusions proposed by all the mathematical arts and concluded by true natural philosophy; and it both adds to them a further scope in the terms of the same arts, and also by its own method and in peculiar terms proceeds, with the help of the aforesaid arts, to the performance of complete experiences which of no particular art can formally be challenged. If you remember how we considered architecture in respect of all common handiworks, some light you may have from that toward understanding the sovereignty and property of this science. I may call it a science rather than an art, for the excellence and mastery it has over so many and so mighty arts and sciences. And because it proceeds by experiences, and searches out the causes of conclusions by experiences, and also puts the conclusions themselves into experience, it is named by some the Experimental Science. Nicolaus Cusanus calls it so in his Statical Experiments, and another philosopher, native to this land (the flower of whose worthy fame can never die nor wither), wrote at length on it at the request of Clement the Sixth. The art carries with it wonderful credit, for it certifies sensibly, fully, and completely, to the utmost power of nature and art. This art certifies by complete and absolute experience; other arts, with their arguments and demonstrations, persuade, and in words prove their conclusions very well.

But words and arguments are no sensible certification, nor the full and final fruit of the sciences as they are practiced. And though some arts have experiences in them, yet they are not complete, nor brought to the utmost they may be stretched to and applied sensibly. As for example: the natural philosopher disputes and makes a goodly show of reason; and the astronomer and the optical mechanician put some things into experience—but neither all that they may, nor yet those they do, sufficiently and to the utmost. There then the Archemaster steps in, and leads the experiences on, by order of his experimental doctrine, to the chief and final power of natural and mathematical arts. Of two or three men in whom this description of Archemastry was experimentally verified, I have read and heard, and there is good record of such perfection in them. So that this art is no fantastic imagination—as some sophister, with his Insolubles, might flourish, and dazzle your imagination, and dash your honest desire and courage from believing these things so unheard-of, so marvelous, and of such importance. Well: as you will. I have warned you. I have done the part of a friend: I have discharged my duty toward God, for my small talent received at his most merciful hands. To this science does the science Alnirangiat render great service. Do not wonder at this name: I do not change a name so used, and published in print by others, being a name proper to the science. Under this comes Ars Sintrillia [title unclear in the source], briefly written by Artephius. But the chief science of the Archemaster (in this world) as yet known is another (as it were) optical science: of which the name shall be told (God willing) when I shall have some more just occasion to discourse of it.

Here I must end, thus abruptly (gentle friend, and unfeigned lover of honest and necessary verities). For they who have, for your sake and virtue's cause, requested me (an old, worn-out mathematician) to take pen in hand (through the confidence they placed in my long experience and tried sincerity), for the declaring and reporting somewhat of the fruit and commodity to be attained by the mathematical arts: even they, sore against their wills, are forced, for sundry causes, to satisfy the workman's request by ending without delay; he so fears this so new an attempt, and so costly, and in a matter so slenderly hitherto considered or esteemed among the common sort of students.

And since I was urged to set forth some reason why, in our vulgar speech, this part of the principal science of geometry, called Euclid's Geometrical Elements, is published for your handling—you who have no Latin, and are not university scholars—truly, I think it needless.

(1.)

For the honor and estimation of the universities and graduates is hereby nothing diminished, seeing that from them, and by those they have reared, you receive all this benefit, however great it be.

(2.)

Neither are their studies in the least hindered: no more than the Italian universities, as the academies of Bologna, Ferrara, Florence, Milan, Padua, Pavia, Perugia, Pisa, Rome, and Siena, or any one of them, find themselves at all disgraced, or their studies anything hindered, by Friar Lucas de Burgo or by Nicolaus Tartalea, who in the vulgar Italian language have published not only Euclid's Geometry, but somewhat of Archimedes: and in arithmetic and practical geometry very large volumes, all in their vulgar speech. Nor in Germany have the famous universities been anything discontent with Albertus Durerus, his geometrical institutions in German; or with Gulielmus Xylander, his learned translation of the first six books of Euclid out of the Greek into high German; nor with Gualterus H. Riffius, his geometrical volume, very diligently translated into the German tongue and published. Nor yet do the universities of Spain or Portugal think their reputation to be decayed, or suppose any of their studies hindered by the excellent P. Nonnius, his mathematical works put forth in vulgar speech. Have you not, likewise, in the French tongue the whole mathematical quadrivium? and yet have neither Paris, Orleans, nor any of the other universities of France ever been offended with the translators or publishers, or any man's study by that hindered?

(3.)

And surely the common and ordinary scholar (much more the grammarian) before coming to the university shall (or may) now be sufficiently instructed, according to Plato's counsel, in arithmetic and geometry, for the better and easier learning of all manner of philosophy, academic or peripatetic; and by that means go forward more cheerfully, more skillfully, and more speedily in his studies there to be learned; and so, in less time, profit more than otherwise he should or could do.

(4.)

Also many good and pregnant English wits, of young gentlemen and of others who never intend to meddle with the profound search and study of philosophy (to be learned in the universities), may nevertheless now, with more ease and liberty, have good occasion to occupy the sharpness of their wits virtuously: where otherwise, perhaps, they would spend their time—or rather lose it—in foolish exercises, neither serving God nor furthering the common or private good.

(5.)

And great comfort, with good hope, may the universities have, by reason of this English geometry and mathematical preface, that they hereafter shall be the more regarded, esteemed, and resorted to. For when it shall be known and reported that of the mathematical sciences only such great commodities are ensuing as I have specified, and that indeed some of you students with no Latin can be good witnesses of such rare fruit enjoyed by you by that, as either was not heard of before this, or else not so fully credited: "Well may all men conjecture that far greater aid and better furniture, to win to the perfection of all philosophy,

(Universities.)

may in the universities be had: being the storehouses and treasury of all sciences, and all arts necessary for the best and most noble state of commonwealths."

(6.)

Besides this, how many a common artisan is there in these realms of England and Ireland who deals with numbers, rule, and compass: who, with their own skill and experience already had, will be able (by these good helps and information) to find out and devise new works, strange engines, and instruments, for sundry purposes in the commonwealth? or for private pleasure? and for the better maintaining of their own estate? I will not therefore fight against my own shadow. For no man (I am sure) will open his mouth against this enterprise. No man (I say) who either has charity toward his brother (and would be glad of his furtherance in virtuous knowledge), or who has any care and zeal for the bettering of the common state of this realm. Neither any who make account of what the wiser sort of men (sage and steady) think of them. To none, therefore, will I make any apology for doing a virtuous act, and for commending or setting forth profitable arts to English men in the English tongue. "But to God our Creator let us all be thankful: for that, as he, of his goodness, by his power, and in his wisdom, has created all things in number, weight, and measure: so, to us, of his great mercy, he has revealed means by which to attain the sufficient and necessary knowledge of his three principal instruments aforesaid: which means I have abundantly proved to you to be the sciences and arts mathematical."

And though I have been pinched with straightness of time, that in no way I could pen down the matter (in my mind) as I determined, hoping for convenient leisure: yet if virtuous zeal and honest intent provoke and bring you to the reading and examining of this compendious treatise, I do not doubt but as the truth of it (according to our purpose) will be evident to you, so the pith and force of it will persuade you, and the wonderful fruit of it highly please you. And that you may the easier perceive, and better remember, the principal points of which my preface treats,

(The ground plan of this preface in a table.)

I will give you the ground plan of my whole discourse, in a table annexed, from the first to the last, somewhat methodically contrived.

If haste has caused my poor pen anywhere to stumble, you will (I am sure), in partial recompense for my earnest and sincere good will in pleasing you, consider the huge rocky mountains and the perilous unbeaten ways through which it (both night and day the while) has toiled and labored to bring you this good news and comfortable proof of virtue's fruit.

So I commit you to God's merciful direction for the rest: heartily beseeching him to prosper your studies and honest intentions, to his glory and the benefit of our country. Amen.

Written at my poor house at Mortlake.

In the year 1570. February 9.

J. Dee

Now I end with Archemastrie. The name is not so new as this art is rare. For another art, a degree below it in skill and power, has already been given this English name. And yet this may serve our purpose well enough at present. This art teaches how to bring to actual sensible experience all worthy conclusions proposed by all the mathematical arts and concluded by true natural philosophy; and it both adds to them a further scope in the terms of the same arts, and also by its own method, in peculiar terms, proceeds with the help of the said arts to the performance of complete experiences which cannot (formally) be challenged from any particular art. If you remember how we considered architecture in respect of all common handiwork, you may get some light from that toward understanding the sovereignty and property of this science. I may call it a science rather than an art, for the excellence and mastery it has over so many and so mighty arts and sciences. And because it proceeds by experiences, and searches out the causes of conclusions by experiences, and also puts the conclusions themselves into experience, some name it the experimental science. Nicolaus Cusanus calls it so in his Experimentes Statikall, and another philosopher,

native to this land (the flower of whose worthy fame can never die or wither) wrote about it at length at the request of Clement the Sixth. The art carries with it wonderful credit, because it certifies sensibly, fully, and completely, to the utmost power of nature and art. This art certifies by complete and absolute experience; other arts, with their arguments and demonstrations, persuade, and in words prove their conclusions very well.

☞

But words and arguments are no sensible certifying, nor the full and final fruit of sciences that can be practiced. And though some arts have experiences in them, they are not complete, nor brought to the uttermost they may be stretched to, and applied sensibly. For example: the natural philosopher disputes and makes a goodly show of reason, and the astronomer and the optical mechanician put some things into experience, but neither all that they can, nor yet fully and to the utmost those they do. There the Archemaster steps in and leads the experiences on, by order of his experimental doctrine, to the chief and final power of natural and mathematical arts. Of two or three men in whom this description of Archemastry was verified in practice I have read and heard, and good record exists of such perfection in them. So this art is no fantastic imagination, as some sophister might flourish with his insolubles, dazzle your imagination, and dash your honest desire and courage from believing these things so unheard-of, so marvelous, and of such importance. Well, as you will. I have forewarned you. I have done the part of a friend; I have discharged my duty toward God for the small talent I received from his most merciful hands. To this science the science Alnirangiat does great service. Do not wonder at this name: I do not change the name so used and published in print by others, being a name proper to the science. Under this comes Ars Sintrillia [title unclear in the source], by Artephius, briefly written. But the chief science of the Archemaster (in this world) as yet known is another science, as it were, optical; its name shall be told (God willing) when I have some more just occasion to discourse of it.

Here I must end, thus abruptly (gentle friend, and unfeigned lover of honest and necessary truths). For those who have (for your sake and virtue's sake) requested me (an old, worn-out mathematician) to take pen in hand, through the confidence they placed in my long experience and tried sincerity, for the declaring and reporting somewhat of the fruit and benefit to be attained by the mathematical arts: even they, very much against their own wills, are forced for various reasons to satisfy the workman's request by ending at once. He fears so new an attempt and so costly, and a matter so little (so far) considered or esteemed among the common sort of students.

And whereas I was pressed to allege some reason why, in our common speech, this part of the principal science of geometry, called Euclid's Geometric Elements, is published for you to handle, being people without Latin and not university scholars: truly I think it needless.

(1.)

For the honor and standing of the universities and their graduates is in no way diminished by this, seeing that you receive all this benefit from and through their nurslings, however great it be.

(2.)

Neither are their studies in any way hindered by it, any more than the Italian universities, as the academies of Bologna, Ferrara, Florence, Milan, Padua, Pavia, Perugia, Pisa, Rome, and Siena, or any one of them, find themselves at all disgraced or their studies hindered in the least by Friar Lucas de Burgo or by Nicolaus Tartalea, who in the common Italian language have published not only Euclid's geometry but something of Archimedes, and in arithmetic and practical geometry very large volumes, all in their common speech. Nor have the famous universities in Germany been at all displeased with the geometric institutions of Albertus Durerus in Dutch; nor with the learned translation by Gulielmus Xylander of the first six books of Euclid from Greek into high Dutch; nor with the geometric volume of Gualterus H. Riffius, very diligently translated into the high Dutch tongue and published. Nor do the universities of Spain or Portugal think their reputation decayed, or suppose any of their studies hindered by the excellent mathematical works of P. Nonnius put forth in common speech. Do you not likewise have in French the whole mathematical quadrivium? And yet neither Paris, Orleans, nor any of the other universities of France has at any time been offended with the translators or publishers, nor has any person's study been hindered by it?

(3.)

And surely the common and ordinary scholar (and much more the grammarian) before coming to the university can (or may) now be instructed well enough (according to Plato's counsel) in arithmetic and geometry, for the better and easier learning of all manner of philosophy, academic or Peripatetic. And by that means go on more cheerfully, more skillfully, and more quickly in his studies there to be learned, and so profit more in less time than otherwise he should or could do.

(4.)

Also many good and fertile English wits, of young gentlemen and of others who never intend to meddle with the profound search and study of philosophy (to be learned in the universities), may nevertheless now, with more ease and liberty, have good occasion to put the sharpness of their wits to virtuous use; where otherwise they might (perhaps) spend their time in foolish exercises, or rather lose it, serving neither God nor furthering the common or private good.

(5.)

And great comfort with good hope may the universities have from this English geometry and mathematical preface, that they hereafter shall be more regarded, esteemed, and resorted to. For when it shall be known and reported that from the mathematical sciences only such great benefits follow as I have specified, and that indeed some of you students without Latin can be good witnesses of such rare fruit enjoyed by you by that, as either was not heard of before or else not so fully credited: "Well, may all men conjecture that far greater aid and better furniture to win to the perfection of all philosophy,

Universities.

may be had in the universities, being the storehouses and treasury of all sciences,

☞

and all arts necessary for the best and most noble state of commonwealths."

(6.)

Besides this, how many a common craftsman is there in these realms of England and Ireland that deals with numbers, rule, and compass, who, with their own skill and experience already had, will be able (by these good helps and information) to find out and devise new works, strange engines, and instruments: for various purposes in the commonwealth, or for private pleasure, and for the better maintaining of their own estate? I will not (therefore) fight against my own shadow. For no man, I am sure, will open his mouth against this enterprise; no one, I say, who either has charity toward his brother (and would be glad to further him in virtuous knowledge), or who has any care and zeal for the bettering of the common state of this realm; neither any who make account of what the wiser sort of men (sage and steady) think of them. To none, therefore, will I make any apology for doing a virtuous act, and for commending or setting forth profitable arts to English people in the English tongue. "But to God our Creator let us all be thankful: that as he, of his goodness, by his power, and in his wisdom,

☞

has created all things in number, weight, and measure; so to us, of his great mercy, he has revealed means by which to attain the sufficient and necessary knowledge of the said three principal instruments of his: which means I have abundantly proved to you to be the sciences and mathematical arts."

And though I have been pressed by the straightness of time, so that in no way could I set the matter down (in my mind) as I determined, hoping for convenient leisure: yet if virtuous zeal and honest intent provoke and bring you to the reading and examining of this compendious treatise, I do not doubt but that, as the truth of it (according to our purpose) will be evident to you, so its pith and force will persuade you, and its wonderful fruit highly please you. And that you may the more easily perceive and better remember the principal points my preface treats of,

The ground plan of this preface in a table.

I will give you the ground plan of my whole discourse in an annexed table, from the first to the last, somewhat methodically devised.

If haste has made my poor pen stumble anywhere, you will (I am sure) partly repay me, for my earnest and sincere good will to please you, by considering the rocky, huge mountains and the perilous, untrodden ways it has toiled and labored through (night and day the while) to bring you this good news and comfortable proof of virtue's fruit.

So I commit you to God's merciful direction for the rest, heartily beseeching him to prosper your studies and honest intents, to his glory and the benefit of our country. Amen.

Written at my poor house at Mortlake.

In the year 1570. February 9.

J. DEE