Architecture

(An objection.)

Architecture seems to many not worthy, or not fit, to be reckoned among the mathematical arts. To them I think it good to give some account of my doing so. Not worthy, they will say, because it is only for the building of a house, palace, church, fort, or such like gross works. And you also defined the mathematical arts to be such as dealt with no material or corruptible thing, and also did demonstratively proceed in their faculty by number or magnitude. First,

(The answer.)

You see that I count Architecture here among those mathematical arts which are derived from the principal arts; and you know that such may deal with natural things and sensible matter. Of which, "some draw nearer to simple and absolute mathematical speculation than others do.

And though the architect procures, informs, and directs the mechanic in the handwork and the actual building of house, castle, or palace, and is chief judge of the same, yet with himself (as chief master and architect) remains the demonstrative reason and cause of the mechanic's work: in line, plane, and solid; by geometric, arithmetic, optic, musical, astronomical, cosmographic" (to be brief) by all the former derived mathematical arts and other natural arts, able to be confirmed and established. If this be so, then you may think that Architecture has good and due allowance in this honest company of derived mathematical arts. I will here crave the judgment of two most perfect architects: the one, Vitruvius the Roman, who wrote ten books of it to the Emperor Augustus (in whose days our heavenly Archemaster was born); and the other, Leo Baptista Albertus, a Florentine, who also published ten books of it. Architecture (says Vitruvius) is a science garnished with many doctrines and diverse instructions, by whose judgment all works finished by other workmen are judged. It follows: Architecture grows of framing and reasoning, etc. Reasoning is that which, of things framed with forecast and proportion, can make demonstration and manifest declaration. Again: In all things, therefore chiefly in Architecture, these two things are: the thing signified, and that which signifies. The thing propounded, of which we speak, is the thing signified. But demonstration, expressed with the reasons of diverse doctrines, signifies the same thing. After that: An architect (says he) ought to understand languages, to be skilled in painting, well instructed in geometry, not ignorant of perspective, furnished with arithmetic, to have knowledge of many histories, and diligently to have heard philosophers, to have skill in music, not ignorant of medicine, to know the answers of lawyers, and to have astronomy and the courses of the heavens in good knowledge. He gives orderly reason why all these arts, doctrines, and instructions are requisite in an excellent architect. And (for brevity) omitting the Latin text, thus he has it. Secondly, it is helpful for an architect to have the knowledge of painting: that he may the more easily fashion out, in painted patterns, the form of whatever work he likes. And geometry gives to architecture many helps: and first teaches the use of the rule and the compass, by which (chiefly and easily) the descriptions of buildings are dispatched in ground plans, and the directions of squares, levels, and lines. Likewise, by perspective, the lights of the sky are well led in buildings from certain quarters of the world. By arithmetic the charges of buildings are summed together, the measures are expressed, and the hard questions of symmetries are discoursed on by geometric means and methods, etc. Besides this, of the nature of things (which in Greek is called φυσιολογία) philosophy makes declaration. Which it is necessary for an architect diligently to have learned, because it has many and diverse natural questions, as especially in aqueducts. For in their courses, their leadings about in the level ground and in the mountings, the natural spirits or breaths are engendered diverse ways. The hindrances which they cause no man can help, but he who out of philosophy has learned the original causes of things. Likewise, whoever shall read Ctesibius or Archimedes' books (and others who have written such rules) cannot think as they do, unless he shall have received from philosophers instruction in these things. And he must know music too, that he may have understanding both of regular and mathematical music: that he may tune well his ballistas, catapults, and scorpions, etc. Moreover, the bronze vessels which in theaters are placed by mathematical order in niches beneath the steps, and the diversities of the sounds (which the Greeks call ηχεῖα) are ordered according to musical symphonies and harmonies, being distributed through the compass by Diatessaron, Diapente, and Diapason: so that the fitting voice of the players' sound, coming to these preparations made in order and there being increased, might with that increase come more clear and pleasant to the ears of the listeners, etc. And by astronomy are known the east, west, south, and north; the fashion of the sky, the equinox, the solstice, and the course of the stars. Which things, unless one knows, he cannot perceive anything at all of the reason of horologies. Seeing therefore this ample science is garnished, beautified, and stored with so many and sundry skills and knowledges, I think that none can justly account themselves architects all at once. But only those who, from their childhood years, ascending by these degrees of knowledge, being fostered up with the attainment of many languages and arts, have won their way to the high tabernacle of architecture, etc. And to whom nature has given such quick discernment, sharpness of wit, and memory that they may be thoroughly skilled in geometry, astronomy, music, and the rest of the mathematical arts: such surpass and pass the calling and state of architects:

(A mathematician.)

and have become mathematicians, etc. And they are found seldom. As in times past was Aristarchus Samius; Philolaus and Archytas, Tarentines; Apollonius Pergaeus; Eratosthenes Cyreneus; Archimedes and Scopas, Syracusians. Who also left to their posterity many engines and gnomonical works, invented and declared by numbers and natural means.

Thus much, and the same words (in sense) in one single chapter of this incomparable architect Vitruvius shall you find. And if you should but take his book in hand and look through it ever so slightly, you would say at once:

(Vitruvius.)

This is geometry, arithmetic, astronomy, music, anthropography, Hydragogie, horometry, etc. And (to conclude) the storehouse of all workmanship. Now let us listen to our other judge, our Florentine Leo Baptista, and narrowly consider how he determines of architecture. But before I proceed any further (says he) I think that I ought to express what man I would have allowed an architect. For I will not bring in place a carpenter, as though you might compare him to the chief masters of other arts. For the hand of the carpenter is the architect's instrument.

(Who is an architect.)

But I will appoint the architect to be "that man who has the skill (by a certain and marvelous means and way) both in mind and imagination to determine, and also in work to finish, whatever works, by motion of weight and the coupling and framing together of bodies, may most aptly be made useful for the worthiest uses of man." And that he may be able to perform these things he needs attainment and knowledge of the best and most worthy things, etc. The whole practice of architecture in building consists in lineaments and in framing. And the whole power and skill of lineaments tends to this: that the right and absolute way may be had of adapting and joining lines and angles, by which the face of the building or frame may be comprehended and concluded. And it is the property of lineaments to prescribe to buildings and every part of them a fitting place and certain number: a worthy manner and a seemly order: that so the whole form and figure of the building may rest in the very lineaments, etc. And we may prescribe in mind and imagination the entire forms,

(The immateriality of perfect architecture.)

all material stuff being excluded. Which point we shall attain by noting and forepointing the angles and lines by a sure and certain direction and connection. Seeing then that these things are thus:

(What lineament is.)

Lineament shall be the certain and constant prescribing, conceived in mind: made in lines and angles: and finished with a learned mind and wit. "We thank you, Master Baptist, that you have so aptly brought your art and the phrase of it to a certain mathematical perfection:

by certain order, number, form, figure, and mental symmetry:" all natural and sensible stuff set aside. Now, then, it is evident, gentle reader, how aptly and worthily I have preferred Architecture to be bred and fostered in the dominion of the peerless princess Mathematics, and to be a natural subject of hers. And the name of Architecture comes from the principality which this science has above all other arts. And Plato affirms the architect to be master over all who make any work. So he is neither smith nor builder, nor separately any craftsman, but the head, provost, director, and judge of all artificial works and all craftsmen. For the true architect is able to teach, demonstrate, distribute, describe, and judge all works wrought. And he alone searches out the causes and reasons of all artificial things. Thus excellent is architecture, though few in our days attain to it; yet the art must not be thought of as anything less than it truly deserves. Nor may we make new and imperfect definitions of ancient arts in our days, for scarcity of craftsmen: no more than we may cut short the definitions of wisdom, or honesty, or friendship, or justice. Neither will I consent to diminish any whit of the perfection and dignity (by just cause) allowed to absolute architecture. Under the direction of this art are three principal, necessary mechanical arts. Namely housing, fortification, and shipbuilding. By housing I understand buildings both for divine service and human common use, public and private. Of fortification and shipbuilding strange matter might be told you; but perhaps some will be tired with this long list already rehearsed, and others will finely pick apart my coarse, homely discourse written in haste, for fear you should lack this true and friendly warning, and this foretaste of mathematical power. Life is short and uncertain; times are perilous, etc. And with the printer still waiting while my pen lingers: all these things, with further matter of ingratitude, give me occasion to move on to the other arts remaining, with all speed possible.

(An objection.)

Many people may think that architecture is not worthy, or not fit, to be counted among the mathematical arts. To them I think it good to give some account of my doing so. Not worthy, they will say, because it is only for the building of a house, palace, church, fort, or such coarse works. And you also defined the mathematical arts to be such as dealt with no material or corruptible thing, and also proceeded demonstratively in their faculty, by number or magnitude. First,

The answer.

you see that I count architecture here among those mathematical arts which are derived from the principals; and you know that such may deal with natural things and sensible matter. Of which, "some come nearer to the simple and absolute mathematical speculation than others do."

☞

And though the architect plans, informs, and directs the craftsman in handiwork, and in the actual building of a house, castle, or palace, and is chief judge of the same, yet with himself (as chief master and architect) remains the demonstrative reason and cause of the craftsman's work: in line, plane, and solid; by geometric, arithmetic, optic, musical, astronomical, cosmographic means (and to be brief) by all the earlier derived mathematical arts, and other natural arts, able to be confirmed and established.

If this is so, then you may think that architecture has good and proper standing in this honorable company of derived mathematical arts. I will here ask the judgment of two most perfect architects: one is Vitruvius, the Roman, who wrote ten books of it to the Emperor Augustus (in whose days our heavenly Archemaster was born); and the other is Leo Baptista Albertus, a Florentine, who also published ten books of it.

Architecture, says Vitruvius, is a science adorned with many doctrines and diverse teachings: by whose judgment all works, finished by other craftsmen, are judged.

It follows: Architecture grows out of framing and reasoning, etc. Reasoning is that which can demonstrate and plainly declare things framed with skill and a sense of proportion.

Again: In all things, and therefore chiefly in architecture, there are these two: the thing signified, and the thing that signifies. The thing proposed, of which we speak, is the thing signified. But demonstration, set out with the reasons of diverse doctrines, signifies the same thing.

After that: An architect, he says, should understand languages, be skilled in painting, well instructed in geometry, not ignorant of perspective, equipped with arithmetic, know many histories, have diligently listened to philosophers, have skill in music, not be ignorant of medicine, know the answers of lawyers, and have good knowledge of astronomy and the courses of the heavens.

He gives the reasons, in order, why all these arts, doctrines, and instructions are required in an excellent architect. And, for brevity, leaving out the Latin text, he has this:

Secondly, an architect needs the knowledge of painting, so that he can more easily shape out, in painted patterns, the form of whatever work he likes. And geometry gives architecture many helps: first it teaches the use of the rule and the compass, by which (chiefly and easily) descriptions of buildings are drawn up in ground plans, and the setting out of squares, levels, and lines.

Likewise, through perspective, the lights of the sky are well led into buildings, from certain quarters of the world. By arithmetic the costs of buildings are added up, the measures are set out, and the difficult problems of symmetry are worked through by geometric means and methods. etc.

Besides this, philosophy declares the nature of things (which in Greek is called φυσιολογία). It is necessary for an architect to have learned this with diligence, because it has many and various natural questions, especially in aqueducts. For in their courses, the turnings about, over level ground and up the rises, natural spirits or airs are generated in various ways. The hindrances they cause no man can remedy, unless he has learned from philosophy the original causes of things.

Likewise, whoever reads the books of Ctesibius or Archimedes (and of others who have written such rules) cannot think as they do, unless he has received instruction from philosophers in these things.

And he must know music, so that he can understand both regular and mathematical music, and tune his ballistas, catapults, and scorpions well. etc.

Moreover, the bronze vessels which in theaters are placed by mathematical order in niches under the steps, and the differences of the sounds (which the Greeks call ηχεῖα) are ordered according to musical symphonies and harmonies, being distributed through the circuits by Diatessaron, Diapente, and Diapason. So that the fitting voice of the players' sound, when it came to these preparations made in order, being increased there, with that increase it might come clearer and more pleasant to the ears of the onlookers. etc.

And by astronomy are known the east, west, south, and north; the shape of the sky, the equinox, the solstice, and the course of the stars. Unless one knows these things, one cannot perceive anything at all of the reason of horologies. Since, then, this ample science is adorned, beautified, and stored with so many and various skills and knowledges, I think no one can rightly call themselves an architect all at once. Only those who, from their childhood years, rising by these degrees of knowledge, being fostered in the attainment of many languages and arts, have reached the high tabernacle of architecture. etc.

And to those to whom nature has given such quick perception, sharpness of wit, and memory, that they can be thoroughly skilled in geometry, astronomy, music, and the rest of the mathematical arts: such surpass and pass the calling and state of architects:

A mathematician.

and have become mathematicians. etc. And they are rarely found. As in times past there were Aristarchus Samius; Philolaus and Archytas, Tarentines; Apollonius Pergaeus; Eratosthenes Cyreneus; Archimedes and Scopas, Syracusians. These also left to their posterity many engines and gnomonic works, invented and explained by numbers and natural means.

All this, and the same words (in sense), in one single chapter of this incomparable architect Vitruvius, you will find. And if you were but to take his book in hand and look through it slightly, you would say at once:

Vitruvius.

This is geometry, arithmetic, astronomy, music, anthropography, hydragogy, horometry, etc., and to conclude, the storehouse of all workmanship.

Now let us listen to our other judge, our Florentine, Leo Baptista, and look closely at how he determines of architecture. But before I go any further, he says, I think I ought to set out what man I would have allowed to be an architect. For I will not bring forward a carpenter, as though you could compare him to the chief masters of other arts. For the hand of the carpenter is the architect's instrument.

Who is an architect.

But I will define the architect as "that man who has the skill (by a certain and marvelous means and way) both in mind and imagination to determine, and also in work to finish, whatever works, by motion of weight, and coupling and framing together of bodies, may most aptly be useful for the worthiest uses of man." And to be able to perform these things, he needs the attainment and knowledge of the best and most worthy things. etc.

The whole craft of architecture in building consists in lineaments and in framing. And the whole power and skill of lineaments tends to this: that the right and absolute way may be had of fitting and joining lines and angles, by which the face of the building or frame may be comprehended and concluded. And it is the property of lineaments to prescribe to buildings, and every part of them, a fitting place and a certain number: a worthy manner and a seemly order: so that the whole form and figure of the building may rest in the very lineaments. etc. And we may prescribe in mind and imagination the whole forms,

The immateriality of perfect architecture.

all material stuff being kept out. This point we shall reach by marking and setting out beforehand the angles and lines, by a sure and certain direction and connection. Since, then, these things are thus:

What a lineament is.

A lineament shall be the certain and constant prescribing, conceived in mind: made in lines and angles: and finished with a learned mind and wit.

We thank you, Master Baptist, that you have so aptly brought your art, and the phrase of it, to some mathematical perfection: "by a certain order, number, form, figure, and mental symmetry;" all natural and sensible stuff set apart.

Now, then, it is evident, gentle reader, how aptly and worthily I have preferred architecture to be bred and fostered in the dominion of the peerless princess Mathematics, and to be a natural subject of hers. And the name of architecture comes from the principality which this science has above all other arts. And Plato affirms the architect to be master over all who make any work. So he is neither smith nor builder, nor separately any craftsman, but the head, the provost, the director, and judge of all artificial works and all craftsmen. For the true architect is able to teach, demonstrate, distribute, describe, and judge all works wrought. And he alone searches out the causes and reasons of all artificial things. Thus excellent is architecture: though few in our days attain to it, yet the art may not be thought of otherwise than it is in very deed worthy. Nor may we make new and imperfect definitions of ancient arts in our days, for scarcity of craftsmen: no more than we may trim down the definitions of wisdom, or honor, or of friendship or of justice. Nor will I consent to diminish in the least the perfection and dignity (by just cause) allowed to absolute architecture.

Under the direction of this art are three principal, necessary mechanical arts. Namely, housing, fortification, and shipbuilding. By housing I understand both divine service and man's common use: public and private. Of fortification and shipbuilding strange matter might be told you: but perhaps some will be tired with this long list already recited, and others will pick apart my rough and homely talk with you, done in a hurry, for fear you should miss this true and friendly warning, and foretaste, of mathematical power. Life is short and uncertain: times are dangerous: etc. And still the printer waiting, while my pen holds back: all these things, with further matter of ingratitude, give me occasion to pass on to the other arts remaining, with all speed possible.