The second Chapter

ALthough the subtill and ingenious Arte of Perspectiue is very difficult and troublesome to set downe in writing, and specially the body, or modell of things, which are drawen out of the ground: for it is an Arte which cannot be so well expressed by figures or writings, as by an vndershewing, which is done seuerally: Notwithstanding, seeing that in my first Booke I haue spoken of Geometry, without the which Perspectiue Arte is nothing: I will labour in the briefest manner that I can in this my second Booke, to shewe the workeman so much thereof, that hee shall bee able to aide and helpe himselfe therewith.

In this worke I will not trouble my selfe to dispute Philosophically what Perspectiue is, or from whence it hath the originall: for learned Euclides writeth darkely of the speculation thereof.

But to proceede to the matter, touching that the workeman shall haue cause to vse, you must vnderstand, that Perspectiue is that, which Vitruuius calleth Scenographie, that is, the vpright part and sides of any building or of any Superficies or bodies.

This Perspectiue then, consisteth principally in three lines: The first line is the Base below, from whence all things haue their beginning. The second line is that, which goeth or reacheth to the point, which some call sight, others, the horison: But the horison is the right name thereof, for the horison is in euery place wheresoeuer sight endeth. The third line, is the line of the distances, which ought alwayes to stand so high as the horison is farre or neere, according to the situation, as when time serueth, I will declare.

This Horison is to be vnderstood to stand at the corners of our sight, as if the workeman would shew a piece of worke against a flat wall, taking his beginning from the ground, where the feete of the beholders should stand. In such case it is requisite, that the Horison should bee as high as our eye, and the distance to see or behold that worke, shall be set or placed in the fittest place thereabouts, as if it were in a Hall, or a Chamber, then the distance shall be taken at the entry thereof: but if it bee within, or at the end of a Gallery or Court, then the distance shall be set at the entry of the same place, and if it bee in a Streete against a wall or an house, then you must set your distance on the other side, right ouer against it. But if in such a case the streete is very narrow, then it were good to imagine a broad distance, lest the shortening fall out to be ouer-tedious or vnpleasant vnto you: for the longer or the wyder the distance is, the worke will shew so much the better and pleasanter.

But if you will begin a piece of worke of fiue or sixe foote high from the ground whereon you stand, then it is requisite that the Horison should stand euen with your eyes (as I sayd before) but if a man should see no ground of the worke, whereon the vppermost part doeth stand (and a man would worke very high) it would not be correspondent with the eyes: In such a case a man must take vpon him to place the Horison somewhat higher, by the aduice of some skilfull workman, which maketh histories or other things vpon Houses, thirtie or fortie foote high aboue a mans sight, which is vnfittingly. But cunning workmen fall into no such errors; for where they haue made any thing aboue our sight, there you could see no ground of the same worke, for that the notable Perspectiue Art hath bridled them: and therefore (as I sayd before) Perspectiue Art is very necessary for a workeman: And no Perspectiue workeman can make any worke without Architecture, nor the Architecture without Perspectiue.

To proue this, it appeareth by the Architectures in our dayes, wherein good Architecture hath begun to appeare and shew it selfe: For, was not Bramant an excellent Architector, and was he not first a Painter, and had great skill in Perspectiue Art, before he applyed himselfe to the Art of Architecture? and Raphael Durbin, was not he a most cunning Paynter, and an excellent Perspectiue Artist, before he became an Architector? And Balthazar Perruzzie of Sienna, was also a Paynter, and so well seene in Perspectiue Art, that he seeking to place certaine Pillars and other Antike works perspectiuely, tooke such a pleasure in the proportions and measures thereof, that he also became an Architector: wherein he so much ex•elled, that his like was almost not to be found. Was not learned Ieronimus Genga also an excellent Paynter and most cunning in Perspectiue Arte, as the faire works, which he made for the pleasure of his Lord Francisco Maria, Duke of Vrbin, can testifie; vnder whom he became a most excellent Architector? Iulius Romanus, a scholler of Raphael Durbin; who, by Perspectiue Arte and Paynting, became an excellent Architector, witnesseth the same. Then to come to my purpose; I say, that a man must be diligent and vigilant in this Arte, wherein I will begin with small things, and then proceed to greater; vntill I haue shewed you the full Arte and manner thereof, as I desire.

TO the ende that men by small matters may attaine to greater, therefore I will begin to shew how to shorten a foure cornerd thing, from whence all the rest shall bee deriued. Then the Base of this foure square thing, shall be A. G. and the height of the Horison (as I sayd before) shall bee imagined according to the fight, and that shall be P. whereunto all the lines doe runne, as the lines of the sides A. P. and G. P. then at the one ende of the Quadrante you must set a Perpendicular line, which is G.H. which done, then drawe the Base A. G. K. long though, and then out of the Horison draw a Paralell or an Equidistant sine from the Base, as far as you will that the eye or sight shall stand from that which you will looke on; for how much the more you will haue the foure square thing to seeme shorter, so much further you must goe with yoin sight I. from H. to behold the foure square thing. And then, taking H. I. for the distance from the point I. to the corner A. draw a line, and where the line cutteth through the Perpendicular line H. G•th it is on B. there the termination of the shortening of the foure square thing shall bee, as you may sée in the figure following. But if you will make more foure squares one aboue the other, vpon the same Horison or poynt: then you must draw another line from the shortening poynt of the foure square or Quadrant, to the letter I. and where it cutteth through the Perpendicular line aforesaid, that is at C, there the second Quadrant shalbe rut off, and in like sort you must draw another line to the poynt of the distance: and where it toucheth the Lead, or Perpendicular line that is on D. you shall make the third Quadrante, the same may be done with E. and so you must goe, vntill you come iust vnder the Horison.

THe rule aforesaid is the perfectest, and you may prooue it by the line G. H. which is called the line of the Quadrante: but because it is cumbred with a greater number of lines, and so more tedious: therefore the rule ensuing shall be shorter, and easilyer to be done then the other: for when the Base A. G. is drawne, and the two side lines make a Triangle A. P. G. then you must draw the Paralels of the Base & of the Horison long inough; and as farre as you will stand from the worke to sée it, so farre you must set the Perpendiculars I. K. from the poynt G. then you must draw a line from the poynt I. to the poynt A. and where it cutteth through the line G. P. there shall be the termination of the first shortened Quadrant: and if you will place more Quadrants vpwards from that Quadrant, you must doe as I sayd before: and although there are other wayes to shorten a Quadrant, yet will I follow this order, as being the shortest and easiest to be set downe in writing.

A Man must also vse himselfe vnto diuers distances and grounds, and therefore you must make the ground following, which is of thrée Quadrantes high, in this manner. First, you must draw the line A. B. as long as the bredth of the worke shall be: which line or Base, must bee deuided into so many equall parts as are needfull, which being all drawne to the Horison or point, then you must place the distances as farre as you desire, according to the rule aforesayd; for here is no place to set it in, although it is a length and a halfe from the Base, as you see it marked with 1½. Which Base, because it is of foure parts, therefore the first Quadrant containeth sixtéene small Quadrantes, which are found by the line B. D. for where that line cutteth through the foure lines, which goe to the poynt; there you must drawe the Paralel ouer, that thereby the sixtéene Quadrantes may be formed: But if you will set other Quadrantes vpon it, then (as aforesayd) you must draw another line to the distance D. and where that cutteth through the other lines that reach to the poynt, that shall bee the termination of the second Quadrant, containing in it also foure times foure Quadrantes: The like must bee vnderstood of the third Quadrant, (and more besides if need bee.) But you must also vnderstand, that the lines marked D. runne all the distances, as it is taught before.

IF you will make a pauement with great Quadrantes to be cut or Compassed with fascion, fasen or lists, as you will terme them, then vpon A. B. you must deuide the fasen or Quadrantes, and draw them all to the Horison; then you must imagine the distances as you are taught before: and the line D B. being drawne from the poynt B. to the point of the distances; then by cutting through of the Horisentall lines, it will show the terminations of the Quadrants, Fasen, or Borders. To draw the Pacalels, then if you will make the like Quadrantes somewhat higher, then you must draw another line to the distances: and where it toucheth the Horisentall or Radiall lines, there also you must draw the Paralels through; so you must also doe with the third, and the poynt of the distances of these figures stand as farre from A. as the line or Base A. B. is long: If you will make diuers formes in these Quadrants, as Rootes, Crosses, sixe poynts, or ryght poynts, I will shew the manner of them particularly, because I will bee as briefe heere in as I may.

THis figure is a Quadrant, containing in it a Rote or an other Quadrant, which with the poynts thereof toucheth the sides of the vttermost Quadrant; whereby it is but halfe so great as the vttermost Quadrant, as I haue taught you in the first Booke of Geometrie, and the maner to make this, is thus. First, you must make a Quadrant (as you are taught before) with his distances; and in this Quadrant you must draw two Diagonall lines, and also the right crosse lines, whereby you may easily finde the Roote, as you sée it in the figure directly against this. In it is sort you may make the Rootes in the other Quadrantes before set downe, that is, to draw Diagonall and crosse lines in them without séeking other distances.

IN this figure there is a crosse shewed (to make it) you must deuide the lowest line or Base of the Quadrant in fiue parts; of the which fiue parts, one parte is the bredth of the crosse: which bredth being dr•w•n to the points, the Di•g•nall lines will shew you the Paralel lines of the crosse, to vse where •éede is.

THE eyght poynted figure you may sée in Perspectiue works in diuers formes, which formes are all difficult inough: but that I may séke the easiest way so neere as I can in this my writing: Therefore I haue set downe the manner thereof hereunto annexed, which is very easily; and that is thus. The Quadrant being mede in shortening, you must deuide the Base into ten equall parts, and on either side you shall leaue three parts, and in the middle foure parts, then the two lines being drawen to the Horison, you shall find the terminations of the Paralel lines, by the Diagonal lines, whereby you may close vp the eyght corners, as you may sée it in the Figure.

THE shortest way to place this sixe cornerd Quadrant, in Perspectiue workes, is thus; When the Quadrant according to the rule aforesaid, is placed in shortening, then you must make foure equall parts of the Bases, whereof two shall be in the middle, and on each side you must leaue one, and then draw the lines vpwards to the Horison or poynts: then you must draw the Diagonall lines, and in the middle where they méet together, you must draw a Paralel line cleaue through, by the which you shall finde all the points to make this sixe cornerd Figure.

NOw I haue shewed how you shall make simple or plaine Perspectiue workes of foure corners, of sixe corners, and eyght square corners: Now I will shew, how you shall make them double, that is, that euery simple figure shal haue his band. When you haue made a plaine Superficies of sixe poynts, according to the rule aforesayd; then as much as you will haue the band or fase to be in bredth, that you must draw vpon the Base, and draw that also vp to the Horison: and where the Diagonall lines cut through it, there you must draw Paralel lines both vnder and aboue: and then draw two Diagonal lines more, out of the foure innermost points or corners of the sixe cornerd Superficies; and so you shall finde your terminations to shut or close vp your smalest sixe poynts or cornerd Superficies. Which second Diagonal, Paralel, and Horisontall lines are all drawen with prickes, for a difference from the first lines; that you may know them one from another.

THE like must bee done with the eyght cornerd Superficies or Perspectiue work, for when the same is made within a fouresquare, making the Compas of what bredth you will, according to the rule aforesayd: then out of every poynt or corner of the eyght sqare, a small line being drawen to the Center, you shall fin•e the termination to shut vp the innermost eyght squares and then, when from poynt to poynt the lines are drawen, then one square or Compasse is full made. This eyght squa•e forme may bee changed into a round, fou•ng the middle on eyther side, or else without. ouer the poynts or corners; a good workeman may easily draw a Circuler shortening round line with his hand.

ALthough I haue said before that a man may make a round Circle about an eyght square, yet for more securitie you may by this way attaine to a more persection therein; for that the more points or sides the Circuler forme hath, the round Compasse or Circle will be the fuller. But to make this Figure, it is necessary to make halfe a Circle vnder the Bases, and to deuide the Circumference into as many parts as you will, so that they be euen; in this forme the halfe Circle is deuided into eyght parts, so that the whole Circle must bee sixteene parts: which being done, you must set Perpendicular lines in all the parts of the Circumference, as farre as to the Bases of the shortened Quadrant, these parts being eleuated to the Horison, and two Diagonall lines drawen in the Quadrante, they by cutting through the Horisentall or Radiall lines, will shew you the Paralel lines. Then if you will draw a little Diagonall line, beginning at the middle poynt of the Base, from the •ne side vnto the other, and so from the one poynt vnto the other vpwards going euer the points: then the formes will be closed, as you see them heere; whereby it will be easie for you to draw around forme with your hand, for it is vnpossible to bee done with the Compasse to make it short•n well. This figure you must be expert in, and you must also vnderstand it well, and so you must those that I haue before set downe, before you proceed further: for they will serue you for many pieces of worke hereafter ensuing, as you shall both see and find to be true.

WHen you vnderstand the Figure aforesayd perfectly, then you must procéed further, and shut the cound Circle also with an edge or border, according to the bredth that you will haue; you must also make the vttermost halfe Circle, and the aforesayd parts of the great Circle drawen towards the Center, will come into the smale Circle: the which parts of the small Circle being also set downe in Perpendicular lines with prickes not to darken the other lines, and those likewise that are drawen to the Horison. Then by cutting through of the Diagonall lines, you shall finde the Paralel lines. To make the innermost shortening a round or Circle according to the first example set downe, as you may see; the first round with perfect lines, and the second with prickes, as you sée in this Figure.

But, friendly Reader, you must not be weary to bee long in learning this Figure, or in making it often times, vntill you can doe it perfectly and vnderstand it well: for I am sure and certaine, that it will hee very hard vnto many men, yet without this, you cannot doe much; and he that can doe it well, shall easily vnderstand and make all the things hereafter ensuing.

IT salleth out many times shat a workeman will shew a House b•th without and within, which to doe, he must place the ground in Perspectiue forme, that he may the surer and better draw that vp which hee will haue séene, and to leane the rest on the ground: if then you will place a soundation in Perspectiue manner, to make it well, you must first set it on a flat forme, that out of that you may draw it into a Perspectiue forme.

To doe this, I haue set downe a kinde of open Building, that a man may the easelier conceiue it for a beginuing, for when a man can doe this well, he may after that place many other and harder things in Perspectiue forme. I néed not to take any great paines to write or show how this shortening should bee done, because it is so easily and so openly placed in a figure that a man may presently centeaue it: for that leading all the lines that goe from the corners and outsides of the flat ground to the Base, which you will make in the shortening; and the same being drawne vp to the Horison, together with the imagination of the distances: then you may shut or close vp the shortening foure square. Then you must draw the Diagonall lines therein, through drawing the Paralel lines, presently you shall find the way how to forme the Columnes and pilasters, so that it is vnpossible to faile therein; and especially for those that doe well conceaue and vnderstand that, which I haue set downe before.

THis Figure following is somewhat harder then that before, but when you goe from the smalest to the greatest, you conceaue things the easier, and specially he that will learne this Arte; he must not leaue nor refuse to exercise any of the Figures before set downe, but must vse all the diligence he can to be persect in them all, and hee must also take a pleasure to doe them all, otherwise he that will omit now one, and then another, because he can hardly vnderstand or conceaue them (although I labour and striue at all times in setting downe these rules to shew all difficulties) shall little profit himselfe in this Arte. The manner how to place this ground in Perspectiue forme, is easily conceaued, without any other demonstration: for you must follow the manner or opperation of the figure before set downe, with this aduertisement; that the two Diagonal lines euermore direct the worke, together with the Horisentall lines: and although a man may shew many formes of grounds that are to bee placed in shortening, yet these two shall suffice for this time, because I haue other things to entreat off: for a skilfull workeman, by the helpe of these, may forme others for his purpose, and such as he shall haue occasion to vse. And if he will erect any péece of worke for a show, he must necessarily first measure the Ortographie with the same measure that he measureth the ground withal, and then place it in a shortening manner, as when time serueth, shall be she wed.