T R A I T E
DE
P-ERSPECTIVE
FOR USE
ARTISTS.
Where one demonstrates - geometrically all the practices of this Science, & where one teaches, according to the Method of M. le Clerc, to put all strong objects in perspective, their reverberation in the water, & their shadows; as much in the Sun as in the torch.
By M. EDME - SEBASTJ.EN JEAURAT
Engineer -Geographer of the Roy.
 
IN PARIS, QUAY DES AUGUSTINS, 
At CHARLES-ANTOINE JOMBERT, Libraire du Roi pour l'Artillerie & le G?nie, at the corner of rue Gille -c?ur, at the Image Notre-Dame.
M. D C C. L.
WITH THE APPROVAL AND PRIVILEGE OF THE KING

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PREFACE
THE Perspective, which I undertake to give a Treatise to the Public, is not one of those Sciences which by some unsure rules lead to uncertain operations. This Science is one of the most beautiful productions of Geometry. It consists in a sequence of mathematical principles, & of necessary consequences; its operations are all geometric. It leads us, by the evidence, to imitate & place in their right proportion, all the objects that the Author of nature exposes to our eyes in a beautiful horison. It is the Reduced Natural Perspective in Art, to compose the faithful picture of the most brilliant beauties. Its execution seems to have something even more pungent than a glance at nature, because an ingenious imitation awakens the mind, which enjoys discovering all its relationships. But it is less a question here of considering the amenities than the usefulness of this Science.
Perspective is a part of Optics, which gives rules to present objects in the natural aspect where they should be, because of their distance, & the position of the eye. This Science is the basis of the proportions that a Painter must give to his figures, according to the place where they are. It is used to direct him in the distribution of the various objects; for in order to do this distribution well, it is necessary to know the effect that each object must have on the eye, according to the place it occupies. If he makes this distribution at random, he will make frequent mistakes, which the knowledge of the rules at the right prevents. 
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P R E FA C E.
But, it may be said, aren't there tables that are fairly estimated, even though they contain errors of Perspective? I agree, but it must also be agreed that they are less valuable in this respect than if they were free of them. An Artist, jealous of his reputation, must always strive for the greatest perfection, & what is even defective in the Ancients, must excite him to surpass them in this respect. Their faults are in truth compensated by a greater number of beauties, but they are always faults, capable of delaying the progress of the Arts, since they were imitated. 
It is true that it is not Perspective that gives a Painter the elegance, & the character of the design, & that there are no other rules on this than that of grasping the natural. But this Science will give him the plan of his figures, & this Aerial Perspective which appears so surprising on a flat surface, & which produces such beautiful effects by means of a seductive degradation. For the best traced Perspective, according to all the rules, will not prevent, fi the degradations of tone are prominent, that the parts which must flee do not advance, & that those which must advance do not move away : a Painter cannot be too attentive to the degradation of his colours. Thus there part of the colour, which one could believe to be more independent of this Science, must also respect the rules: it is a question of reconciling all the objects that the Perspective contains. Enough, it seems to me, to convince any reasonable mind of the need to learn about Perspective. 
It only remains for me to explain to my Readers, the reasons which determined me to present a crazy Treatise on Perspective on a new day, & the order I thought I should follow in its execution. It is not that we do not have, in this matter, several Treaties, some of them, 
which one cannot deny his esteem, are a fairly clear indication of the practice. But, if I may say so, fans wanting to attack the merit of those who have so far dealt with this matter, it is far from being the case that they have developed all its principles. Some research that I have made in their Books, to learn me thoroughly, I have not been able to meet a single Treaty, where these principles, which have their source in Geometry, are carried to the evidence of which they are susceptible. Now, as one cannot make a solid progress in any Science whatsoever, fans of having deepened the true principles, my goal is to make them known, & to ennoble even the practice of Perspective, by raising the mind to Theory. Thus, in this Treaty, the rules of Perspective are reduced to an easy practice, preceded by geometric demonstrations. As most men, satisfied with the pleasure of the pleasant objects of Perspective, or limiting their emulation to operating the compass by hand, do not want, or cannot bother to go into the Geometrical Principles, & as my aim is to bring Perspective within everyone's reach, I have left Geometry out of the Practical Lessons, whose order and linkage develop the subject. 
Those who do not have, what can be called, the Geometric mind-set, may neglect the demonstrations, & consult only the practice. For those who wish to go up to Theory, and deepen the pure ideas on which the Lessons of Practice are based, we flatter ourselves that they will find satisfaction in them. I thought, in favour of the latter, that I could not dispense with giving the Geometrical section of the rays, as the only one capable of giving an exact account. 
of the principles of Perspective. It had also occurred to me to give a description of the eye; but apart from the fact that this description concerns more particularly those who deal with the Dioptric, & the Catoptric, as one can find it in an infinity of Authors, it seemed to me useless to infer it in a Treatise, where I limited myself to what is proper to Perspective. 
One will find there the method of putting the plans-in perspective, their elevations, their inclinations; square steps; solid, curved and inclined crosses; doors, arcades, mouldings and entablatures; with a separate method for the tori and the pediments: finally one will see there what concerns the degradation of the figures, the reflection of the shadows, both in the sun and in the torch. This is how I end this Treatise, in which I intend to supplement Theory with practice, for those who are not Surveyors, & for those who are, to enlighten practice with Theory. 
The system of vision, of the late Mr. Cleric, leads one to presume that he could have given a Treaty of this kind, if his other occupations had allowed him to do so. It is to be wished that he would have enriched the Public avid for his productions. One finds there the analysis of the lessons he has given for nearly twenty years, & that his son, Mr. Cleric, continues to do so with considerable increases. The honour that I have of being the grandson of one, and nephew of the other, imposes on me silence on the merit of these two famous Professors; I even feel all the danger of parish, after them, in a career where they have shone; but I dare to hope that I will be appreciated for the emulation which leads me to follow in their footsteps, and for the zeal which makes me present to the Public, the solid principles of a too neglected SCIENCE.
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Approval of the Royal Censor.
By order of Monsignor the Chancellor, I have read the Perspective for the use of Artists: I found this work useful. Done in Paris this 25 March 1749.

						MONTCARVILLE
ROYAL PRIVILEGE.
LOUIS, by the grace of Dien, King of France & Navarre: To our Friends & Fellow Councillors, the People holding our Courts of Parliament, Masters of the Ordinary of our Hotel, Grand Council, Provost of Paris, Bailiffs, Seneschals, their Civil Lieutenants & other our Justiciers that it will belong. HELLO. Our good Am? CGARLES-ANTOINE JOMBERT), Bookseller in Paris, having made Us expose that it wishes to make print & give to the Public of the Works, which have for title : Le Guide des jeunes Math?maticiens, translated from English, by the R. P. Pezenas, Jesuit. New Treatise on the Microscope, available to everyone, translated from English. Trait? des Fluxions & Trait? d'Alg?bre, by Colin Maclaurin. New Carpentry Tariff, with details & prices of all the Carpentry books. La M?canique du Feu, or Treatise on the Construction of New Chimneys, by M. Gauger. Principles of Physics related to Medicine, & Treatise on Metals & Minerals, by M. Chambon, King's Physician. New explanation of the Flow & Reflux of the Sea, following a new System of Cosmography & General Physics. Treatise of Perspective for the use of Artists, geometrically demonstrated, by M. Jeaurat. Trait? Analytique des Sections Coniques, Fluxions & Fluentes, by M. Muller. L'Ing?nieur de Campagne, or Trait? de la Fortification, by M. le Chevalier de Clairac. Perit Dictionnaire Universel , abbreviated & made available to people who have no study, by Thomas Dyche , translated from English. The Chronological Historian, or the History of England, from its origin to the present, translated from the English by M. Salmon; If We are pleased to grant him Our Letters of Privilege for this necessary purpose, THEREFORE, wishing to treat the Exhibitor favourably, We have allowed & permit him, by these Presents, to have the said Works printed in one or more Volumes, & as many times as he may wish, & to sell them, to have them sold & debited by all our Kingdom during the period of nine consecutive years, starting from the date of the said Presents: Let us forbid all kinds of persons of any quality and condition whatsoever, to introduce foreign printing in any place of our obedience, as well as all Booksellers, Printers & others, to print or have printed, sell, have sold, have sold, debit, nor counterfeit the said Works, nor to make any Extracts, under any pretext whatsoever, of increase, correction, change or otherwise, without the express written permission of the said Exhibitor, or of those who have the right to do so, on pain of confiscation of the counterfeit copies, a fine of one thousand pounds against each of the offenders, of which one third will be paid to Us, one third to the H?tel-Dieu de Paris, and the other third to the said Exhibitor, or to those who have the right to do so, and of all costs, damages and interest; on the condition that these Presents will be registered throughout on the Register of the Community of Booksellers & Printers of Paris, within three months of the date hereof: that the said Works shall be printed in our Kingdom & not elsewhere, on good paper &: fine type, in accordance with the sheet printed & attached as a model, under the counter-seal of the said Presents; that the Applicant shall comply in all respects with the Regulations of the Bookstore, & in particular with those of April 1725, & that before
To exhibit it for sale, the Manuscripts or Printed Works which will have been used as a copy for the printing of the said Works, will be returned in the same state in which the Approval was given, in the hands of Our very dear & feal Chevalier le Sieur Daguesseau, Chancellor of France, Commander of our Orders; that two copies of each will then be handed over in our Public Library, one in that of our Ch?teau du Louvre, and one in that of our Most Dear & Feal Knight Sieur Daguesseau, Chancellor of France, Commander of our Orders; the whole on pain of the nullity of these Presents, the contents of which you instruct and enjoin the Exhibitor or his Beneficiaries to enjoy fully and peacefully, without suffering any disturbance or impediment: Wish that the Copy of the said Presents which will be printed throughout -at the beginning or at the end of the said Works, be held to be duly served, & that to the Copies collated by one of our Friends & Fellow Counsellors & Secretaries, faith be added as to the Original: Let us command the first our Bailiff, or Sergeant, to do, for the execution of these, all Acts required & necessary, fans ask for further permission, &: notwithstanding the clamor of Haro, Norman Charter & Letters to the contrary: BECAUSE this is our pleasure. GIVES in Paris on the fourteenth day of April in the Year of Grace one thousand seven hundred and forty-nine, & of our Regne on the thirty-fourth. By the King in Council.

SEASON

Register on the Register XII. of the Chambre Royale & Syndicale des Libraires & Imprimeurs de Paris, No. 160. Fol. 16o. in accordance with the Reglemens confirmed by that of 28 February 1723. In Paris on May 16, 1749.
				Signed, G. CAVELIER, Trustee.
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T R A I -T E
DE
P-ERSPECTIVE
FOR USE
ARTISTS.
PART ONE.

Containing the Theory of Perspective.

INTRODUCTION.

A PERSPECTIVE is the art of representing objects as they appear to us; & objects are said to be seen in Perspective, when they are represented according to the impression they make on the eyes.
The eye is a round & spherical body, considered as a point from which objects are perceived. 
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TREATED
The vision is done by rays that draw objects to the eye, which are like so many small channels through which the object communicates itself to the eye.
We can suppose that there are as many rays as there are mathematical points in objects; the action of these rays is to bring to the eyes the points of these objects which together make up a Perspective which appears to merge in the eye, but which manages in proportion as one moves away. If we assume that these rays are cut by a glass pane, this glass pane will receive as many points as there are rays, which will form a more or less uncluttered perspective in the glass pane depending on how close the glass pane is to the spectator. 
There are two types of perspective: the Natural Perspective, & the Curious Perspective. 
In the Natural or Ordinary Perspective, which is the one we are going to deal with, we suppose the glass (or the painting) to be vertical and flat. In the Curious Perspective, we assume this glass or concave, or convex, or inclined at the choice of the Perspecteur. This is precisely & only what can distinguish these two strengths of Perspectives, which, one & the other, do nothing more than a cut of visual rays.
But as the cut of rays, in the curious Perspectve, is prone to disfigure objects, and as a square could have a circular appearance, depending on whether the glass is concave or convex, it is necessary for the viewer to get to the real point from which this Perspective must be perceived: one feels this necessity in the cylindrical figures.
As this strong Perspective only takes place in domes or ceilings, it is not so widely used, nor is it as common as the Natural Perspective, which is the one that Painters, whose aim is to imitate nature, usually propose to follow in their works. It is also for this reason that it is called Ordinary Perspective.
The Perspective considered in its rules gives the means to represent objects according to their different impressions, because we fear that the objects appear more or less large, according to whether they are more or less distant, & that their various positions make them see in as many forms, & crazy different degrees, of light, which are nothing else than various impressions made on the view, which we imitate in painting. 
Objects are represented in two ways; either geometrically, or in perspective.
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OF PERSPECTIVE. I. PART.
In the way of representing them geometrically, one considers in these objects two sections: one vertical, the other horizontal. The vertical representation, called elevation, gives their perpendicular height; the horizontal one, called plane, shows their extent.
This way of representing objects is: in some ways the most perfect, because it gives a certain account of the proportion of each of their parts, & that, moreover, we can only get to know the Perspective by knowing the Geometrical. Architects therefore prefer to use it, because it is more suitable for Workers, for whom exact coats are needed rather than beautiful execution. 
In the way of representing objects in perspective, it is assumed that the rays drawn from the objects to the eye are cut by a plane. If this plane is inclined, or concave, or convex, the perspective is called curious, which, as we have just observed, appears deformed if we do not take care to get to the real point of view. If, on the contrary, this plane or this glass is vertical & flat, it is called Ordinary Perspective. This Perspective, in paintings, expresses & makes, so to speak; the same impression as the objects themselves.
Thus in the way of representing objects geometrically, we have the real proportion of the objects: & in the way of representing them perspectively, we have their appearance. 
There is still what is called the Cavalier or Military Perspective, which the Engineers use to draw the Fortifications; but it must be considered more as the Geometrical of the objects than as their Perspective. For the purpose of this representation of the objects is to give their true dimension & not their natural aspect as the word Perspective itself indicates.
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TREATS DEFINITIONS
Key terms used in the Outlook.

The earth line is the basis of the painting, which is always assumed to be level. 
The horison is a plane that is assumed to pass through the eyes, parallel, to the earth line, & which, therefore, marks the elevation of the eye. 
The point of view is a point taken from the horison to mark the place from which perspective is to be perceived, or better said, it is the point of section of the perpendicular lowered from the eye to the glass. It is also called the point of figurative vision, since the real one cannot be in the painting.
The point of distance is a point set in the horison, as far from the point of vision as one has to move away from the painting to see it in the true point. -· 
The elusive ones make all the lines, which are supposed to enter the painting, & by whose conduct objects seem to move away from us. 
The earthy Perspective is the enclosed space in the painting between the earth line & the horison, & as the horison is the term for the largest expanse of view, so it contains all the Aryan points of the horizontal lines.
The vanishing point is the meeting of the lines in the table; for if one considers two or more parallel lines between them one will see that they tend to approach each other in proportion as they move apart, & so that they meet at a point of the horison when they are entirely escaped from our eyes. 
If the vanishing point is the same as that of the eye which responds perpendicularly to the surface of the painting, it will be called the figurative point of view.
If the vanishing point is equidistant from the point of figurative vision, as assumed to be the real eye away from the painting, it will be called a distance point, or distance point.
If the vanishing point is neither one nor the other, i.e., whether it is below or beyond these two points, it is called an accidental point.
Hence it follows that the figurative point of view is the vanishing point of the lines that make a right angle with the base of the painting. 
That the distance point is the vanishing point of the lines that are at a 45 degree angle with the base of the painting.
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PERSPECTIVE.I.PART.
And that the accidental point is the vanishing point of the lines that make unequal angles with the base of the painting.

CHAPTER ONE
Demonstrations made in a glass pane considered as a diaphanous painting through which one can see the objects behind it.
IN the perspective we consider two distances; s?avoir, the distance of the spectator from the interposed body, & that of the body interposed to the objects. These objects having their appearances in the glass, determine two other distances, which will make the vertical distance of their appearance on the horizon, & their perpendicular height. These two distances are proportional to the first two, as will be demonstrated in the following proposals. 
NOTE
These demonstrations are made for people who are curious to learn the geometric principles of perspective; those who do not want to bother studying them can go straight to their recapitulation on page 30, or even to the second Part of this Book, which teaches the practice of Perspective.

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