The vanishing point of the shadows on an inclined plane is on a vertical dropped from the luminary to a point (F) on a level with the vanishing point (P) of that inclined plane. ThusPis the vanishing point of the inclined planeK. Draw horizontalPFto meetfL(the line drawn from the luminary to the horizon). ThenFwill be the vanishing point of the shadows on the inclined plane. To find the shadow ofMdraw lines fromFthrough thebaseegtocd. From luminaryLdraw lines throughab, also tocd, where they will meet those drawn fromF. DrawCD, which determines the length of the shadowegcd.
When the sun is in front of the picture we have exactly the opposite effect to that we have just been studying. The shadows, instead of coming towards us, are retreating from us, and the objects throwing them are in full light, consequently we have to reverse our treatment. Let us suppose the sun to be placedabove the horizon atL·, on the right of the picture and behind the spectator (Fig. 276). If we transport the lengthL·f·to the opposite side and draw the vertical downwards from the horizon, as atFL, we can then suppose pointLto be exactly opposite the sun, and if we make that the vanishing point for the sun's rays we shall find that we obtain precisely the same result. As in Fig. 277, if we wish to find the length ofC, which we may suppose to be the shadow ofP, we can either draw a line fromAthroughOtoB, or fromBthroughOtoA, for the result is the same. And as we cannot make use of a point that is behind us and out of the picture, we have to resort to this very ingenious device.
figure
Fig. 276.
In Fig. 276 we draw linesL1,L2,L3 from the luminary to the top of the object to meet those drawn from the footF, namelyF1,F2,F3, in the same way as in the figures we have already drawn.
Fig. 278 gives further illustration of this problem.
figure
Fig. 278.
The two portions of this inclined plane which cast the shadow are first the sidefbd, and second the farther endabcd. The points we have to find are the shadows ofaandb. From luminaryLdrawLa,Lb, and fromF, the foot, drawFc,Fd. The intersection of these lines will be ata·b·. If we joinfb·anddb·we have the shadow of the sidefbd, and if we joinca·anda·b·we have the shadow ofabcd, which together form that of the figure.
figure
Fig. 279.
To draw the shadow of the figureMon the inclined planeK(or a chimney on a roof). First find the vanishing pointPof the inclined plane and draw horizontalPFto meet vertical raised fromL, the luminary. ThenFwill be the vanishing point of the shadow. FromLdrawL1,L2,L3 to top of figureM, and from the base ofMdraw 1F, 2F, 3FtoF, the vanishing point of the shadow. The intersections of these lines at 1, 2, 3 onKwill determine the length and form of the shadow.
figure
Fig. 280.
To find the shadow of the objectKon the wallW, drop verticalsOOtill they meet the base lineB·B·of the wall. Then from the point of sightSdraw lines throughOO, also drop verticalsDd·,Cc·, to meet these lines ind·c·; drawc·Fandd·Fto foot of luminary. From the pointsxxwhere these lines cut the baseBraise perpendicularsxa·,xb·. FromD,A, andBdraw lines to the luminaryL. These lines or rays intersecting the verticals raised fromxxata·b·will give the respective points of the shadow.
figure
Fig. 281.
The shadow of the eave of a roof can be obtained in the same way. Take any point thereon, mark its trace on the ground, and then proceed as above.
LetLbe the luminary. Raise verticalLF.Fwill be the vanishing point of the shadows on the ground. DrawLf·parallel toFS. DropSf·from point of sight;f·(so found) is the vanishing point of the shadows on the wall. For shadow of roof drawLEandf·B, giving use, the shadow ofE. JoinBe, &c., and so draw shadow of eave of roof.
For shadow ofKdraw lines from luminaryLto meet those fromf·the foot, &c.
The shadow ofDover the door is found in a similar way to that of the roof.
figure
Fig. 282.
Figure 283 shows how the shadow of the old man in the preceding drawing is found.
figure
Fig. 283.
Having drawn the arch, divide it into a certain number of parts, say five. From these divisions drop perpendiculars to base line. From divisions onABdraw lines toFthe foot, and from those on the semicircle draw lines toLthe luminary. Their intersections will give the points through which to draw the shadow of the arch.
figure
Fig. 284.
In this figure a similar method to that just explained is adopted. Drop perpendiculars from the divisions of the arch 1 2 3 to the base. From the foot of each draw 1S, 2S, 3Sto foot of luminaryS, and from the top of each,A1 2 3B, draw lines toLas before. Where the former intersect the curve on the floor of the niche raise verticals to meet the latter atP1 2B, &c. These points will indicate about the position of the shadow; but the niche being semicircular and domed at the top the shadow gradually loses itself in a gradated and somewhat serpentine half-tone.
figure
Fig. 285.
This is so similar to the last figure in many respects that I need not repeat a description of the manner in which it is done. And surely an artist after making a few sketches from the actual thing will hardly require all this machinery to draw a simple shadow.
figure
Fig. 286.
Shadows thrown by artificial light, such as a candle or lamp, are found by drawing lines from the seat of the luminary through the feet of the objects to meet lines representing rays of light drawn from the luminary itself over the tops or the corners of the objects; very much as in the cases of sun-shadows, but withthis difference, that whereas the foot of the luminary in this latter case is supposed to be on the horizon an infinite distance away, the foot in the case of a lamp or candle may be on the floor or on a table close to us. First draw the table and chair, &c. (Fig. 287), and letLbe the luminary. For objects on the table such asKthe foot will be atfon the table. For the shadows on the floor, of the chair and table itself, we must find the foot of the luminary on the floor. DrawSo, find trace of the edge of the table, drop verticaloP, drawPSto point of sight, drop vertical from foot of candlestick to meetPSinF. ThenFis the foot of the luminary on the floor. From this point draw lines through the feet or traces of objects such as the corners of the table, &c., to meet other lines drawn from the point of light, and so obtain the shadow.
figure
Fig. 287.
Although the figures we have been drawing show the principles on which sun-shadows are shaped, still there are so many more laws to be considered in the great art of light and shade that it is better to observe them in Nature herself or under the teaching of the real sun. In the study of a kitchen and scullery in an old house in Toledo (Fig. 288) we have an example of the many things to be considered besides the mere shapes of shadows of regular forms. It will be seen that the light is dispersed in all directions, and although there is a good deal of half-shade there are scarcely any cast shadows except on the floor; but the light on the white walls in the outside gallery is so reflected into the cast shadows that they are extremely faint. The luminosity of this part of the sketch is greatly enhanced by the contrast of the dark legs of the bench and the shadows in the roof. The warm glow of all this portion is contrasted by the grey door and its frame.
figure
Fig. 288.
Note that the door itself is quite luminous, and lighted up by the reflection of the sun from the tiled floor, so that the bars in the upper part throw distinct shadows, besides the mystery of colour thus introduced. The little window to the left, though not admitting much direct sunlight, is evidence of the brilliant glare outside; for the reflected light is very conspicuous on thetop and on the shutters on each side; indeed they cast distinct shadows up and down, while some clear daylight from the blue sky is reflected on the window-sill. As to the sink, the table, the wash-tubs, &c., although they seem in strong light and shade they really receive little or no direct light from a single point; but from the strong reflected light re-reflected into them from the wall of the doorway. There are many other things in such effects as this which the artist will observe, and which can only be studied from real light and shade. Such is the character of reflected light, varying according to the angle and intensity of the luminary and a hundred other things. When we come to study light in the open air we get into another region, and have to deal with it accordingly, and yet we shall find that our sciagraphy will be a help to us even in this bewilderment; for it will explain in a manner the innumerable shapes of sun-shadows that we observe out of doors among hills and dales, showing up their forms and structure; its play in the woods and gardens, and its value among buildings, showing all their juttings and abuttings, recesses, doorways, and all the other architectural details. Nor must we forget light's most glorious display of all on the sea and in the clouds and in the sunrises and the sunsets down to the still and lovely moonlight.
These sun-shadows are useful in showing us the principle of light and shade, and so also are the shadows cast by artificial light; but they are only the beginning of that beautiful study, that exquisite art of tone orchiaro-oscuro, which is infinite in its variety, is full of the deepest mystery, and is the true poetry of art. For this the student must go to Nature herself, must study her in all her moods from early dawn to sunset, in the twilight and when night sets in. No mathematical rules can help him, but only the thoughtful contemplation, the silent watching, and the mental notes that he can make and commit to memory, combining them with the sentiments to which they in turn give rise. Theplein air, or broad daylight effects, are but one item of the great range of this ever-changing and deepening mystery—from the hard reality to the soft blending of evening when form almost disappears, even to the merging of the whole landscape, nay, the whole world, into a dream—which is feltrather than seen, but possesses a charm that almost defies the pencil of the painter, and can only be expressed by the deep and sweet notes of the poet and the musician. For love and reverence are necessary to appreciate and to present it.
There is also much to learn about artificial light. For here, again, the study is endless: from the glare of a hundred lights—electric and otherwise—to the single lamp or candle. Indeed a whole volume could be filled with illustrations of its effects. To those who aim at producing intense brilliancy, refusing to acknowledge any limitations to their capacity, a hundred or a thousand lights commend themselves; and even though wild splashes of paint may sometimes be the result, still the effort is praiseworthy. But those who prefer the mysterious lighting of a Rembrandt will find, if they sit contemplating in a room lit with one lamp only, that an endless depth of mystery surrounds them, full of dark recesses peopled by fancy and sweet thought, whilst the most beautiful gradations soften the forms without distorting them; and at the same time he can detect the laws of this science of light and shade a thousand times repeated and endless in its variety.
Note.—Fig. 288must be looked upon as a rough sketch which only gives the general effect of the original drawing; to render all the delicate tints, tones and reflections described in the text would require a highly-finished reproduction in half-tone or in colour.
As many of the figures in this book had to be re-drawn, not a light task, I must here thank Miss Margaret L. Williams, one of our Academy students, for kindly coming to my assistance and volunteering her careful co-operation.
Reflections in still water can best be illustrated by placing some simple object, such as a cube, on a looking-glass laid horizontally on a table, or by studying plants, stones, banks, trees, &c., reflected in some quiet pond. It will then be seen that the reflection is the counterpart of the object reversed, and having the same vanishing points as the object itself.
figure
Fig. 289.
Let us supposeR(Fig. 289) to be standing on the water or reflecting plane. To find its reflection make square[R]equal to the original squareR. Complete the reversed cube by drawing its other sides, &c. It is evident that this lower cube is the reflection of the one above it, although it differs in one respect, for whereas in figureRthe top of the cube is seen, in its reflection [R] it is hidden, &c. In figureAof a semicircular arch we see theunderneath portion of the arch reflected in the water, but we do not see it in the actual object. However, these things are obvious. Note that the reflected line must be equal in length to the actual one, or the reflection of a square would not be a square, nor that of a semicircle a semicircle. The apparent lengthening of reflections in water is owing to the surface being broken by wavelets, which, leaping up near to us, catch some of the image of the tree, or whatever it is, that it is reflected.
In this view of an arch (Fig. 290) note that the reflection is obtained by dropping perpendiculars from certain points on the arch, 1, 0, 2, &c., to the surface of the reflecting plane, and then measuring the same lengths downwards to corresponding points, 1, 0, 2, &c., in the reflection.
In Fig. 291 we take a side view of the reflected object in order to show that at whatever angle the visual ray strikes the reflecting surface it is reflected from it at the same angle.
figure
Fig. 291.
We have seen that the reflected line must be equal to the original line, thereforemBmust equalMa. They are also at right angles toMN, the plane of reflection. We will now draw the visual ray passing fromE, the eye, toB, which is the reflection ofA; and just underneath it passes throughMNatO, which is the point where the visual ray strikes the reflecting surface. DrawOA. This line represents the ray reflected from it. We have now two triangles,OAmandOmB, which are right-angled triangles and equal, therefore angleaequals angleb. But anglebequals anglec. Therefore angleEcMequals angleAam, and the angle at which the ray strikes the reflecting plane is equal to the angle at which it is reflected from it.
In this sketch the four posts and other objects are represented standing on a plane level or almost level with the water, in order to show the working of our problem more clearly. It will be seen that the postAis on the brink of the reflecting plane, and therefore is entirely reflected;BandCbeing farther back are only partially seen, whereas the reflection ofDis not seen at all. I have made all the posts the same height, but with regard to the houses, where the length of the vertical lines varies, we obtain their reflections by measuring from the pointsooupwards and downwards as in the previous figure.
figure
Fig. 292.
Of course these reflections vary according to the position they are viewed from; the lower we are down, the more do we see of the reflections of distant objects, and vice versa. When the figures are on a higher plane than the water, that is, above the plane of reflection, we have to find their perspective position,and drop a perpendicularAO(Fig. 293) till it comes in contact with the plane of reflection, which we suppose to run under the ground, then measure the same length downwards, as in this figure of a girl on the top of the steps. Pointomarks the point of contact with the plane, and by measuring downwards toa·we get the length of her reflection, or as much as is seen of it. Note the reflection of the steps and the sloping bank, and the application of the inclined plane ascending and descending.
figure
Fig. 293.
I had noticed that some of the figures in Titian’s pictures were only half life-size, and yet they looked natural; and one day, thinking I would trace myself in an upright mirror, I stood at arm’s length from it and with a brush and Chinese white, I made a rough outline of my face and figure, and when I measured it I found that my drawing was exactly half as long and half as wide as nature. I went closer to the glass, but the same outline fitted me. Then I retreated several paces, and still the same outline surrounded me. Although a little surprising at first, the reason is obvious. The image in the glass retreats or advances exactly in the same measure as the spectator.
Suppose him to represent one end of a parallelograme·s·, and his imagea·b·to represent the other. The mirrorABis a perpendicular half-way between them, the diagonale·b·is the visual raypassing from the eye of the spectator to the foot of his image, and is the diagonal of a rectangle, therefore it cutsABin the centreo, andAOrepresentsa·b·to the spectator. This is an experiment that any one may try for himself. Perhaps the above fact may have something to do with the remarks I made about Titian at the beginning of this chapter.
figure
Fig. 295.
figure
Fig. 296.
If an object or lineABis inclined at an angle of 45° to the mirrorRR, then the angleBACwill be a right angle, and this angle is exactly divided in two by the reflecting planeRR. And whatever the angle of the object or line makes with its reflection that angle will also be exactly divided.
Now suppose our mirror to be standing on a horizontal plane and on a pivot, so that it can be inclined either way. Whatever angle the mirror is to the plane the reflection of that plane in the mirror will be at the same angle on the other side of it, so that if the mirrorOA(Fig. 298) is at 45° to the planeRRthen thereflection of that plane in the mirror will be 45° on the other side of it, or at right angles, and the reflected plane will appear perpendicular, as shown in Fig. 299, where we have a front view of a mirror leaning forward at an angle of 45° and reflecting the squareaobwith a cube standing upon it, only in the reflection the cube appears to be projecting from an upright plane or wall.
figure
Fig. 299.
If we increase the angle from 45° to 60°, then the reflection of the plane and cube will lean backwards as shown in Fig. 300. If we place it on a level with the original plane, the cube will be standing upright twice the distance away. If the mirror is still farther tilted till it makes an angle of 135° as atE(Fig. 298), or 45° on the other side of the verticalOc, then the plane and cube would disappear, and objects exactly over that plane, such as the ceiling, would come into view.
In Fig. 300 the mirror is at 60° to the planemn, and the plane itself at about 15° to the planean(so that here we are using angular perspective,Vbeing the accessible vanishing point). The reflection of the plane and cube is seen leaning back at anangle of 60°. Note the way the reflection of this cube is found by the dotted lines on the plane, on the surface of the mirror, and also on the reflection.
figure
Fig. 300.
In Fig. 301 the mirror is vertical and at an angle of 45° to the wall opposite the spectator, so that it reflects a portion of that wall as though it were receding from us at right angles; and the wall with the pictures upon it, which appears to be facing us, in reality is on our left.
figure
Fig. 301.
An endless number of complicated problems could be invented of the inclined mirror, but they would be mere puzzles calculated rather to deter the student than to instruct him. What we chiefly have to bear in mind is the simple principle of reflections. When a mirror is vertical and placed at the end or side of a room it reflects that room and gives the impression that we are in one double the size. If two mirrors are placed opposite to each other at each end of a room they reflect and reflect, so that we see an endless number of rooms.
Again, if we are sitting in a gallery of pictures with a hand mirror, we can so turn and twist that mirror about that we can bring any picture in front of us, whether it is behind us, at the side, or even on the ceiling. Indeed, when one goes to those old palaces and churches where pictures are painted on the ceiling, as in the Sistine Chapel or the Louvre, or the palaces at Venice, it is not a bad plan to take a hand mirror with us, so that we can see those elevated works of art in comfort.
There are also many uses for the mirror in the studio, well known to the artist. One is to look at one's own picture reversed, when faults become more evident; and another, when the model is required to be at a longer distance than the dimensions of the studio will admit, by drawing his reflection in the glass we double the distance he is from us.
The reason the mirror shows the fault of a work to which the eye has become accustomed is that it doubles it. Thus if a line that should be vertical is leaning to one side, in the mirror it will lean to the other; so that if it is out of the perpendicular to the left, its reflection will be out of the perpendicular to the right, making a double divergence from one to the other.
Before we part, I should like to say a word about mental perspective, for we must remember that some see farther than others, and some will endeavour to see even into the infinite. To see Nature in all her vastness and magnificence, the thought must supplement and must surpass the eye. It is this far-seeing that makes the great poet, the great philosopher, and the great artist. Let the student bear this in mind, for if he possesses this quality or even a share of it, it will give immortality to his work.
To explain in detail the full meaning of this suggestion is beyond the province of this book, but it may lead the student to think this question out for himself in his solitary and imaginative moments, and should, I think, give a charm and virtue to his work which he should endeavour to make of value, not only to his own time but to the generations that are to follow. Cultivate, therefore, this mental perspective, without forgetting the solid foundation of the science I have endeavoured to impart to you.
1.Leonardo da Vinci'sTreatise on Painting.
2.There is another book calledThe Jesuit's Perspectivewhich I have not yet seen, but which I hear is a fine work.
3.In a sea-view, owing to the rotundity of the earth, the real horizontal line is slightly below the sea line, which is noted in Chapter I.
4.Some will tell us that Nature abhors a straight line, that all long straight lines in space appear curved, &c., owing to certain optical conditions; but this is not apparent in short straight lines, so if our drawing is small it would be wrong to curve them; if it is large, like a scene or diorama, the same optical condition which applies to the line in space would also apply to the line in the picture.
Index citations in the original book referred to page numbers. Where possible, links will lead directly to a chapter header or illustration. Note that the last two entries for Toledo are figure numbers rather than pages; these have not been corrected.
AAlbertDürer,2,9.Angles of Reflection,259.Angular Perspective,98-123,133,170.Ang"lar Persp"ctive,New Method,133,134,135,136.Arches, Arcades, &c.,198,200-208.Architect's Perspective,170,171.Art Schools Perspective,112-118,217.Atmosphere,1,74.BBalcony, Shadow of,246.Base or groundline,89.CCampanile Florence,5,59.Cast Shadows,229-253.Centre of Vision,15.Chessboard,74.Chinese Art,11.Circle,145,151-156,159.Columns,157,159,161,169,170.Conditions of Perspective,24,25.Cottage in Angular Perspective,116.Cube,53,65,115,119.Cylinder,158,159.Cylindrical picture,227.DDe Hoogh,2,62,73.Depths, How to measure by diagonals,127,128.Descending plane,92-95.Diagonals,45,124,125,126.Disproportion, How to correct,35,118,157.Distance,16,77,78,85,87,103,128.Distorted perspective, How to correct,118.Dome,163-167.Double Cross,218.EEllipse,145,146,147.Elliptical Arch,207.FFarningham,95.Figures on descending plane,92,93,94,95.Fig"res"nan inclined plane,88.Fig"res"na level plane,70,71,72,73,74,75.Fig"res"nuneven ground,90,91.GGeometrical and Perspective figures contrasted,46-48.Geom"tricalplane,99.Giovanni da Pistoya, Sonnet to, by Michelangelo,60.Great Pyramid,190.HHexagon,177,183,185.Hogarth,9.Honfleur,83,142.Horizon,3,4,15,20,59,60.Horizontal line,13,15.Horizontals,30,31,36.IInaccessible vanishing points,77,78,136,140-144.Inclined plane,33,118,213,244,245.Interiors,62,117,118,128.JJapanese Art,11.Jesuit of Paris, Practice of Perspective by,9.KKiosk, Application of Hexagon,185.Kirby, Joshua, Perspective made Easy (?),9.LLadder, Step,212,216.Landscape Perspective,74.Landseer, Sir Edwin,1.Leonardo da Vinci,1,61.Light, Observations on,253.Light-house,84.Long distances,85,87.MMeasure distances by square and diagonal,89,128,129.Mea"urevanishing lines, How to,49,50.Measuring points,106,113.Meas"ringpoint O,108,109,110.Mental Perspective,269.Michelangelo,5,57,58,60.NNatural Perspective,12,82,95,142,144.New Method of Angular Perspective,133,134,135,141,215,219.Niche,164,165,250.OOblique Square,139.Octagon,172-175.O, measuring point,110.Optic Cone,20.PParallels and Diagonals,124-128.Paul Potter, cattle,19.Paul Veronese,4.Pavements,64,66,176,178,180,181,183.Pedestal,141,161.Pentagon,186,187,188.Perspective, Angular,98-123.Persp"ctive,Definitions,13-23.Persp"ctive,Necessity of,1.Persp"ctive,Parallel,42-97.Persp"ctive,Rules and Conditions of,24-41.Persp"ctive,Scientific definition of,22.Persp"ctive,Theory of,13-24.Persp"ctive,What is it?6-12.Pictures painted according to positions they are to occupy,59.Point of Distance,16-21.Po"nt"fSight,12,15.Points in Space,129,137.Portico,111.Projection,21,137.Pyramid,189,190,191,193-196.RRaphael,3.Reduced distance,77,78,79,84.Reflection,257-268.Rembrandt,59,256.Reynolds, Sir Joshua,9,60.Rubens,4.Rules of Perspective,24-41.SScale on each side of Picture,141,142-144.Sc"leVanishing,69,71,81,84.Serlio,5,126.Shadows cast by sun,229-252.Sha"ows ca"st"yartificial light,252.Sight, Point of,12,15.Sistine Chapel,60.Solid figures,135-140.Square in Angular Perspective,105,106,109,112,114,121,122,123,133,134,139.Sq"areand diagonals,125,138,139,141.Sq"areof the hypotenuse (fig. 170),149.Sq"arein Parallel Perspective,42,43,50,53,54.Sq"areat 45°,64-66.Staircase leading to a Gallery,221.Stairs, Winding,222,225.Station Point,13.Steps,209-218.TTaddeoGaddi,5.Terms made use of,48.Tiles,176,178,181.Tintoretto,4.Titian,59,262.Toledo,96,144,259,288.Trace and projection,21.Transposed distance,53.Triangles,104,106,132,135,138.Turner,2,87.UUbaldus, Guidus,9.VVanishing lines,49.Vani"hingpoint,119.Vani"hingscale,68-72,74,77,79,84.Vaulted Ceiling,203.Velasquez,59.Vertical plane,13.Visual rays,20.WWinding Stairs,222-225.Water, Reflections in,257,258,260,261.
A
AlbertDürer,2,9.
Angles of Reflection,259.
Angular Perspective,98-123,133,170.
Ang"lar Persp"ctive,New Method,133,134,135,136.
Arches, Arcades, &c.,198,200-208.
Architect's Perspective,170,171.
Art Schools Perspective,112-118,217.
Atmosphere,1,74.
B
Balcony, Shadow of,246.
Base or groundline,89.
C
Campanile Florence,5,59.
Cast Shadows,229-253.
Centre of Vision,15.
Chessboard,74.
Chinese Art,11.
Circle,145,151-156,159.
Columns,157,159,161,169,170.
Conditions of Perspective,24,25.
Cottage in Angular Perspective,116.
Cube,53,65,115,119.
Cylinder,158,159.
Cylindrical picture,227.
D
De Hoogh,2,62,73.
Depths, How to measure by diagonals,127,128.
Descending plane,92-95.
Diagonals,45,124,125,126.
Disproportion, How to correct,35,118,157.
Distance,16,77,78,85,87,103,128.
Distorted perspective, How to correct,118.
Dome,163-167.
Double Cross,218.
E
Ellipse,145,146,147.
Elliptical Arch,207.
F
Farningham,95.
Figures on descending plane,92,93,94,95.
Fig"res"nan inclined plane,88.
Fig"res"na level plane,70,71,72,73,74,75.
Fig"res"nuneven ground,90,91.
G
Geometrical and Perspective figures contrasted,46-48.
Geom"tricalplane,99.
Giovanni da Pistoya, Sonnet to, by Michelangelo,60.
Great Pyramid,190.
H
Hexagon,177,183,185.
Hogarth,9.
Honfleur,83,142.
Horizon,3,4,15,20,59,60.
Horizontal line,13,15.
Horizontals,30,31,36.
I
Inaccessible vanishing points,77,78,136,140-144.
Inclined plane,33,118,213,244,245.
Interiors,62,117,118,128.
J
Japanese Art,11.
Jesuit of Paris, Practice of Perspective by,9.
K
Kiosk, Application of Hexagon,185.
Kirby, Joshua, Perspective made Easy (?),9.
L
Ladder, Step,212,216.
Landscape Perspective,74.
Landseer, Sir Edwin,1.
Leonardo da Vinci,1,61.
Light, Observations on,253.
Light-house,84.
Long distances,85,87.
M
Measure distances by square and diagonal,89,128,129.
Mea"urevanishing lines, How to,49,50.
Measuring points,106,113.
Meas"ringpoint O,108,109,110.
Mental Perspective,269.
Michelangelo,5,57,58,60.
N
Natural Perspective,12,82,95,142,144.
New Method of Angular Perspective,133,134,135,141,215,219.
Niche,164,165,250.
O
Oblique Square,139.
Octagon,172-175.
O, measuring point,110.
Optic Cone,20.
P
Parallels and Diagonals,124-128.
Paul Potter, cattle,19.
Paul Veronese,4.
Pavements,64,66,176,178,180,181,183.
Pedestal,141,161.
Pentagon,186,187,188.
Perspective, Angular,98-123.
Persp"ctive,Definitions,13-23.
Persp"ctive,Necessity of,1.
Persp"ctive,Parallel,42-97.
Persp"ctive,Rules and Conditions of,24-41.
Persp"ctive,Scientific definition of,22.
Persp"ctive,Theory of,13-24.
Persp"ctive,What is it?6-12.
Pictures painted according to positions they are to occupy,59.
Point of Distance,16-21.
Po"nt"fSight,12,15.
Points in Space,129,137.
Portico,111.
Projection,21,137.
Pyramid,189,190,191,193-196.
R
Raphael,3.
Reduced distance,77,78,79,84.
Reflection,257-268.
Rembrandt,59,256.
Reynolds, Sir Joshua,9,60.
Rubens,4.
Rules of Perspective,24-41.
S
Scale on each side of Picture,141,142-144.
Sc"leVanishing,69,71,81,84.
Serlio,5,126.
Shadows cast by sun,229-252.
Sha"ows ca"st"yartificial light,252.
Sight, Point of,12,15.
Sistine Chapel,60.
Solid figures,135-140.
Square in Angular Perspective,105,106,109,112,114,121,122,123,133,134,139.
Sq"areand diagonals,125,138,139,141.
Sq"areof the hypotenuse (fig. 170),149.
Sq"arein Parallel Perspective,42,43,50,53,54.
Sq"areat 45°,64-66.
Staircase leading to a Gallery,221.
Stairs, Winding,222,225.
Station Point,13.
Steps,209-218.
T
TaddeoGaddi,5.
Terms made use of,48.
Tiles,176,178,181.
Tintoretto,4.
Titian,59,262.
Toledo,96,144,259,288.
Trace and projection,21.
Transposed distance,53.
Triangles,104,106,132,135,138.
Turner,2,87.
U
Ubaldus, Guidus,9.
V
Vanishing lines,49.
Vani"hingpoint,119.
Vani"hingscale,68-72,74,77,79,84.
Vaulted Ceiling,203.
Velasquez,59.
Vertical plane,13.
Visual rays,20.
W
Winding Stairs,222-225.
Water, Reflections in,257,258,260,261.