The Theory and Practice of Perspective Part 7

_Note._--Whilst on this subject, I may note that the painter in his large decorative work often had difficulties to contend with, which arose from the form of the building or the shape of the wall on which he had to place his frescoes. Painting on the ceiling was no easy task, and Michelangelo, in a humorous sonnet addressed to Giovanni da Pistoya, gives a burlesque portrait of himself while he was painting the Sistine Chapel:--

_"I'ho gia fatto un gozzo in questo stento."_

Now have I such a goitre 'neath my chin That I am like to some Lombardic cat, My beard is in the air, my head i' my back, My chest like any harpy's, and my face Patched like a carpet by my dripping brush.

Nor can I see, nor can I budge a step; My skin though loose in front is tight behind, And I am even as a Syrian bow.

Alas! methinks a bent tube shoots not well; So give me now thine aid, my Giovanni.

At present that difficulty is got over by using large strong canvas, on which the picture can be painted in the studio and afterwards placed on the wall.

However, the other difficulty of form has to be got over also. A great portion of the ceiling of the Sistine Chapel, and notably the prophets and sibyls, are painted on a curved surface, in which case a similar method to that explained by Leonardo da Vinci has to be adopted.

In Chapter CCCI he shows us how to draw a figure twenty-four braccia high upon a wall twelve braccia high. (The braccia is 1 ft. 10-7/8 in.).

He first draws the figure upright, then from the various points draws lines to a point _F_ on the floor of the building, marking their intersections on the profile of the wall somewhat in the manner we have indicated, which serve as guides in making the outline to be traced.

[Ill.u.s.tration: Fig. 67.

'Draw upon part of wall _MN_ half the figure you mean to represent, and the other half upon the cove above (_MR_).' Leonardo da Vinci's _Treatise on Painting_.]

XXI

INTERIORS

[Ill.u.s.tration: Fig. 68. Interior by de Hoogh.]

To draw the interior of a cube we must suppose the side facing us to be removed or transparent. Indeed, in all our figures which represent solids we suppose that we can see through them, and in most cases we mark the hidden portions with dotted lines. So also with all those imaginary lines which conduct the eye to the various vanishing points, and which the old writers called 'occult'.

[Ill.u.s.tration: Fig. 69.]

When the cube is placed below the horizon (as in Fig. 59), we see the top of it; when on the horizon, as in the above (Fig. 69), if the side facing us is removed we see both top and bottom of it, or if a room, we see floor and ceiling, but otherwise we should see but one side (that facing us), or at most two sides. When the cube is above the horizon we see underneath it.

We shall find this simple cube of great use to us in architectural subjects, such as towers, houses, roofs, interiors of rooms, &c.

In this little picture by de Hoogh we have the application of the perspective of the cube and other foregoing problems.

XXII

THE SQUARE AT AN ANGLE OF 45

When the square is at an angle of 45 to the base line, then its sides are drawn respectively to the points of distance, _DD_, and one of its diagonals which is at right angles to the base is drawn to the point of sight _S_, and the other _ab_, is parallel to that base or ground line.

[Ill.u.s.tration: Fig. 70.]

To draw a pavement with its squares at this angle is but an amplification of the above figure. Mark off on base equal distances, 1, 2, 3, &c., representing the diagonals of required squares, and from each of these points draw lines to points of distance _DD'_. These lines will intersect each other, and so form the squares of the pavement; to ensure correctness, lines should also be drawn from these points 1, 2, 3, to the point of sight _S_, and also horizontals parallel to the base, as _ab_.

[Ill.u.s.tration: Fig. 71.]

XXIII

THE CUBE AT AN ANGLE OF 45

Having drawn the square at an angle of 45, as shown in the previous figure, we find the length of one of its sides, _dh_, by drawing a line, _SK_, through _h_, one of its extremities, till it cuts the base line at _K_. Then, with the other extremity _d_ for centre and _dK_ for radius, describe a quarter of a circle _Km_; the chord thereof _mK_ will be the geometrical length of _dh_. At _d_ raise vertical _dC_ equal to _mK_, which gives us the height of the cube, then raise verticals at _a_, _h_, &c., their height being found by drawing _CD_ and _CD'_ to the two points of distance, and so completing the figure.

[Ill.u.s.tration: Fig. 72.]

XXIV

PAVEMENTS DRAWN BY MEANS OF SQUARES AT 45

[Ill.u.s.tration: Fig. 73.]

[Ill.u.s.tration: Fig. 74.]

The square at 45 will be found of great use in drawing pavements, roofs, ceilings, &c. In Figs. 73, 74 it is shown how having set out one square it can be divided into four or more equal squares, and any figure or tile drawn therein. Begin by making a geometrical or ground plan of the required design, as at Figs. 73 and 74, where we have bricks placed at right angles to each other in rows, a common arrangement in brick floors, or tiles of an octagonal form as at Fig. 75.

[Ill.u.s.tration: Fig. 75.]

XXV

THE PERSPECTIVE VANISHING SCALE

The vanishing scale, which we shall find of infinite use in our perspective, is founded on the facts explained in Rule 10. We there find that all horizontals in the same plane, which are drawn to the same point on the horizon, are perspectively parallel to each other, so that if we measure a certain height or width on the picture plane, and then from each extremity draw lines to any convenient point on the horizon, then all the perpendiculars drawn between these lines will be perspectively equal, however much they may appear to vary in length.

[Ill.u.s.tration: Fig. 76.]

Let us suppose that in this figure (76) _AB_ and _AB_ each represent 5 feet. Then in the first case all the verticals, as _e_, _f_, _g_, _h_, drawn between _AO_ and _BO_ represent 5 feet, and in the second case all the horizontals _e_, _f_, _g_, _h_, drawn between _AO_ and _BO_ also represent 5 feet each. So that by the aid of this scale we can give the exact perspective height and width of any object in the picture, however far it may be from the base line, for of course we can increase or diminish our measurements at _AB_ and _AB_ to whatever length we require.

As it may not be quite evident at first that the points _O_ may be taken at random, the following figure will prove it.