This text describes the method of dividing a window's width and height into equal sections to analyze perspective and distance using points of convergence in a drawing. It explains the procedure to draw open window shutters and suggests techniques for comparing lengths and angles with a protractor. The lesson further includes steps for drawing objects, towers, and terrains using perspective to match observed shapes and dimensions on a drawing.
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The width of the window is divided into two equal parts by a vertical line represented here by GH; we count the panes, which are three in number. We divide, on paper, the height of the window into three equal parts, and we determine the widths of the wooden strips between each glass pane by comparing these widths to the height of the panes.
We can suppose that one of the window shutters is open as represented here by JKLM. If this side is open so that the bottom of this side represented by JK is perpendicular to the bottom of the other shutter represented by CD, the top and bottom lines of JKLM and all the vanishing lines of this shutter would converge at the viewpoint; but since this shutter is more open and JK forms an obtuse angle with CD, its lines will converge at an accidental point, and we will draw this side in the following manner. Holding the protractor horizontally, we compare the distance between lines JM and KL, or the width of the shutter as seen here, with the total width of the window. Here, the distance from JM to KL is one-fifth of the total width up to line OB. On the paper, we take a width EN from a point E on the vertical line CA, equal to one-fifth of the total width that we have previously taken for the window, and from point N, we raise a vertical line. We now observe that the side of the shutter represented here by KL is closer to the observer than the other side JM, to which it is equal in reality: therefore KL should actually appear larger than JM. We find this difference by holding the protractor horizontally to see, by leveling, how much longer the angle represented by M appears than the angle represented by L. Here, angle M would cut the line KL at point q, and we find that the distance do, compared to the width qM, equals ten-thirds of this width. On the drawing, we will therefore extend the vertical KL to a point L, which will be raised above the level of point M by an amount equal to two-thirds of the width represented here by qM. By a similar comparison, we will then find the lines KJ and LM. We divide the height KL into three parts for the panes. These panes can be drawn in perspective in two ways. By the first method, line KL is divided into three equal parts, and JM is also divided into three equal parts: draw OR and PS, and by comparison, determine the width of the wooden strips. One could also extend the lines KJ and LM, which would eventually meet at a point that is the point of convergence of these lines, and then, from the points of division of side KL, draw to this point of convergence. We have just found lines that denote the separation strips of the panes. If the point of convergence is too far from the board, we use the first of these two methods.
After drawing the window, whether open or closed, we start by drawing the objects visible from the closed side, as this method is easier.
The foreground, which is a mound, begins a third of the way through the paving slab, marked point F by F, passes through the lower angle of this tile to the left of the observer and disappears slightly lower towards the left below the base of the window. On the drawing, we will mark a point at a third of the first tile to represent point F, and from this point to the angle T of the tile, we draw a line whose curve follows the shape of the object we have in front of us. We extend this curve beyond GH. We determine the height of the bushes by comparing it with the height of the tile, and we draw these bushes after determining their height.
To draw the tower and the terrain on which it is situated, we see that the base of this terrain cuts the right side of the first tile at a point f: it is a third of the height of the tile from top to bottom. We will mark this point on the drawing, at a third of the way down the side of the first tile. The point of terrain marked g is advanced so as to be on a vertical line that cuts the tile's width at its greater half from right to left of the observer. We draw this terrain in such a way that the point g corresponds to the greater half of the width of the tile. The tower is seen a bit below the first wooden strip that separates the panes: we mark this position with a point on the paper. We find on the protractor the height of the tower marked by cd, comparing it with the height of the second tile.