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Mathematics practically applied to the useful and fine arts / by Charles Dupin; adapted to the state of the arts in England by George Birkbeck
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PERSPECTIVE OF MACHINERY.

165

When we know that some of the lines are parallel, andthey are seen in perspective, we ought immediately toexamine if these lines, when prolonged, would meet at asiugle point properly placed, which is their point of con-currence in the picture.

When an edifice is drawn in perspective, on a verticalplane, fig. 25, which, as already stated, is the mostusual case, both in plan drawing and in painting, thepoints of concurrence of all the possible groupes of ho-rizontal parallel lines are placed on the horizontal plane,which passes through the point of sight. This is, in ef-fect, the only plane which can be drawn through thispoint, parallel to the horizontal lines. Thus, on the onehand, the point of concurrence for the perspective of thehorizontal lines, parallel to the front of the building, andon the other, the point of concurrence for the perspec-tive of the horizontal lines, perpendicular to the front,are both placed on a level with the point of sight. Con-sequently, at this height, the horizontal lines of both di-rections are put in perspective in the direction of a hori-zontal line, Oo, fig. 25, situated at the same height as thepoint of sight.

It will be easily perceived, fig. 25, that the parts aboveand below the windows, which are in a right line in thebuilding, are also in a right line in the perspective. Thisresults, in fact, from a property of the different parts ofright lines, whether separated or not; for if these parts bejoined, though only by an imaginary line, they will forma continued right line ; the perspective of which is asingle right line, including, consequently, the representa-tion of all the portions of a right line, which were to beplaced in perspective.

Application to painting .In pictures in which severalpersons are represented, the artist is careful not to placethem all in the same plane, nor in the same attitude.Were he to do this, they would appear either all of thesame height, or lessening, according to some regular law;so that if they were all in a. standing posture, and equal in