How to Draw a Cube on a Given Square, using only One Vanishing Point
ABCD is the given square (Fig. 131). At A raise vertical Aa equal to side of square AB·, from a draw ab to the vanishing point. Raise Bb. Produce VD to E to touch the base line. From E raise vertical EF, making it equal to Aa. From F draw FV. Raise Dd and Cc, their heights being determined by the line FV. Join da and the cube is complete. It will be seen that the verticals raised at each corner of the square are equal perspectively, as they are drawn between parallels which start from equal heights, namely, from EF and Aa to the same point V, the vanishing point. Any other
line, such as OO·, can be directed to the inaccessible vanishing point in the same way as ad, &c.
Fig. 131.
Note. This is only one of many original figures and problems in this book which have been called up by the wish to facilitate the work of the artist, and as it were by necessity.
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A Courtyard or Cloister Drawn with one Vanishing Point
In this figure I have first drawn the pavement by means of the diagonals GA, Go, Go, &c., and the vanishing point V, the square at A being given. From A draw diagonal through opposite corner till it cuts the horizon at G. From this same point G draw