An introduction to linear drawing/Chapter 2

by M. Francoeur

SECOND CLASS.

1.⁠Make two triangles of perpendicular sides.

After having made one angle, the pupil will draw a perpendicular to one of the sides, and then a perpendicular to the other side, until the perpendiculars cross each other.

One of the angles is acute, and the other obtuse; and if you lengthen one of the perpendiculars, a new angle will be formed exactly like the angle first made, as the dotted continuation of the perpendicular in fig. 1 shows.

2.⁠Make two triangles of perpendicular sides.⁠(fig.2.)

Make one triangle, and then draw a perpendicular to each side, until the perpendiculars touch and form angles. Each side of each triangle must be perpendicular to some side of the other triangle.

3.⁠Make a trapezoid.⁠(fig. 3.)

A trapezoid has four sides, of which, two, called the bases, are parallel. In the figure, these are the upper and lower sides. The height is a perpendicular from base to base. As this figure is easily made, the length of the bases and the height may be given: thus, "Make a trapezoid whose height shall be one inch,and whose bases shall be an inch and a half and two inches." When no two of the sides are parallel the figure is called a Trapezium.

4.⁠Make a six sided polygon of unequal sides.⁠(fig.4.)

The word polygon means many-angled. To make a polygon, the best method is, first to place dots at the angles and then draw right lines from dot to dot.

5.⁠Make a five sided polygon of unequal sides.⁠(fig.5.)

6.⁠Make two polygons of unequal but parallel sides.⁠(figs. 5 and 6.)

7.⁠Make a six sided polygon of equal sides.

8.⁠Make a five sided polygon of equal sides.

A polygon of equal sides is called a regular polygon.

9.⁠From one point of a polygon draw diagonals, and then draw a parallel polygon within the first.⁠(fig. 7.)

After drawing a polygon, from either of the points carry right lines to all the rest, thus making several triangles. These lines are called diagonals. Then you have only to draw parallels to the several sides from diagonal to diagonal.

To vary the exercise, let the pupil draw a polygon outside of the first drawn. He will then only have to lengthen the diagonals.

10.⁠Draw a polygon, and from a central point draw diagonals, then draw a parallel polygon within and outside of the first drawn.⁠(fig. 8.)

11.⁠Make a triangular pyramid.⁠(fig. 9.)

First draw the triangle which forms the base, then place a dot for the point or apex, and draw right lines from the point to each angle of the base.

12.⁠Draw a quadrangular (or four angled) pyramid.⁠(fig. 10.) then cut it by a plane parallel to its base.

The process is the same as in the preceding figure. The plane, or parallel to the base, must be the last thing done. The height of the pyramid is a perpendicular dropped from the apex or summit to the base. The pupil must be careful to distinguish the front lines from the back lines of the figure.

13.⁠Make a six sided pyramid.⁠(fig. 11.)

14.⁠Make a five sided pyramid.⁠(fig. 12.)

15.⁠Make a five sided pyramid, and cut it by a plane parallel to the base.⁠(fig. 12.) Note.⁠When the base of the pyramid is a regular polygon, and the height falls upon the centre of it, the pyramid is upright and regular; such are figures 10, 11 and 12.

16.⁠On two polygons of parallel sides, raise a pyramid, (fig. 12.)

This is merely another way of performing the last figure, by drawing both polygons before you draw the trunk of the pyramid.

17.⁠Make an upright triangular prism. (fig. 13.)

A prism is a body formed from two equal and parallel polygons, whose corresponding points are joined by lines, all parallel, and equal to each other; such are figures 13 to 20 inclusive.

The height of a prism is a perpendicular to the two bases. A prism is said to be upright when its sides are perpendicular, and oblique when its sides lean or are inclined.

18.⁠Make an oblique triangular prism. (fig. 14.)

19.⁠Make an oblique five sided prism. (fig. 15.)

20.⁠Make an upright parallelopiped. (fig. 16.)

When the bases of the prism are parallelograms, the body is called a parallelopiped. All the six faces are then parallelograms, and the two opposite faces are equal.

21.⁠Make an oblique parallelopiped. (fig. 17.)

22.⁠Make a Cube. (fig. 18.)

The cube is a parallelopiped, all of whose faces are equal squares, and each placed at right angles with the contiguous or next squares.

A cube is a solid square, but it will be perceived, that in consequence of perspective, only the front and back faces appear square. These two faces should be traced first, and the rest will easily be added. Dice are cubes.

23.⁠Draw an oblique cube. (fig. 17. if you make its sides equal.)

24.⁠Cut a prism by a plane parallel to its bases. (fig. 19.)