In writing the original edition of this text it seemed wise to the author to base its arrangement and content upon two principles which considerable experience proved sound. These principles are: first, that the student can just as well and perhaps better, be taught the use of instruments on work that will at the same time have educational value; second, that for greatest efficiency in teaching drawing the text should be made so complete and follow the class room work so closely that lecturing is unnecessary.
The above principles were followed by first designing a very flexible course in drafting, substituting drawings of machine parts for the conventional geometrical figures. The work was arranged into definite groups, according to subject, each group being scheduled for a definite amount of time. Second, the text was so arranged that section, lesson or chapter one, gave all information necessary for the work included in group one, etc.

After three years' very satisfactory trial of the text, the department of drawing has undertaken a complete revision with the desire that the work shall be not only a text, more complete than the first, but also a book of reference that will be of service after the student has completed the course.

(31) Definition. An orthographic projection of any object is such a representation on a given plane (usually vertical or horizontal) as will show in true proportion the contours of the object as seen in a direction perpendicular to the plane; i. e., as though viewed from an infinite distance, when all the lines of sight would be parallel to each other and perpendicular to the plane of prjection.


PRINCIPLES OF ORTHOGRAPHIC PROJECTION

(32) It is seen from Fig. 1, which is a representation of a machine part that, tho the object is represented as we are accustomed to see it, the picture gives us absolutely no conception of the ratio of the several parts of the object to each other; i. e., tho the sides of the square hole in the top may appear to be equal to the thickness of the object, one has no means of knowing exactly what the relation is; hence, unless actual dimensions were given for every detail of such a drawing, and these dimensions could be depended upon to be absolutely accurate, one would have no means of making, except approximately, the object which the drawing represents. Hence, it will be appreciated that in making drawings for the use of workmen in shops, such an application of Descriptive Geometry should be employed as will represent each line of the object at least once, in its true mathematical ratio to other lines; i.e., such a representation, that if no dimensions were given, one could compare lines by means of a scale or dividers and be certain of their exact ratio to each other. This branch of Descriptive Geometry is known as Orthographic or Proportional Measurement Projection.

Orthographic projection. To obtain such a projection of the machine part represented in Fig. 1, let us imagine that we have suspended it in space with the face containing the square hole horizontal; then, see Fig. 2, let us imagine that four planes be drawn about this machine part in the positions shown, one, a horizontal plane, a second a vertical plane parallel to the face A, and two other planes perpendicular to both the vertical and horizontal planes just drawn.

Coordinate planes and coordinate angles. The three planes just constructed about the machine part in Fig. 2 are known in orthographic projection as coordinate planes and are named individually, the Horizontal or H plane, Vertical or V plane, Profile or End plane; see Fig. 3. The four dihedral angles formed by the H and V planes are known as 1st, 2nd, 3rd, and 4th and are numbered in the order shown.

Projections or orthographic representations. In explaining the method used in obtaining the orthographic representations of the machine part, the corner A, Fig. 4, will be taken as typical of all significant points of the object. It is desired to represent this point on each of the three coordinate planes, the second End plane being for the time eliminated. From point A are dropped three perpendiculars, one to each of the coordinate planes; the points in which these perpendiculars pierce these coordinate planes are known as the projections of point A, and are called, V or Vertical projection or Front View (always lettered a' if lettered at all), H or Horizontal projection or Top View (always lettered a if lettered at all), and Profile, End Projection, End or Side View (always lettered a" if lettered at all); if then from all of the points of the object perpendiculars were dropped to the Vertical plane and lines drawn connecting the piercing points of these perpendiculars in regular order, Fig. 4, we would have on the Vertical plane a drawing or projection representing perfectly the appearance of the front of the machine part; a similar process would give us on the Horizontal plane a correct representation of the top of the object and on the End plane a representation of the side of the object.

1st and 3rd angle projections. If the object be placed in the 1st angle, as in Fig. 4, the projections referred to above are known as first angle projections. If the object is placed in the 3rd angle, as in Fig. 6, the projections are known as third angle projections; i. e., the projections of an object are known as First or Third Angle projections according to the angle in which the object is placed. It should be noted that Figs. 4 and 6 show only those parts of the coordinate planes that enclose the angle of projection under consideration. No mention is made of the Second or Fourth Angle projections because it would be impracticable to use either as working drawings.

Projections of objects. Advancing from the point A just discussed, to all other elemental points of the object and projecting them in turn in the same manner as was A, we find the representation of the machine part in the first angle, when the several points are properly joined by lines, to be as shown in Fig. 5. Proceeding in the same manner with the object in the third angle we obtain the views as shown in Figs. 6 and 7. It should be noted that the views are identical in character but appear in different positions in respect to each other. In practice it is the universal custom to omit both ground lines together with the boundary lines of the three planes. The resulting projections of the object appear as in Fig. 8.

Elimination of the first angle. From Fig. 1, it is noted that as we ordinarily see objects the top appears above the front and the right end to the right of the front or the left end to the left of the front, according to the position from which the object is seen. When the object is placed in the first angle and the projections revolved into the positions shown in Fig. 5, it is seen that the left end projection comes in a position to the right of the front and that the top is under the front, an arrangement by no means natural. While, when the object is placed in the third angle, Fig. 6, and projections revolved as shown in Fig. 7, the views assume a grouping identical with their order on the object itself; i.e., the right end to the right of the front, and the top above the front. Merely for the sake of this natural arrangement the third angle will be selected in preference to the first in making working drawings; i. e., all working drawings will be third angle orthographic projections.


SUMMARY OF PRINCIPLES

(33) It may be well to summarize a number of principles brought out in this discussion, likewise to mention several violations of pure orthographic projection. The top view, Fig. 8, represents the exact appearance, with lines in true proportions, of the top of the object; the front view represents the same of the front of the object, and the side view the same of the side of the object.

The top and front views must be directly above and below each other and the front and end views must be on the same horizontal lines as shown in Fig. 7, if the group is to represent the true orthographic projection of the object; a violation of this renders the whole drawing incorrect.


PERMISSIBLE VIOLATIONS

(34) In Fig. 5, it is shown that the portion of the End or Profile plane in front of V is revolved to the right; this of course means that the portion of the Profile plane behind V revolves to the left; while, in Fig. 7, the portion of the Profile plane behind V is represented as being revolved to the right. This revolution to the right of the portion of the Profile plane behind V is orthographically incorrect; however, in the case of the third angle projections it is tolerated for the natural order of projections which it produces.


PROJECTIONS OF HIDDEN LINES

(35) In Figs. 5 and 7 certain lines of the projections are shown dotted lines. This is the custom always followed for showing hidden or invisible lines. For ex- ample in the projection on the V plane, the two dotted lines show that the hole thru the object is invisible when viewed in a direction perpendicular to the V plane. A simple rule for determining the visibility of a line is to always consider the H projection a view from the top and the V projection a view from the front. This applies equally to first and third angle projection. The projection on the P plane is considered a view from the corresponding side of the object, that is, looking perpendicularly thru the P plane at the object.


AUXILIARY PLANES OF PROJECTION

(36) Frequently an object is so shaped that it can- not be placed in an entirely simple position with respect to the planes of projection. The face K on the corner brace shown in Fig. 9 will not be shown in its true size on either the H, V, or P planes when the object is placed in its simplest position with respect to these planes.

The use of a fourth plane, which is perpendicular to H but parallel to face K, will give an additional view which will show K in its true size. Fig. 10.