DIAGRAM (Lat. dia gramma, Gk. dai;pappa, figure front rir;r1c5rtv, diayraphein, to describe, from Jai, dia. through ypOrtv, graphein, to write). A timure so drawn that its geometric relations may illustrate the relations between other quantities. The area of a reetangle is the product of the numbers representing its length and breadth: the diagram of a rectangle is the visible symbol. corresponding to the equation a = bl; and. by analogy, the rectangle may be used to symbolize any quantity which is the product of two factors. Similarly, a parallelopi ped may symbolize any quantity which is the product of three factors.
The purpose of many mathematical diagrams is simply illustration. and it is necessary only that the idea be ch•arly presented, a•cura• of drawing being relatively unimportant—e.g. those showing electric connections require only a prop er representation of the parts in their association with one another. Other diagrams, as those drawn for workmen by architects and engineers, are in tended to furnish magnitudes or distances by actual measurement, and their execution cannot be too accurate.
A pro/i/e diagram shows such an outline as would be formed, for example, if a hill were cut through by a vertical plane, and the material on one side of the plane were removed. Evi dently a succession of such profiles might be laid on the same sheet of paper, the lines being dis tinctly drawn, and the whole would serve to com pare several vertical profiles of the same mass. It is not necessary that vertical and horizontal should conform to the same scale, provided each series of measurements is consist ent in itself. Thus geotp•aphic profiles, which include upon a single sheet the outlines of entire continents and ocean beds, usually have the ver tical measurements on a scale several time as great as that used for horizontal distances: otherwise the diagram would he made incon veniently long, or the heights would be incon spicuously small. A topographer's contour map
exhibits a series of curves, such as would be formed if a series of horizontal sections were made, and the outlines carefully drawn on paper. The drawing really shows the horizontal projec tions of the contour lines upon a surface parallel to the system. In mechanical drawings, particu larly those designed to guide workmen in the construction of machinery, several connected views of the same object are required, each view giving some information which the others can not furnish. Suppose three planes perpendicular to one another. like the bottom, one side. and one end of a rectangular box, and let an object, as a hexagonal nut. be placed within the tri hedral angle thus formed. Looking from the front, we see an image of the nut projected against the back of the box: from the side, a different image is seen against the end of the box: from above, a third form appears against the bottom, from or all of these fig ures the necessary measurements may be ob tained. if now the end of the box is swung out ward into the plane of its back. and then both together are laid hack into the plane of the bottom, we have the three coexistent drawings in one plane. and they may he transferred to, or be constructed on, one sheet of paper. In many cases the same points will find representa tion upon each diagram. and the fact may be indicated by the same letter: while the eye may lie led from one position of the point to another by lines distinctively to show that they are merely guides and not parts of the outline. See