[From the Encyclopedia Britanmca.] 



XC. Diagrams. 



A DIAGRAM is a figure drawn in such a manner that the geometrical 

 relations between the parts of the figure help us to understand relations between 

 other objects. A few have been selected for description in this article on account 

 of their greater geometrical significance. 



Diagrams may be classed according to the manner in which they are 

 intended to be used, and also according to the kind of analogy which we 

 recognize between the diagram and the thing represented. 



Diagrams of Illustration. 



The diagrams in mathematical treatises are intended to help the reader 

 to follow the mathematical reasoning. The construction of the figure is defined 

 in words so that even if no figure were drawn the reader could draw one 

 for himself. The diagram is a good one if those features which form the 

 subject of the proposition are clearly represented. The accuracy of the drawing 

 is therefore of smaller importance than its distinctness. 



Metrical Diagrams. 



Diagrams are also employed in an entirely different way namely, for 

 purposes of measurement. The plans and designs drawn by architects and 

 engineers are used to determine the value of certain real magnitudes by 

 measuring certain distances on the diagram. For such purposes it is essential 

 that the drawing be as accurate as possible. 



We therefore class diagrams as diagrams of illustration, which merely 

 suggest certain relations to the mind of the spectator, and diagrams drawn to 

 scale, from which measurements are intended to be made. 



