Page:First six books of the elements of Euclid 1847 Byrne.djvu/15

Rh

Either the red or blue angle is less than the yellow angle.



In other terms, the yellow angle made less by the blue angle equal the red angle.



That is, the square of the yellow line is equal to the sum of the squares of the blue and red lines.

In oral demonstrations we gain with colours this important advantage, the eye and the ear can be addressed at the same moment, so that for teaching geometry, and other linear arts and sciences, in classes, the system is the best ever proposed, this is apparent from the examples just given.

Whence it is evident that a reference from the text to the diagram is more rapid and sure, by giving the forms and colours of the parts, or by naming the parts and their colours, than naming the parts and letters on the diagram. Besides the superior simplicity, this system is likewise conspicuous for concentration, and wholly excludes the injurious though prevalent practice of allowing the student to commit the demonstration to memory; until reason, and fact, and proof only make impressions on the understanding.

Again, when lecturing on the principles or properties of figures, if we mention the colour of the part or parts referred to, as in saying, the red angle, the blue line, or lines, &c. the part or parts thus named will be immediately seen by all in the class at the same instant; not so if we say the angle ABC, the triangle PFQ, the figure EGKt, and so on;