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

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INTRODUCTION.
xi
4. or < .

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

5. minus = .

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 praƈtice of allowing the ſtudent to commit the demonſtration to memory; until reaſon, and faƈt, and proof only make impreſſions on the underſtanding.

Again, when leƈturing 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;