Sunday, February 08, 2009

Euclid's Triangle Definitions

[I was struck yesterday, perhaps the day before, while reading from Robert Rhea's "The Dow Theory" how useful the "axiom-theorem" organization of knowledge in any field can be -- and not necessarily in mathematics alone. I looked at Euclid's Elements in a new light -- it represents the first successful attempt at such an organization. Although it might be ridiculous, I've decided to enter a few simple but powerful axioms and theorems from The Elements. In this case, simply a few definitions.]

Of trilateral figures, an equilateral triangle is that which has its three sides equal, an isosceles triangle that which has two of its sides alone equal, and a scalene triangle that which has its three sides unequal.

Further, of trilateral figures, a right-angled triangle is that which has a right angle, an obtuse-angled triangle that which has an obtuse angle, and an acute-angled triangle that which has its three sides acute.

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