Home Geometry Euclid's Elements Post a comment Proposition 5 Proposition 7       By Antonio Gutierrez
Euclid's Elements Book I, Proposition 6:
If in a triangle two angles be equal to one another, the sides which subtend the equal angles will also be equal to one another.

Let ABC be a triangle having the angle BAC equal to the angle ACB;

I say that the side AB is also equal to the side BC. "Proof by contradiction," also called reductio ad absurdum.

Euclid's Elements Book 1,I, Proposition 6

Geometrical conversion

Proposition I.6 is the geometrical, but not the logical, converse of proposition I.5. 

The Elements: Books I-XIII

Euclid's Elements is the oldest mathematical and geometric treatise consisting of 13 books written by Euclid in Alexandria c. 300 BC. It is a collection of definitions, postulates, axioms, 467 propositions (theorems and constructions), and mathematical proofs of the propositions.

The Thirteen Books of the Elements by Euclid


In its broad sense, education refers to any act or experience that has a formative effect on the mind, character, or physical ability of an individual...In its technical sense education is the process by which society, through schools, colleges, universities, and other institutions, deliberately transmits its cultural heritage--its accumulated knowledge, values, and skills--from one generation to another. George F. Kneller, Introduction to the Philosophy of Education (New York: John Wiley and Sons, 1971.) 

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