Home Geometry Euclid's Elements Post a comment Proposition 3 Proposition 5        By Antonio Gutierrez
Euclid's Elements Book I, Proposition 4: (Side-Angle-Side SAS) If two triangles have two sides equal to two sides respectively, and have the angles contained by the equal sides also equal, then the two triangles are congruent

Let ABC and DEF be two triangles having the two sides AB and AC equal to the two sides DE and DF respectively, and the angle BAC equal to the angle EDF. I say that the base BC also equals the base EF, the triangle ABC equals the triangle DEF, and the remaining angles equal the remaining angles respectively.
 

Euclid's Elements Book I,1, Proposition 4
 


Construction

Euclid's Elements Book I,1, Proposition 4

 


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


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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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