Euclid of Alexandria

Euclid of Alexandria

(Father of Geometry)

Euclid's Proof and Theorems

Sources

B equals C. Assume AB doesn't equal AC.

Assume AB>AC. Make D so that DC=AB.

Now argue that triangles ABC and DBC are congruent.

Thus, the part is equal to the whole.

• Things which are equal to the same thing are also equal to one another.
• If equals be added to equals, the wholes are equal.
• If equals be subtracted from equals, the remainders are equal.
• Things which coincide with one another are equal to one another.
• The whole is greater that the part.

• http://www.math.tamu.edu/~dallen/history/euclid/euclid.html
• http://en.wikipedia.org/wiki/Euclid%27s_Elements
• http://www-history.mcs.st-and.ac.uk/Biographies/Euclid.html
• http://www.britannica.com/EBchecked/topic/194880/Euclid
• http://biography.yourdictionary.com/articles/who-is-euclid-and-what-did-he-do.html

Books Euclid wrote:

• The 'Elements'
• Data
• On Division
• Phaenomena
• Optics
• Porisms

Childhood and Background

'The Elements'

Euclid was born in 330 BC-260 BC, and authors believe that he was born from a wealthy family in Tyre in Saudi Arabia. He then moved to Alexandria to study Mathematics and made path breaking formulas and theorems. It was here in Alexandria where Euclid spread his knowledge of Math and Geometry. Most of Euclid's personal life is unknown and most information comes from a Greek Scholar named Proclus. He is also assumed to be taught by the students of Plato in Athens, Greece.

The Elements is still considered a masterpiece in the application of logic to mathematics. In historical context, it has proven enormously influential in many areas of science. Scientists Nicolaus Copernicus, Johannes Kepler, Galileo Galilei, and Sir Isaac Newton were all influenced by the Elements, and applied their knowledge of it to their work. Einstein recalled a copy of the Elements and a magnetic compass as two gifts that had a great influence on him as a boy, referring to the Euclid as the "holy little geometry book".

The 'Elements' Impact

The 'Elements' is Euclid's most influential book with thirteen editions in which he explains proofs on:

• Plane Geometry ( flat shapes such as lines, circles, or triangles). Books I-VI
• Theory of Numbers (concerned with properties of the positive integers). Books VII-IX
• Incommensurable ( lines that are the same but do not have the same ratio or value). Books X
• Solid Geometry ( The geometry of 3-dimensional shapes). Books XI-XIII

Contribution

A common misconception is that Euclid invented all concepts of geometry. This is certainly not so, as he really only pulled together ideas and developed them as his own within a textbook. However, he definitely developed the discipline in this regard, making it a concrete, organized study that people could learn from by following his written work.

He is also famous for his theories on other parts of life: in Optiks, he discusses perspective and gives insight to how we view the world through our eyes.

Euclid's Theorems and proofs cont.

Assume AGH> GHD .

Then the sum of AGH and BGH is greater than the sum of BGH and GHD.

But the first sum is two right angles.

Thus the second sum is less than two right angles and thus the line are not parallel.

By Alex Fernandez

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