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Euclid of Alexandria
Transcript of Euclid of Alexandria
http://jwilson.coe.uga.edu/emat6680/greene/emat6000/greek%20geom/Euclid/euclid.html EUCLID of ALEXANDRIA “It is possible to draw
a straight line
between any two points.” Only a little is known about
Euclid of Alexandria But how much
do we know about him? -because Euclid was a common name during his time, and thus any reference to “Euclid” does not necessarily mean Euclid of Alexandria. -only very little of his works have survived from back then. ElementS was the textbook of elementary geometry and logic up to the early twentieth century probably the most reproduced book
in the Western world,
next to the Bible 13 volume compilation of Greek mathematics and geometry. Each volume lists a number of definitions and postulates followed by theorems, which are followed by proofs using those
definitions and postulates GREECE Alexandria, Egypt was probably born around 325 BC
in He first studied under the
great philosopher Plato
in Athens where he learned the geometry of Eudoxus and Theaetetus He was invited by Ptolemy I to teach at his newly founded university in Alexandria in Egypt (the Museum - was established as a great center of learning) he established his own school of mathematics where he tutored Archimedes he died around 270 B.C Greek mathematician he is known as the
Father of geometry famous for his treatise on geometry:
"The Elements" was described as a kind, fair, patient man who quickly helped and praised the works of others many of the theorems found can be traced to previous thinkers including: Euxodus, Thales, Hippocrates and Pythagoras. was translated into both Latin and Arabic Book 1 & book 2: deals with basic properties of triangles, parallels, parallelograms, rectangles, and squares
Book 3: addresses properties of the circle Book 4: deals with problems about circles
Book 5: looks at proportion
Book 6: looks at applications to book 5. Book 7-9: Euclid addresses number theory.
Book 7: in particular explains the Euclidean algorithm, which we have all learned to use in order to find the greatest common divisor of any two positive integers. Book 10: appreciates the theory of irrational numbers. Book 11, 12, 13: deal with three-dimensional
geometry Other Works Data On Division
of Figures Phenomena
(Astronomy) Optics Lost works Conics Porisms Pseudaria or
Book of Fallacies Surface Loci POSTULATES 1.To draw a straight line from any point to any point.
2.To produce a finite straight line continuously in a straight line.
3.To describe a circle with any center and distance.
4.That all right angles are equal to one another.
5.That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles. COMMON NOTIONS
or AXIOMS 1.Things which are equal to the same thing are also equal to one another.
2.If equals be added to equals, the wholes are equal.
3.If equals be subtracted from equals, the remainders are equal.
4.Things which coincide with one another are equal to one another.
5.The whole is greater than the part. Definitions 1.A point is that which has no part.
2.A straight line - is a line which lies evenly with the points on itself.
3.A surface is that which has length and breadth only.
4. An obtuse angle is an angle greater than a right angle.
5. An acute angle - is an angle less than a right angle. BOOK 1: Holes
in his works: The fifth postulate or the parallel postulate.
-states that for a straight line and a point not on the line, there is exactly one line that passes through the point parallel to the original line.
19th century people chose to disregard Euclid's 5th and create "hyperbolic geometry" in which there can be many different parallel lines through one point to any given line. Causes some modern day mathematicians and scientists to doubt him.
Euclid has lost much status in the eyes of many prominent mathematicians.
But still he is still referred to as "The Father of Geometry," DRILL 1 2 3 4 5 This book deals with basic properties of triangles, parallels, parallelograms, rectangles, and squares book 1 & 2 This book
consists of propositions
the division of various figures
into two or
more equal parts On Division of Figures This book addresses properties of the circle book 3 This book deals with problems about circles book 4 who invited Euclid to teach in Alexandria in Egypt Ptolemy I 6 Pythagoras Archimedes Plato How are they related? teacher Refference Student