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800 BCE
Hindu Algebra
When solving problems they only stated steps – no proof or reasoning was provided
•First to recognize that quadratic equations have two roots
•Known for invention of decimal system which we use today -
300 BCE
Egyptian Algebra
Solve algebra problems equivalent to linear equations and 1 unknown
Algebra was rhetorical – use of no symbols
Problems were stated and solved verbally
Cairo Papyrus (300 B.C.) – solve systems of 2 degree equations -
300 BCE
Babylonian Algebra
Babylonians were more advanced than Egyptians
Like Egyptians, algebra was also rhetorical
Could solve quadratic equations
Method of solving problems was rhetorical, taught through examples
No explanations to findings were given
Recognized on positive rational numbers -
200 BCE
Rhetorical Algebra
Early Babylonian and Egyptian algebras were both rhetorical
•In Greece, the wording was more geometric but was still rhetorical.
•The Chinese also started with rhetorical algebra and used it longer. -
100
Greek Algebra
The Greeks originally learned algebra from Egypt as indicated in their writings of the 6th century BCE. Later they learned Mesopotamian geometric algebra from the Persians. They studied number theory, beginning with Pythagoras -
200
Fundamental Limitations of Greek Algebra
Negative and complex solutions of equations were rejected as “absurd” or “impossible”. -
300
Diophantine Algebra
Represents the end of a movement among Greeks away from geometrical algebra to a system of algebra that did not depend on geometry -
1540
European Algebra
Algebra was still largely rhetorical, slightly syncopated
•Solution to cubic and quartic equations
•Negative numbers were known, but not fully accepted
•No one could solve 5th degree equation
•Algebraists were called “cossists” and algebra was called “cossic art”