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Short Description
axiom out of other four by adding another theory, namely, analytic geometry. One can develop a trigonometry theory that only depends on the first’s four …

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Euclid’s Geometry and the Greek
The most important contribution that Euclid made, arguably, is that he
incorporated logical thinking into mathematics by the introduction of what today
known as axioms. In addressing plane geometry, he basically made five assumptions
about this world then proceed to derive other properties of this reality out of it, these
assumptions are:
1.) Given any two distinct points, we can draw a straight line segment connecting its
2.) All line segment can be extended as far out as ones wish
3.) Given a line segment with two end points, we can create a circle with one
endpoint as the center
4.) All rights angle are congruence to one anther
5.) It is best that we just take the picture from Wiki1:
It is now known that Euclid’s axioms-he referenced to them as postulates-were not
sufficient (for example what are points) as pointed out by others who came later. This
means nothing for us however. Our study and focus in this note will only on a faction of
plane geometry and not Euclid’s entire monumental book-hopefully we all will come
to appreciate what it gives us.
We will not get into the…