I have started to read Euclid’s ‘Elements’. This is perhaps the most influential book in mathematics and was used for more than two-thousand years in schools all over the western world. My edition is written by Christian Fredrik Lindman lecturer of mathematics at the upper secondary school in Strängnäs, Sweden and it was printed in 1867.
In the first chapter many central terms and mathematical entities are defined.
Mathematics is the science dealing with quantities.
A quantity is an entity that can be increased or decreased by the addition or subtraction of more of the same quantity.
Geometry is the science dealing with quantities that have an extension in space.
Definition is a list of characteristics typical of that object
Postulat is a theorem that cannot be proved.
An axiom is an obvious statement.
Problem is a theorem where you must show how the problem shall be solved and then prove that it is solved.
Theorem Is a statement of a mathematical truth that must be proved.
Corollary is a theorem that is a direct consequence of another theorem,