Introduction to Euclid's Geometry
Definitions in Euclidean Geometry:
During Euclid’s period, the notations of points, line, plane (or surface), and so on were
derived from what was seen around them.
Some of the definitions given in him are as follows:
o A point is that which has no part.
o A line is breadth-less length.
o A straight line is one that lies evenly with the points on itself.
o A surface is that which has length and breadth only.
o The edges of a surface are lines.
o A plane surface is one that lies evenly with the straight lines on itself.
Euclid’s axioms:
Axioms are the assumptions that are obvious universal truths, but are not proved. These
are used throughout mathematics and are not specifically linked to geometry.
Some of Euclid’s axioms are as follows:
o Things that are equal to the same things are equal to one another.
o If equals are added to equals then the wholes are also equal.
o If equals are subtracted from equals then the remainders are equal.
o Things that coincide with one another are equal to one another.
o The whole is greater than the part.
o Things that are double of the same things are equal to one another.
o Things that are halves of the same things are equal to one another.
Euclid's postulates:
Postulates are also universal truths that need not be proved. Euclid used the term
“postulate” for the assumptions that were specific to geometry.
Definitions in Euclidean Geometry:
During Euclid’s period, the notations of points, line, plane (or surface), and so on were
derived from what was seen around them.
Some of the definitions given in him are as follows:
o A point is that which has no part.
o A line is breadth-less length.
o A straight line is one that lies evenly with the points on itself.
o A surface is that which has length and breadth only.
o The edges of a surface are lines.
o A plane surface is one that lies evenly with the straight lines on itself.
Euclid’s axioms:
Axioms are the assumptions that are obvious universal truths, but are not proved. These
are used throughout mathematics and are not specifically linked to geometry.
Some of Euclid’s axioms are as follows:
o Things that are equal to the same things are equal to one another.
o If equals are added to equals then the wholes are also equal.
o If equals are subtracted from equals then the remainders are equal.
o Things that coincide with one another are equal to one another.
o The whole is greater than the part.
o Things that are double of the same things are equal to one another.
o Things that are halves of the same things are equal to one another.
Euclid's postulates:
Postulates are also universal truths that need not be proved. Euclid used the term
“postulate” for the assumptions that were specific to geometry.
