Sentences with PARALLEL-AXIOM
Check out our example sentences below to help you understand the context.Sentences
1
"Euclid's parallel axiom states that two parallel lines never intersect."
2
"The parallel axiom is one of the five postulates in Euclidean geometry."
3
"In non-Euclidean geometries, the parallel axiom may not hold true."
4
"The parallel axiom can be used to prove many geometric theorems."
5
"Euclid's parallel axiom assumes that there is only one line parallel to a given line through an external point."
6
"The parallel axiom is fundamental to the study of geometry."
7
"The parallel axiom is sometimes referred to as the parallel postulate."
8
"The parallel axiom is essential in establishing the properties of parallel lines."
9
"The parallel axiom allows the construction of parallel lines by using a compass and straightedge."
10
"Euclid's parallel axiom is a statement about the relationship between lines and angles."
11
"The validity of the parallel axiom was debated by mathematicians for centuries."
12
"Many attempts were made to prove the parallel axiom from other axioms but were unsuccessful."
13
"The parallel axiom is independent of the other axioms in Euclidean geometry."
14
"Euclid's parallel axiom has been widely accepted as a basic assumption in geometry."
15
"The parallel axiom is a starting point for reasoning about parallel lines."
16
"The parallel axiom allows for the construction of geometric objects such as squares and rectangles."
17
"In hyperbolic geometry, the parallel axiom is replaced by a different assumption."
18
"The parallel axiom is a statement about the behavior of lines in space."
19
"The parallel axiom is related to the concept of transversals and interior angles."
20
"Euclid's parallel axiom is one of the oldest surviving mathematical axioms."
1
"Euclid's parallel axiom states that given a line and a point not on that line, there exists exactly one line parallel to the given line that passes through the point."
2
"The parallel axiom is one of the five postulates in Euclidean geometry."
3
"The concept of parallel axiom is fundamental in geometry."
4
"The parallel axiom is sometimes referred to as the fifth postulate."
5
"Euclidean geometry assumes the truth of the parallel axiom."
6
"The parallel axiom allows us to define parallel lines."
7
"The parallel axiom is often contrasted with non-Euclidean geometries."
8
"Euclid's parallel axiom has been a subject of study for centuries."
9
"The parallel axiom is independent of the other axioms in Euclidean geometry."
10
"The parallel axiom has implications for the properties of triangles and circles."
