Euclid's Axioms and Postulates ˚ ༘ 🦕𖦹⋆｡˚

A set for Shormann Lesson 9 - happy studying!

Axiom 1

things that are equal to the same thing are also equal to one another (if a=c and b=c, then a=b)

Axiom 2

if equals are added to equals, the wholes are equal (if a=b and c=d, then a+c=b+d)

Axiom 3

if equals are subtracted from equals, the remainders are equal (if a=b and c=d, then a-c=b-d)

Axiom 4

things which coincide with one another are equal to one another (a=a)

Axiom 5

the whole is greater than the part

Postulate 1

two, and only two points determine one unique straight line

Postulate 2

a straight line extends an indefinite length in either direction

Postulate 3

a circle may be drawn with any given center and any given radius

Postulate 4

all right angles are equal to one another

Postulate 5

given a line N and a point P not on that line, there exists in the plane of P and N and through P only one line M, which does not intersect line N