Euclidean geometry

Thales of miletus

calculated the height of pyramids and distance of ships from the shore. credited with the first use of deductive reasoning applied to geometry

plato of athens

founded the academy in athens, inscribed on its doors “let no one enter who is ignorant of geometry”

Alexandria, egypt

library and museum of alexandria

Eratosthenes of cyrene

best known for calculating the circumference of the earth

archimedes of syracuse

used the method of exhaustion to calculate areas and volumes of solids

euclid’s first notion

things that are equal to the same thing are equal

euclid’s second notion

if equals are added to equals, then the wholes are equal

euclid’s third notion

if equals are subtracted from equals, then the remainders are equal

euclid’s fourth notion

things that coincide with one another are equal to one another

euclid’s fifth notion

the whole is greater than the part

postulate 1

a straight line can be drawn from any point to any point

postulate 2

a finite straight line can be produced continuously in a straight line

postulate 3

a circle may be drawn with any point as center and any distance as radius

postulate 4

all right angles are equal to one another

postulate 5

if a transversal falls on two lines such that the interior angles on one side of the transversal are less than two right angles, then the lines meet on that side on which the interior angles are less than two right angles

true

a point has no dimension

true

a line is 1-dimensional and lines are straight

true

a plane is 2-dimensional and it is flat

triangle inequality

the sum of two sides must be equal to or greater than the last side

congruence of triangles

two triangles are congruent if and only if they have exactly the same size and shape

sss

three corresponding sides are congruent

sas

two corresponding sides and the angle between them are congruent

asa

two corresponding angles and the side they include are congruent

similar triangles

two triangles are similar if they have the same shape

posidonius

two parallel lines are equidistant

proclus

if a line intersects one of two parallel lines, then it intersects the other

legendre

the sum of the angles of a triangle is 180

john playfair

through a point p not on a line l, there exists exactly one line parallel to l