# Study sets matching "term:geometry = euclid"

Study sets

Diagrams

Classes

Users

point

line

straight line

surface

that which has no part

breathless length ... --the extremities of a line are points

a line which lies evenly with the points on itself

that which has length and breadth only ... --the extremities of a…

point

that which has no part

line

breathless length ... --the extremities of a line are points

Postulate 1

Postulate 2

Postulate 3

Postulate 4

A straight line may be drawn from any one point to any other p…

A terminated line can be produced indefinitely

A circle can be drawn with any center and any radius

All right angles are equal to one another

Postulate 1

A straight line may be drawn from any one point to any other p…

Postulate 2

A terminated line can be produced indefinitely

point

line

straight line

surface

that which has no part

breathless length ... --the extremities of a line are points

a line which lies evenly with the points on itself

that which has length and breadth only ... --the extremities of a…

point

that which has no part

line

breathless length ... --the extremities of a line are points

#1: AB and CD are equally distant from…

Point D is center of the circle

Straight line joined from G to F and pr…

A line joined from F to G passes throug…

#1: Circle ABCD, AB and CD are equal straight lines... #2: Circle…

Circle ABC with point D inside it, and DA, DB, and DC fall upo…

Circles ABC, ADE touching internally at A, and F is the center…

Circles ABC, ADE touching at A externally, F the center of ABC…

#1: AB and CD are equally distant from…

#1: Circle ABCD, AB and CD are equal straight lines... #2: Circle…

Point D is center of the circle

Circle ABC with point D inside it, and DA, DB, and DC fall upo…

Egypt and Babylon

To survey land, to build things, and to…

Yes

Thales of Miletus

Two civilizations that excelled in geometry pre-Euclid

What were the typical three reasons for pre-Euclidean civiliza…

Did proofs exist before Euclid?

Who brought geometry to Greece?

Egypt and Babylon

Two civilizations that excelled in geometry pre-Euclid

To survey land, to build things, and to…

What were the typical three reasons for pre-Euclidean civiliza…

Postulate 1

Postulate 2

Postulate 3

Postulate 4

To draw a straight line from any point

To produce a finite straight line continuously in a straight l…

To describe a circle with any center and radius

All right angles are equal to one another

Postulate 1

To draw a straight line from any point

Postulate 2

To produce a finite straight line continuously in a straight l…

Prop 4

Prop 5

Prop 6

Prop 8

SAS

If a triangle is isosceles then the base angles are congruent.

If two angles in a triangle are congruent then the two opposit…

If three corresponding sides of one triangle are congruent to…

Prop 4

SAS

Prop 5

If a triangle is isosceles then the base angles are congruent.

Finish the quote by Euclid: "The laws o…

'geo' is from ge, the Greek word for

'metry' is from metria, the Greek word…

Why is Euclid considered to be the fath…

but the mathematical thoughts of God"

Earth

measurement

Because Euclid's book, Elements, is still the basis for what w…

Finish the quote by Euclid: "The laws o…

but the mathematical thoughts of God"

'geo' is from ge, the Greek word for

Earth

Postulate 1

Postulate 2

Postulate 3

Postulate 4

Any two points A and B determine a unique line segment AV

Any line segment may be extended

Given line segment AB, there is a circle with center A and rad…

All right angles are equal

Postulate 1

Any two points A and B determine a unique line segment AV

Postulate 2

Any line segment may be extended

1

2

3

4

A point is that of which there is no part

And a line is a length without breadth

And the extremities of a line are points

A straight-line is whatever lies evenly with points upon itself

1

A point is that of which there is no part

2

And a line is a length without breadth

Definition 1

Definition 2

Definition 4

Definition 10

A point is that which has no part.

A line is breadthless length.

A straight line is a line which lies evenly with the points on…

When a straight line set up on a straight line makes the adjac…

Definition 1

A point is that which has no part.

Definition 2

A line is breadthless length.

Common Notion 1

Common Notion 2

Common Notion 3

Common Notion 4

Things which equal the same thing are also equal to one another

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

If equals are subtracted from equals, then the reminders are e…

Things which coincide with one another are equal

Common Notion 1

Things which equal the same thing are also equal to one another

Common Notion 2

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

I.1

I.2

I.3

I.4

Construct an equilateral triangle on a given line.

Construct a line equal to a given line at a given point.

Cut a line equal to a given line from a given longer line.

If two triangles have two sets of sides and the angle between…

I.1

Construct an equilateral triangle on a given line.

I.2

Construct a line equal to a given line at a given point.

I.1

I.2

I.3

I.4

Given: straight line... To do: construct an equilateral triangle

Given: straight line and a point not on it... To do: construct a…

Given: two unequal lines... To do: cut off from the greater line…

Given: two triangles with side angle side... To prove: all sides…

I.1

Given: straight line... To do: construct an equilateral triangle

I.2

Given: straight line and a point not on it... To do: construct a…

Definition 1

Definition 2

Definition 3

Definition 4

A point is that which has no part

A line is a breadthless length

The extremities of a line are points

A straight line is a line which lies evenly with the points on…

Definition 1

A point is that which has no part

Definition 2

A line is a breadthless length

Geometry

Euclidean Geometry

Undefined terms

Point

word composed of two Greek terms, "geos" meaning earth and "me…

identifies a geometry which Euclid formalized and which was ad…

terms in Euclidean geometry which mathematicians consider only…

one of the undefined terms; it has only position and has no le…

Geometry

word composed of two Greek terms, "geos" meaning earth and "me…

Euclidean Geometry

identifies a geometry which Euclid formalized and which was ad…

Postulate 1

Postulate 2

Postulate 3

Postulate 4

You can draw a straight line from one point to another

You can produce a finite straight line continuously in a strai…

You can describe a circle with any center and distance

All right angles are equal to one another

Postulate 1

You can draw a straight line from one point to another

Postulate 2

You can produce a finite straight line continuously in a strai…

right angle

obtuse angle

straight angle

complimentary angles

angle that measures exactly 90 degrees.

angle that is >90 degrees and <180 degrees.

angle that measures exactly 180 degrees.

Angles whose measure adds up to 90 degrees.

right angle

angle that measures exactly 90 degrees.

obtuse angle

angle that is >90 degrees and <180 degrees.