# Study sets matching "term:geometry = euclid"

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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

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

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…

#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…

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…

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

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.

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.

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

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.

Who was Euclid?

How much do we know about Euclid's life?

Where do the few historical references…

What does Proclus state regarding Eucli…

A Greek mathematician, often referred to as the "Father of Geo…

Very few original references to Euclid survive, so little is k…

The few historical references to Euclid were written centuries…

According to Proclus, Euclid belonged to Plato's "persuasion"…

Who was Euclid?

A Greek mathematician, often referred to as the "Father of Geo…

How much do we know about Euclid's life?

Very few original references to Euclid survive, so little is k…

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…

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

Euclid

Euclid's work

The Elements Book 1

The Elements Book 2

Father of Geometry... -possible his work isnt really his

-Proofs are not necessarily his ... -Most famous mathematical wor…

Definitions of basic terms, and 5 axioms and 5 postulates

-"Basic Figures"... -All theorems in this book are actually const…

Euclid

Father of Geometry... -possible his work isnt really his

Euclid's work

-Proofs are not necessarily his ... -Most famous mathematical wor…

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.