# Study sets matching "term:geometry = euclid"

Study sets

Diagrams

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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

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

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…

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

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.

Describe the methods and procedures of…

Explain the important contributions to…

Commensurable quantities

In commensurable quantities

Rope was the main instrument. ... Documented on clay tablets and…

Number theory... Parallel lines... Sum of the angles in a triangle... P…

Rational

Irrational

Describe the methods and procedures of…

Rope was the main instrument. ... Documented on clay tablets and…

Explain the important contributions to…

Number theory... Parallel lines... Sum of the angles in a triangle... P…

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

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

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.

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

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

II.Definition 1

II.Definition 2

III.Definition 1

III.Definition 2

Any rectangular parallelogram is said to be contained by the t…

And in any parallelogrammic area let any one whatever of the p…

Equal circles are those whose diameters are equal, or whose ra…

A straight line is said to touch a circle which, meeting the c…

II.Definition 1

Any rectangular parallelogram is said to be contained by the t…

II.Definition 2

And in any parallelogrammic area let any one whatever of the p…

point

Line

plane

Collinear

a point names a location it has NO SIZE... Name: use capital let…

A line is a straight path that has NO THICKNESS and EXTENDS FO…

A plane is a flate surface that has NO THICKNESS, and EXTENDS…

Points that lie on the same line.

point

a point names a location it has NO SIZE... Name: use capital let…

Line

A line is a straight path that has NO THICKNESS and EXTENDS FO…

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…

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…

a = a

If a = b... Then b = a

If a = b, and b = c ... Then a = c

If a = b ... Then a + c = b + c

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Addition Property of Equality

a = a

Reflexive Property of Equality

If a = b... Then b = a

Symmetric Property of Equality

What makes a good definition?

Postulate vs Common Notion

surface

obtuse angle

genus and specific difference

both truths that don't need to be proved... postulates used speci…

that which has length and breadth only

an angle greater than a right angle

What makes a good definition?

genus and specific difference

Postulate vs Common Notion

both truths that don't need to be proved... postulates used speci…

Archimedes (p.297)

Herodotus (p.298)

Thucydides (p.298)

Hippocrates (p.299)

the renowned Greek thinker who discovered the principle of dis…

the Greek historian who wrote about the history of the ancient…

the great Greek historian and writer

the Greek doctor who taught that disease causes illness; known…

Archimedes (p.297)

the renowned Greek thinker who discovered the principle of dis…

Herodotus (p.298)

the Greek historian who wrote about the history of the ancient…