# Study sets matching "term:geometry = euclid"

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

Axiom1

Axiom2

Axiom3

Axiom4

Things which are equal to the same thing are equal to one anot…

If Equals are added to equals,the wholes are equal

If equals are subtracted from equals,the remainders are equal

Things which coincide with one another are equal to one another

Axiom1

Things which are equal to the same thing are equal to one anot…

Axiom2

If Equals are added to equals,the wholes are equal

Point

Line

Straight line

Surface

That which has no part. The extremities of a line.

Breadthless length. The extremities of a surface.

A line which lies evenly with the points on itself.

That which has length and breadth only.

Point

That which has no part. The extremities of a line.

Line

Breadthless length. The extremities of a surface.

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…

Postulate1

Postulate2

Postulate3

Postulate4

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 centre and any radius

All right angles are equal to one another

Postulate1

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

Postulate2

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.

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.

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.

Midpoint

Slope

Distance

Parallel lines

The middle point of a line segment

Thus describes the direction and steepness of a line.

This describes the length of a segment or how far apart an obj…

Two lines that never meet.

Midpoint

The middle point of a line segment

Slope

Thus describes the direction and steepness of a line.

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

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…

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

line segment

ray

A location; it has no dimension. Represented by a dot.

A straight path that continues forever in both directions; has…

Part of a line; has two endpoints.

Part of a line; has one endpoint and the other end goes on for…

point

A location; it has no dimension. Represented by a dot.

line

A straight path that continues forever in both directions; has…

Postulate 1

Postulate 2

Postulate 3

Postulate 4

To draw a straight line from any point to any point

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

To describe a circle with any center and distance

That all right angles are equal to each other

Postulate 1

To draw a straight line from any point to any point

Postulate 2

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

Proposition 1

Proposition 2

Proposition 3

Proposition 4

If there are two straight lines, and one of them is cut into a…

If a straight line is cut at random, then the sum of the recta…

If a straight line is cut at random, then the rectangle contai…

If a straight line is cut at random, the square, on the whole,…

Proposition 1

If there are two straight lines, and one of them is cut into a…

Proposition 2

If a straight line is cut at random, then the sum of the recta…

Book 1

Book 2

Book 3

Book 4

-triangles, parallelograms, parallel lines... -1.47 Pythagorean…

-Divided lines and areas they give rise to... -straight lines div…

-Circles ... -diameter, tangent, angles in circles, segments of c…

-Regular polygons and their relationship with circles... -inscrib…

Book 1

-triangles, parallelograms, parallel lines... -1.47 Pythagorean…

Book 2

-Divided lines and areas they give rise to... -straight lines div…

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…