Study sets matching "term:geometry = euclid"

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Study sets matching "term:geometry = euclid"

29 terms
EUCLIDS GEOMETRY
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…
point
that which has no part
line
breathless length ... --the extremities of a line are points
7 terms
Euclids geometry
Axiom1
Axiom2
Axiom3
Axiom4
Things which are equal to the same thing are equal to one ano…
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 ano…
Axiom2
If Equals are added to equals,the wholes are equal
Geometry: Euclid's Definitions
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.
29 terms
Geometry: Euclid Book 1
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…
point
that which has no part
line
breathless length ... --the extremities of a line are points
9 terms
Geometry Euclid Quiz Study
#1: AB and CD are equally distant from…
Point D is center of the circle
Straight line joined from G to F and p…
A line joined from F to G passes throu…
#1: Circle ABCD, AB and CD are equal straight lines... #2: Circl…
Circle ABC with point D inside it, and DA, DB, and DC fall up…
Circles ABC, ADE touching internally at A, and F is the cente…
Circles ABC, ADE touching at A externally, F the center of AB…
#1: AB and CD are equally distant from…
#1: Circle ABCD, AB and CD are equal straight lines... #2: Circl…
Point D is center of the circle
Circle ABC with point D inside it, and DA, DB, and DC fall up…
5 terms
Euclids geometry-postulates
Postulate1
Postulate2
Postulate3
Postulate4
A straight line may be drawn from any one point to any other…
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…
Postulate2
A terminated line can be produced indefinitely
Geometry Euclid Props 4-22
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 opposi…
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.
The Deductive Method in Euclid's Geometry
first postulate
second postulate
third postulate
fourth postulate
To draw a straight line from any point to any point.
To produce a finite straight line continuously in a straight…
To describe a circle with any center and distance.
That all right angles are equal to one another.
first postulate
To draw a straight line from any point to any point.
second postulate
To produce a finite straight line continuously in a straight…
25 terms
GEOMETRY - Chapter 1: Euclid's Elements
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 o…
When a straight line set up on a straight line makes the adja…
Definition 1
A point is that which has no part.
Definition 2
A line is breadthless length.
Euclid Geometry Ennunciations Book 1 (I.1-I.41)
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.
8 terms
Euclid
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 ob…
Two lines that never meet.
Midpoint
The middle point of a line segment
Slope
Thus describes the direction and steepness of a line.
31 terms
Geometry
Geometry
Euclidean Geometry
Undefined terms
Point
word composed of two Greek terms, "geos" meaning earth and "m…
identifies a geometry which Euclid formalized and which was a…
terms in Euclidean geometry which mathematicians consider onl…
one of the undefined terms; it has only position and has no l…
Geometry
word composed of two Greek terms, "geos" meaning earth and "m…
Euclidean Geometry
identifies a geometry which Euclid formalized and which was a…
13 terms
Euclid
Euclid
Mathematics
Geo-
-metry
"The laws of nature are but the mathematical thoughts of god.…
Underpins all of the laws of nature.
Earth
Measure
Euclid
"The laws of nature are but the mathematical thoughts of god.…
Mathematics
Underpins all of the laws of nature.
31 terms
Geometry
Geometry
Euclidean Geometry
Undefined terms
Point
word composed of two Greek terms, "geos" meaning earth and "m…
identifies a geometry which Euclid formalized and which was a…
terms in Euclidean geometry which mathematicians consider onl…
one of the undefined terms; it has only position and has no l…
Geometry
word composed of two Greek terms, "geos" meaning earth and "m…
Euclidean Geometry
identifies a geometry which Euclid formalized and which was a…
12 terms
Euclid
what does geometry mean?
Euclid wrote ___________
Euclid is from what country?
Euclid is know as _____________
Geos = earth ... Metron = meausre
Elements
Greece
"Father of Geometry"
what does geometry mean?
Geos = earth ... Metron = meausre
Euclid wrote ___________
Elements
13 terms
Euclid's Elements
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 di…
-Circles ... -diameter, tangent, angles in circles, segments of…
-Regular polygons and their relationship with circles... -inscri…
Book 1
-triangles, parallelograms, parallel lines... -1.47 Pythagorean…
Book 2
-Divided lines and areas they give rise to... -straight lines di…
Geometry Final Review
point
line
line segment
ray
A location; it has no dimension. Represented by a dot.
A straight path that continues forever in both directions; ha…
Part of a line; has two endpoints.
Part of a line; has one endpoint and the other end goes on fo…
point
A location; it has no dimension. Represented by a dot.
line
A straight path that continues forever in both directions; ha…
31 terms
Geometry Unit 1
Geometry
Euclidean Geometry
Undefined terms
Point
word composed of two Greek terms, "geos" meaning earth and "m…
identifies a geometry which Euclid formalized and which was a…
terms in Euclidean geometry which mathematicians consider onl…
one of the undefined terms; it has only position and has no l…
Geometry
word composed of two Greek terms, "geos" meaning earth and "m…
Euclidean Geometry
identifies a geometry which Euclid formalized and which was a…
33 terms
Euclid's Book 1 Definitions, Postulates, and Common Notions
D1. Point
D2. Line
D3. Extremities of lines
D4. Straight line
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 o…
D1. Point
A point is that which has no part.
D2. Line
A line is a breadthless length.
Geometry
Geometry
Euclidean Geometry
Undefined terms
Point
word composed of two Greek terms, "geos" meaning earth and "m…
identifies a geometry which Euclid formalized and which was a…
terms in Euclidean geometry which mathematicians consider onl…
one of the undefined terms; it has only position and has no l…
Geometry
word composed of two Greek terms, "geos" meaning earth and "m…
Euclidean Geometry
identifies a geometry which Euclid formalized and which was a…
Mathematicians
Geometry
Analytic Geometry
Calculus
Trigonometry
Euclid
Descartes
Leibniz
Hipparchus
Geometry
Euclid
Analytic Geometry
Descartes
31 terms
Geometry
Geometry
Euclidean Geometry
Undefined terms
Point
word composed of two Greek terms, "geos" meaning earth and "m…
identifies a geometry which Euclid formalized and which was a…
terms in Euclidean geometry which mathematicians consider onl…
one of the undefined terms; it has only position and has no l…
Geometry
word composed of two Greek terms, "geos" meaning earth and "m…
Euclidean Geometry
identifies a geometry which Euclid formalized and which was a…
Geometry
Geometry
Euclidean Geometry
Undefined terms
Point
word composed of two Greek terms, "geos" meaning earth and "m…
identifies a geometry which Euclid formalized and which was a…
terms in Euclidean geometry which mathematicians consider onl…
one of the undefined terms; it has only position and has no l…
Geometry
word composed of two Greek terms, "geos" meaning earth and "m…
Euclidean Geometry
identifies a geometry which Euclid formalized and which was a…
33 terms
Definitions, Postulates, and Common Notions by Euclid
1. a point
2. a line
3. ends (extremities) of a line
4. a straight line
A point is that which has no parts.
A line is length without width.... [We normally today use the te…
The ends of a line are points.
A straight line is a line that lies symmetrically with the po…
1. a point
A point is that which has no parts.
2. a line
A line is length without width.... [We normally today use the te…
Euclid Book 1: Definitions, Postulates, & Common Notions
Defintion 1- Point
Defintion 2- Line
Definition 3- Points
Definition 4- Straight Line
Has no part
Has no width
Extremities of a line
Line wich lies evenly with the points on itself
Defintion 1- Point
Has no part
Defintion 2- Line
Has no width
26 terms
Geometry
father of Geometry
segment addition postulate
Postulate 1:1
Point
Euclid
If A, B, C, are collinear and B is between A and C, then AB+…
through any 2 points there is exactly one line
A location in the coordinate plane. Symbol- A
father of Geometry
Euclid
segment addition postulate
If A, B, C, are collinear and B is between A and C, then AB+…
16 terms
Math Unit 1 Euclid
Postulate 1
Postulate 2
Postulate 3
Postulate 4
a straight line can be drawn from any point to any point
a finite straight line can be produced continuously in a stra…
a circle may be described with any center and distance
all right angles are equal to one another
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 stra…
Geometry: History of Geometry
geometry
where geometry originated
father of geometry
why known as father of geometry
to measure the earth
greece
euclid
organized everything
geometry
to measure the earth
where geometry originated
greece
48 terms
Guebert - Geometry Honors Chapter 1a
Undefined Terms
Angle
Acute Angle
Euclid
point, line, plane
the union of two rays with a common endpoint
An angle whose measure is less than 90º
The father of Geometry, wrote "The Elements"
Undefined Terms
point, line, plane
Angle
the union of two rays with a common endpoint
47 terms
Unit 2 - Coordinate Geometry and Transformations
Composition of Transformations
Congruent segments
Degree of Rotation
Dilation
combination of two or more transformations
line segments whose lengths are equal
number of degrees a figure is rotated about the point (center…
a similarity transformation in which a figure is enlarged or…
Composition of Transformations
combination of two or more transformations
Congruent segments
line segments whose lengths are equal
Geometry
Geometry
Geo+metria
Thales
Pythagoras
Branch of mathematics that deals with the sizes, shapes, posi…
Earth+measurement
Brought geometry from egypt to greece
Most famous geometer
Geometry
Branch of mathematics that deals with the sizes, shapes, posi…
Geo+metria
Earth+measurement
31 terms
Geometry
Geometry
Euclidean Geometry
Undefined terms
Point
word composed of two Greek terms, "geos" meaning earth and "m…
identifies a geometry which Euclid formalized and which was a…
terms in Euclidean geometry which mathematicians consider onl…
one of the undefined terms; it has only position and has no l…
Geometry
word composed of two Greek terms, "geos" meaning earth and "m…
Euclidean Geometry
identifies a geometry which Euclid formalized and which was a…
12 terms
CSET II Geometry
Surface
Edges
Plane Surface or (Plane)
Plane angle
Something with two dimensions
If a surface has edges then the edges (or boundaries) are lin…
A surface which lies evenly with the straight lines on itself…
The inclination to one another of two lines in a plane which…
Surface
Something with two dimensions
Edges
If a surface has edges then the edges (or boundaries) are lin…
Geometry Test 2
Definition
Postulate
Theorem
Deductive Reasoning
The meaning of something
A statement that is assumed proven.
A statement that has proof to back it up.
Proven statements based of other proven statements.
Definition
The meaning of something
Postulate
A statement that is assumed proven.
18 terms
The Alexandria School: Euclid Part 1
The Hellenistic Period 300 B.C.E-100 B…
Alexander the Great
The Museum... Many people went when the f…
Euclid
What was the most productive periods in history for math?
Who founded Alexandria, Egypt?
What was the famous school in Alexandria?
Who studied at the famous school in Alexandria?
The Hellenistic Period 300 B.C.E-100 B…
What was the most productive periods in history for math?
Alexander the Great
Who founded Alexandria, Egypt?
14 terms
geometry
geometry
Euclid
three undefined terms of geometry
point
study of shapes, means the measure of the Earth.
lived 500 BCE, father of geometry, axiomatic method
point... line... plane
no size... represented by a dot,•A
geometry
study of shapes, means the measure of the Earth.
Euclid
lived 500 BCE, father of geometry, axiomatic method
25 terms
Jacob's Geometry 3rd edition ch 1 sections 1-5
line segment
collinear
noncollinear
concurrent
a part of a line bounded by 2 endpoints
points that are on the same line
points that are not on the same line
lines that contain the same point
line segment
a part of a line bounded by 2 endpoints
collinear
points that are on the same line
9 terms
Geometry vocab
Perpendicular
Hypotenuse
Euclid
Vertical
intersects at right angles
The long side of right angles
Father of plane geometry
Columns in the caf
Perpendicular
intersects at right angles
Hypotenuse
The long side of right angles
Geometry quotes
"The Knowledge of which geometry aims…
"There is no royal road to geometry"
"... being perpetually charmed by his…
"Which was to be proved."
Plato, The Republic
Euclid
Plutarch, The life of Archimedes
Euclid, The elements
"The Knowledge of which geometry aims…
Plato, The Republic
"There is no royal road to geometry"
Euclid
36 terms
Ch 3.1-4.2 Review
Ways to prove lines parallel (7 of them)
corresponding angles
Alternative Interior angles
Alternative Exterior Angles
converse corresponding angle post... converse alt interior angle…
1 & 5,... 3 & 7,... 2 & 6, ... 4 & 8
3 & 6... 4 & 5
1 & 8... 2 & 7
Ways to prove lines parallel (7 of them)
converse corresponding angle post... converse alt interior angle…
corresponding angles
1 & 5,... 3 & 7,... 2 & 6, ... 4 & 8
Geometry cardz
Point
Line
Plane
Euclid
No dimention
One demention
Two dementions
The man who event ed the geometry we do.
Point
No dimention
Line
One demention
82 terms
Morrissey Honors Geometry Vocab
theorem
postulate
corollary
parallel
...
...
...
...
theorem
...
postulate
...
53 terms
Geometry
Who is the "father of geometry"
What did Euclid write?
Point
Line
Euclid of Alexandria
The Elements
Indication of an exact location. A point has location and not…
A straight, unbroken set of points that goes on forever. It h…
Who is the "father of geometry"
Euclid of Alexandria
What did Euclid write?
The Elements
13 terms
geometry
whole numbers
no. of arith.
natural numbers
integers
0,1,2,3...
0 and on
1,2,3...
-2,-1,0,1,2...
whole numbers
0,1,2,3...
no. of arith.
0 and on
Famous People, Famous Discoveries
Descartes
Galileo
Shakespeare
Euclid
Philosophy
Astronomy
Drama
Geometry
Descartes
Philosophy
Galileo
Astronomy
51 terms
Honors Geometry Chapter 1
Point
Line
Plane
Euclid
Names location, has no dimensions (0 dimensional)
Straight path that goes forever in both directions, has no wi…
Flat surface that extends forever, has no thickness (2 dimens…
Father of geometry
Point
Names location, has no dimensions (0 dimensional)
Line
Straight path that goes forever in both directions, has no wi…
13 terms
middle school geometry vocabulary
Euclid
point
line
line segment
Greek mathematician who organized known geometry in the 4th c…
shown by a dot, it is a location in space
extends infinitely
part of a line with a beginning and ending point
Euclid
Greek mathematician who organized known geometry in the 4th c…
point
shown by a dot, it is a location in space
Geometry Final Exam Review - Basics
point
line
line segment
ray
A location; it has no dimension. Represented by a dot.
A straight path that continues forever in both directions; ha…
Part of a line; has two endpoints.
Part of a line; has one endpoint and the other end goes on fo…
point
A location; it has no dimension. Represented by a dot.
line
A straight path that continues forever in both directions; ha…
Geometry (Chapter 1)
net
geometry
Euclid
Three Undefined Terms
a two-dimensional diagram that can be folded to form a three-…
- the measure of the earth... - the study of shapes
@ 500 B.C.E.... - father of geometry... - axiomatic era
- point... - line... - plane
net
a two-dimensional diagram that can be folded to form a three-…
geometry
- the measure of the earth... - the study of shapes
Euclid's proof of the Pythagorean theorem
Eudoxus
Eudoxus theory of proportion
Eudoxus theory of Exhaustion
Alexander the Great
geometry and astronomy (has craters name after self)
a,b,c,,d where a/b=c/d... (ma>nb) implies (mc>nd)... (ma=nb)…
-areas of a circle are to one another as the squares of their…
-expanded Greece in 13 years ... -names at least 70 cities after…
Eudoxus
geometry and astronomy (has craters name after self)
Eudoxus theory of proportion
a,b,c,,d where a/b=c/d... (ma>nb) implies (mc>nd)... (ma=nb)…
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