Transcript JM-PPT1-EUCLIDS

EUCLID’ S GEOMETRY
• A point has no part or dimension.
• A line has no breadth.
• Ends of a line are points.
• A straight line is a line which lies evenly with the
points on itself.
• A surface has length and breadth only.
• Edges of a surface are lines.
• A plane surface is a surface which lies evenly with the
straight lines on itself.
Euclid’s
Definitions
EUCLID’ S GEOMETRY
Axioms or
Postulates-
Theorems-
• are basic facts which are
obvious
• universal truths. They are
not proved.
• are statements which are proved , using
definitions, axioms, previously proved
statements and deducting reasoning.
• Are axioms related to geometry.
EUCLID’ S GEOMETRY
EUCLID’S
AXIOMS
• Things that are equal to the same thing are equal to
each other.
If, a=b and b=c then a=c
• If equals are added to equals then wholes are equal.
If a=b then a+c = b+c
• If equals are subtracted from equals then remainders
are equals.
If a=b then a-c = b-c
• Things which coincide with each other are equal to one
another.
• The whole is greater than the part.
• Things which are double or halves of the same thing
are equal.
If a = b then 2a= 2b and (a/2) = (b/2)
• If first thing is greater than the secon and second is
greater than the third , then first is greater than the
third.
If a>b>c then a>c
EUCLID’ S GEOMETRY
• A line contains infinitely many points.
• Through a given point there pass
infinitely many lines.
• Given two points A and B, there is one
and only one line that contains both
the points.
EUCLID’S INCIDENCE • Things which are double of same
AXIOMS
things are equal to one another.
• Things which are halves of the same
things are equal to one another.
EUCLID’ S GEOMETRY
EUCLID’S
POSTULATES
• A straight line may be drawn from any one
point to another point.
• A terminated line may be produced
indefinitely.
• A circle can be drawn with any center and
any radius.
• All right angles are equal to one another
• If a straight line falling on two straight
lines makes the interior angles on the
same side of it taken together less than
two right angles, if produced indefinitely,
meet on that side on which the sum of
angles is less than two right angles.
EUCLID’ S GEOMETRY
EUCLID’ S GEOMETRY
EUCLID’ S GEOMETRY
Answer-1
EUCLID’ S GEOMETRY
EUCLID’ S GEOMETRY
Answer-2
EUCLID’ S GEOMETRY
Answer-2 contd…..
EUCLID’ S GEOMETRY
Answer-3
EUCLID’ S GEOMETRY
Answer-4
EUCLID’ S GEOMETRY
Answer-5
EUCLID’ S GEOMETRY
Answer-5 contd….
EUCLID’ S GEOMETRY
Answer- 6
EUCLID’ S GEOMETRY
Answer- 7
EUCLID’ S GEOMETRY
EUCLID’ S GEOMETRY
EUCLID’ S GEOMETRY