EXERCISE 5.1 Solution| INTRODUCTION TO EUCLID’S GEOMETRY

CHAPTER 5
EXERCISE 5.1

INTRODUCTION TO EUCLID’S GEOMETRY
‘geometry’

Euclid (325 BCE – 265 BCE)

Truncated Pyramid

Thales
(640 BCE – 546 BCE)

Euclid’s Definitions, Axioms and Postulates
Euclid’s axioms, not in his order, are given below :
(1) Things which are equal to the same thing are equal to one another.
(2) If equals are added to equals, the wholes are equal.
(3) If equals are subtracted from equals, the remainders are equal.
(4) Things which coincide with one another are equal to one another.
(5) The whole is greater than the part.
(6) Things which are double of the same things are equal to one another.
(7) Things which are halves of the same things are equal to one another.

Euclid’s five postulates
Postulate 1 : A straight line may be drawn from any one point to any other point.
Postulate 2 : A terminated line can be produced indefinitely.

Postulate 3 : A circle can be drawn with any centre and any radius.

Postulate 4 : All right angles are equal to one another.


Postulate 5 : 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, then the
two straight lines, if produced indefinitely, meet on that side on which the sum of
angles is less than two right angles.
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