Question

give examples for euclids axioms and postulates

Answer 1

Axioms:1. Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, then the wholes are equal. 3. If equals be subtracted from equals, then 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. Postulates :Postulate 1: It is possible to draw a straight line from any point to any other point. Postulate one suggests that if we have two points P and Q on a plane, then we can draw at least one line that can simultaneously pass through these two points. Euclid does not mention that only one line can pass through two points, but he assumes the same. Postulate 2: A terminated line can be produced indefinitely. This postulate can be considered as an extension of postulate 1. According to this postulate, we can make a different straight line from a given line by extending its points on either sides of the plane. . Postulate 3: It is possible to describe a circle with any centre and radius. According to Euclid, a circle is a plane figure consisting of a set of points that are equidistant from a reference point. It can be drawn with the knowledge of its centre and radius. Postulate 4: All right angles are equal to one another. A right angle is unique in the sense that it measures exactly 90°. Hence, all right angles are of the measure 90° irrespective of the lengths of their arms. Hence, all right angles are equal to each other.

Answer 2

Euclid's Geometry.

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☛ Some of Euclid's definitions :

▪️A point is that which has no part.
▪️A line is Breadthless length.
▪️The ends of a line segment are points.
▪️A straight line extends indefinitely in both the direction.
▪️A surface is that which has length and breadth only.
▪️A plane surface is a surface which lies evenly with the straight lines on itself.

☛ Euclid's Axioms ;

▪️Things which are equal to the same thing are equal to one another.
▪️If equals are added to equals, the wholes are equal.
▪️If equals are subtracted from equals the, reminders are equal.
▪️ Things which coincide with one another are equal to one another.
▪️The whole is greater than the part
▪️Things which are double of the same thing are equal to one another.
▪️Things which are halves of the same thing are equal to one another.

☛ Euclid's 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 into 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.