Class 9 Maths Euclid Geometry Undefined Terms

Undefined Terms:

If you see these 100 definitions, Euclid has used terms like part, length, breadth etc without defining it.  E.g A point is that which has no part. Here part is not defined.

Even if we define Part as something that occupied area, again we have to define new term; in this case it is area. To define, many things have to be defined & the chain is endless. Thus mathematicians agreed to leave some geometric terms as undefined. However we do have intuitive feeling for the geometric concepts f point with the definition provided by Euclid. So we represent point as a dot, even though dot has some dimension.  Similar issues were there with terms length & breadth & thus these terms were not defined as well.  Thus we take point, line & plane as undefined terms.

1. A point is that which has no part.
2. A line is breathless
3. A surface is that which has length and breadth
4. A plane surface is a surface which lies evenly with the straight lines on itself.

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