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Math: Geometry: Euclid's Elements Book I, Definitions

Euclid's Book 1 begins with 23 definitions — such as point, line, and surface. Following a visual illustration.

Euclid Elements Book I, 23 definitions

The definitions presented in Book I lay the groundwork for all of Euclidean geometry. A point is the most basic geometric object, and lines, planes, and angles are constructed from points. By defining these basic concepts, Euclid was able to develop a systematic and logical approach to understanding geometry.

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     The first few definitions are:

  • Definition 1. A point is that which has no part.

  • Definition 2. A line is breadthless length.

  • Definition 3. The extremities of a line are points.

  • Definition 4. A straight line is a line which lies evenly with the points on itself.

Poem: Euclid's Elements Book I, Definitions

In Euclid's book, so ancient and grand,
The Elements of Geometry, so carefully planned.
In Book 1, the foundations were laid,
With definitions and axioms, to never evade.

A point, as before, has no size or space,
A single location, in a certain place.
A line is a length, without any breadth,
Made of points, in a straight path ahead.

A straight line, so simple and plain,
Is one that, on itself, does never change.
A surface, like a flat, infinite sheet,
Is made of lines, and has no depth to meet.

A plane, too, is without any height,
A surface that extends, with infinite might.
An angle, by two lines, is always formed,
Measuring the space, between them adorned.

A right angle, at ninety degrees,
Is formed by lines, that form a T with ease.
Parallel lines, are those that never meet,
No matter how far, they always retreat.

A triangle, of three sides and three angles,
Is the simplest of polygons, with no tangles.
A square, with sides equal and right angles at four,
Has area, of sides multiplied for sure.

These definitions, so clear and precise,
Form the foundation, of geometry devices.
And in Euclid's Elements, we find,
A timeless treasure, for our curious mind.

Euclid Elements Book I, 23 definitions

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