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Euclids Elements

A selection of illustrations from a few propositions in Books 1, 2 and 6 of Euclids Elements

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Euclid Book 1 Proposition 35
Euclid Book 1 Proposition 35
Two parallelograms on the same base and between the same parallel lines have the same area

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Euclid Book 1 Proposition 36
Euclid Book 1 Proposition 36
Parallelograms which are on equal bases and in the same parallels are equal.

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Euclid Book 1 Proposition 38
Euclid Book 1 Proposition 38
Triangles which are on equal bases and in the same parallels are equal to one another.

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Euclid 1:47
Euclid 1:47
Euclid's proof of the Pythagorean Theorem is illustrated.

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Euclid Book 2 Proposition 11
Euclid Book 2 Proposition 11
To cut a given straight line so that the rectangle contained by the whole and one of the segments is equal to the square on the remaining segment.

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Euclid Book 6 Proposition 1
Euclid Book 6 Proposition 1
Triangles and parallelograms which are under the same height are to one another as their bases

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Euclid Book 6 Proposition 8
Euclid Book 6 Proposition 8
If in a right-angled triangle a perpendicular is drawn from the right angle to the base, the triangles adjoining the perpendicular are similar both to the whole and to one another.

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Euclid Book 6 Proposition 15
Euclid Book 6 Proposition 15
In equal triangles which have one angle equal to one angle the sides about the angle are reciprocally proportional; and those triangles which have one angle equal to one angle, and in which the sides about the equal angle are reciprocally proportional are equal.

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Euclid Book 6 Proposition 19
Euclid Book 6 Proposition 19
Similar triangles are to one another in the duplicate ratio of the corresponding sides.

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Euclid Book 6 Proposition 31
Euclid Book 6 Proposition 31
In right angled triangles, the figure on the side subtending the right angle is equal to the similar and similarly described figures on the sides containing the right angle

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