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Euclids Elements
A selection of illustrations from a few propositions in Books 1, 2 and 6 of Euclids ElementsTags: Euclid
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Euclid Book 1 Proposition 35
Two parallelograms on the same base and between the same parallel lines have the same area
Euclid Book 1 Proposition 36
Parallelograms which are on equal bases and in the same parallels are equal.
Euclid Book 1 Proposition 38
Triangles which are on equal bases and in the same parallels are equal to one another.
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.
Euclid Book 6 Proposition 1
Triangles and parallelograms which are under the same height are to one another as their bases
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.
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.
Euclid Book 6 Proposition 19
Similar triangles are to one another in the duplicate ratio of the corresponding sides.