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Proposition: 1.35: Parallelograms On the Same Base and On the Same Parallels

Euclid's Formulation

Parallelograms which are on the same base and between the same parallels are equal¹ to one another.

• Let $ABCD$ and $EBCF$ be parallelograms on the same base $BC$, and between the same parallels $AF$ and $BC$.
• I say that $ABCD$ is equal to parallelogram $EBCF$.

Modern Formulation

Parallelograms on the same base (\(\overline{BC}\)) and between the same parallels (\(\overline{AF}\), \(\overline{BC}\)) are equal in area.

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1 2 3

Thank you to the contributors under CC BY-SA 4.0!

Github:

non-Github:

@Calahan

@Casey

@Fitzpatrick

References

Adapted from CC BY-SA 3.0 Sources:

1. Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014

Adapted from (Public Domain)

1. Casey, John: "The First Six Books of the Elements of Euclid"

Adapted from (subject to copyright, with kind permission)

1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"

Footnotes