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Source — Euclid's Elements, encoded as an rrxiv paper — rrxiv

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Source — Euclid's Elements, encoded as an rrxiv paper

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VI.27 Proposition VI.27

Of all parallelograms applied to the same straight line and deficient by parallelogrammic figures similar and similarly situated to that described upon the half of the straight line, the greatest is that which is applied to the half and is similar to the deficient figure.

Proof

Comparison of areas via VI.20 and VI.24: the application to the half exhausts the bound, while any other application produces a smaller parallelogram by a square-on-the-deviation.

lines 74–74 in main.tex

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VI.27 Proposition VI.27

Proof

Comparison of areas via VI.20 and VI.24: the application to the half exhausts the bound, while any other application produces a smaller parallelogram by a square-on-the-deviation.

lines 74–74 in main.tex