Whether Euclid considered squares to be rectangles

Question

When I look up

'that which is right-angled but not equilateral'

there are translations that show the word before the above phrase to 'oblong', some that show 'rectangle' and some that show both with one term in brackets (1 2 3).

Why is this? Guesses:

1. Translation error
2. Euclid didn't consider squares to be rectangles.
3. Euclid made a mistake.
4. Other

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Answer 1

In mathematics, the term "rectangle" includes squares.

"Oblong" is rarely used as a mathematical term.

Answer 2

See Euclid's Elements:

Definition 22.

Of quadrilateral (τετράπλευρος) figures, a square (τετράγωνος) is that which is both equilateral and right-angled; an oblong (ἑτερομήκης: with sides of uneven length) that which is right-angled but not equilateral; a rhombus that which is equilateral but not right-angled; and a rhomboid that which has its opposite sides and angles equal to one another but is neither equilateral nor right-angled. And let quadrilaterals other than these be called trapezia.

And see Heath's commentary, page 188:

Tetragonon was already a square with the Pythagoreans, and it is so most commonly in Aristotle; but in De anima, II.3, 414b31 it seems to be a quadrilateral, and in Metaph., 1054b2, "equal and equiangular tetragona," it cannot be anything else but quadrilateral if "equiangular" is to have any sense. Though, by introducing tetrapleuron for any quadrilateral, Euclid enabled ambiguity to be avoided, there seem to be traces of the older vague use of tetragonon in much later writers.