In Propositions 35 through 45 of Book 1 in Euclid\'s Elements , what is the mean

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In Propositions 35 through 45 of Book 1 in Euclid's Elements, what is the meaning of the word "equal"? Proposition 35. Parallelograms which are on the same base and in the same parallels equal one another. Proposition 36. Parallelograms which are on equal bases and in the same parallels equal one another. Proposition 37. Triangles which are on the same base and in the same parallels equal one another. Proposition 38. Triangles which are on equal bases and in the same parallels equal one another. Proposition 39. Equal triangles which are on the same base and on the same side are also in the same parallels. Proposition 40. Equal triangles which are on equal bases and on the same side are also in the same parallels. Proposition 41. If a parallelogram has the same base with a triangle and is in the same parallels, then the parallelogram is double the triangle. Proposition 42.          In a given rectilineal angle, a parallelogram can be constructed equal to a given             triangle. Proposition 43. In any parallelogram the complements of the parallelograms about the diameter equal one another. Proposition 44.          To a given straight line, in a given rectilineal angle, a parallelogram equal to a             given triangle can be applied.
Proposition 45.          In a given rectilineal angle, a parallelogram equal to a given rectilineal figure can          be constructed. In Propositions 35 through 45 of Book 1 in Euclid's Elements, what is the meaning of the word "equal"? Proposition 35. Parallelograms which are on the same base and in the same parallels equal one another. Proposition 36. Parallelograms which are on equal bases and in the same parallels equal one another. Proposition 37. Triangles which are on the same base and in the same parallels equal one another. Proposition 38. Triangles which are on equal bases and in the same parallels equal one another. Proposition 39. Equal triangles which are on the same base and on the same side are also in the same parallels. Proposition 40. Equal triangles which are on equal bases and on the same side are also in the same parallels. Proposition 41. If a parallelogram has the same base with a triangle and is in the same parallels, then the parallelogram is double the triangle. Proposition 42.          In a given rectilineal angle, a parallelogram can be constructed equal to a given             triangle. Proposition 43. In any parallelogram the complements of the parallelograms about the diameter equal one another. Proposition 44.          To a given straight line, in a given rectilineal angle, a parallelogram equal to a             given triangle can be applied.
Proposition 45.          In a given rectilineal angle, a parallelogram equal to a given rectilineal figure can          be constructed. Proposition 35. Parallelograms which are on the same base and in the same parallels equal one another. Proposition 36. Parallelograms which are on equal bases and in the same parallels equal one another. Proposition 37. Triangles which are on the same base and in the same parallels equal one another. Proposition 38. Triangles which are on equal bases and in the same parallels equal one another. Proposition 39. Equal triangles which are on the same base and on the same side are also in the same parallels. Proposition 40. Equal triangles which are on equal bases and on the same side are also in the same parallels. Proposition 41. If a parallelogram has the same base with a triangle and is in the same parallels, then the parallelogram is double the triangle. Proposition 42.          In a given rectilineal angle, a parallelogram can be constructed equal to a given             triangle. Proposition 43. In any parallelogram the complements of the parallelograms about the diameter equal one another. Proposition 44.          To a given straight line, in a given rectilineal angle, a parallelogram equal to a             given triangle can be applied.
Proposition 45.          In a given rectilineal angle, a parallelogram equal to a given rectilineal figure can          be constructed. Proposition 42.          In a given rectilineal angle, a parallelogram can be constructed equal to a given             triangle. Proposition 43. In any parallelogram the complements of the parallelograms about the diameter equal one another. Proposition 44.          To a given straight line, in a given rectilineal angle, a parallelogram equal to a             given triangle can be applied.
Proposition 45.          In a given rectilineal angle, a parallelogram equal to a given rectilineal figure can          be constructed. Proposition 43. In any parallelogram the complements of the parallelograms about the diameter equal one another. Proposition 44.          To a given straight line, in a given rectilineal angle, a parallelogram equal to a             given triangle can be applied.
Proposition 44. Proposition 45.          In a given rectilineal angle, a parallelogram equal to a given rectilineal figure can          be constructed. Proposition 45.          In a given rectilineal angle, a parallelogram equal to a given rectilineal figure can          be constructed.

Explanation / Answer

In today's language, we would say 'congruent' or even 'isomorphic'. For example, "In a given rectilineal angle, a parallelogram congruent to a given rectilineal figure can be constructed.

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