Galilei, Galileo, De Motu Antiquiora

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As we will explain later that all natural motion of translation {1}, whether it be upward or downward, is the result of the proper {2} heaviness or lightness of the mobile, we have thought it in accordance with reason to bring forth for every one to see how it should be said that a thing is lighter or heavier than another, or equally heavy.Indeed, it is necessary to determine this: for it often happens that things that are lighter are called heavier, and conversely.Thus, at times we say of a large piece of wood that it is heavier than a small piece of lead, even though, purely and simply,lead is heavier than wood; {1}and of a large piece of lead, we say that it is heavier than a small one, even though lead is not heavier than lead. For this reason, in order that we may escape pitfalls of this kind, those things will have to be said to be equally heavy to one another which, when they are equal in size (1), will also be equal in heaviness: thus, if we take two pieces of lead, which are equal in size, and they are also congruent in heaviness, they will have to be said to really weigh the same.{2}Thus, it is clear that wood and lead must not be said to be equally heavy: for a piece of wood, which weighs the same thing as a piece of lead, will considerably exceed the latter in size.Moreover, a thing should be called heavier than another, if when a piece of it is taken, equal to a piece of the other, it is found to be heavier than the piece of the other: as, for example, if we take two pieces, one of lead and one of wood, which are equal to one another, and the piece of lead is heavier than the piece of wood, then we shall surely be justified in asserting that lead is heavier than wood.That is why, if we find a piece of wood which weighs the same as a piece of lead, wood and lead should certainly not be deemed to be equally heavy; for, we will find

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