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Now since in the preceding {1} chapter those things have been demonstrated that concern the state of rest, we must now consider things that pertain to motion upward.I say, then, that magnitudes lighter than water, when let down into water, are not completely submerged, but that a certain part protrudes.

Accordingly let the first position of the water, before the magnitude is let down, be along surface ef; and let magnitude a, lighter than water, when let down into the water, be completely submerged, if this can be done, and let the water be raised up to surface cd; and, if it is possible, let both the water and the magnitude remain in this position.Now, the heaviness, with which the magnitude exerts pressure and raises water cf, will be equal to the heaviness with which water cf exerts pressure in order to raise magnitude a.But the size of water cf is equal to the size of magnitude a.There are thus two magnitudes, one which is a, the other which is water cf; and the heaviness of this a is equal to that of this cf, and the size a is also equal to the size of this water cf: therefore, the magnitude a is equally as heavy as water: which is surely absurd; for it has been assumed that the magnitude is lighter than water.Consequently, magnitude a will not remain completely submerged under the water; therefore it will necessarily be carried upward.