The Ten Books on Architecture, 10.6.4

Vitruvius  translated by Joseph Gwilt

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4The inclination at which the screw is to be worked, is equal to that of the right angled triangle of Pythagoras: that is, if the length be divided into five parts, three of these will give the height that the head is to be raised; thus four parts will be the perpendicular to the lower mouth. The method of constructing it may be seen in the diagram at the end of the book. I have now described, as accurately as possible, the engines which are made of wood, for raising water, the manner of constructing them, and the powers that are applied to put them in motion, together with the great advantages to be derived from the use of them.

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