The Ten Books on Architecture, 6.1.5

Vitruvius  Parallel editions

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Gwilt translation

5The pitch of the voice is various, and of different qualities in different nations. For the eastern and western boundaries round the level of the earth, where the upper is divided from the under part of the world, and the earth appears to be balanced by nature, are designated by a circle which mathematicians call the horizon; keeping this circumstance in mind, from the edge on the northern extremity, let a line be drawn to that above the southern axis, and therefrom another in an oblique direction up to the pole near the northern stars, and we shall immediately perceive the principle of the triangular instrument called by the Greeks σαμβύκη.

Morgan translation

5The pitch of the voice is likewise different and varying in quality with different nations, for the following reasons. The terminating points east and west on the level of the earth, where the upper and lower parts of the heaven are divided, seem to lie in a naturally balanced circle which mathematicians call the Horizon. Keeping this idea definitely in mind, if we imagine a line drawn from the northern side of the circumference (N) to the side which lies above the southern half of the axis (S), and from here another line obliquely up to the pivot at the summit, beyond the stars composing the Great Bear (the pole star P), we shall doubtless see that we have in the heaven a triangular figure like that of the musical instrument which the Greeks call the “sambuca.”