The Ten Books on Architecture, 9.1.13

Vitruvius  Parallel editions

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Gwilt translation

13One may perhaps ask, whence it happens that the sun, by its heat, causes a detention in the fifth sign from itself, rather than in the second or third, which are nearer. This may be thus explained. Its rays diverge through the heavens in lines which form a triangle whose sides are equal. Those sides fall exactly in the fifth sign. For if the rays fell circularly throughout the system, and were not bounded by a triangular figure, the nearer places would be absolutely burnt. This seems to have struck the Greek poet, Euripides; for he observes, that those places more distant from the sun are more intensely heated than those temperate ones that are nearer to him: hence, in the tragedy of Phaëthon, he says,Καίει τὰ πόῤῥω, τὰ δ᾽ ἐγγὺς εὔκατ᾽ ἔχει. (The distant places burn, those that are near are temperate.)

Morgan translation

13Perhaps the question will be raised, why the sun by his great heat causes these detentions in the fifth sign from himself rather than in the second or third, which are nearer. I will therefore set forth what seems to be the reason. His rays diverge through the firmament in straight lines as though forming an equilateral triangle, that is, to the fifth sign from the sun, no more, no less. If his rays were diffused in circuits spreading all over the firmament, instead of in straight lines diverging so as to form a triangle, they would burn up all the nearer objects. This is a fact which the Greek poet Euripides seems to have remarked; for he says that places at a greater distance from the sun are in a violent heat, and that those which are nearer he keeps temperate. Thus in the play of Phaethon, the poet writes: καἱει τἁ πὁρρω, τἁγγυθεν δ εὑκρατ ἑχει.