The Ten Books on Architecture, 4.2.5

Vitruvius  Parallel editions

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Gwilt translation

5As in works of the Doric order triglyphs and mutuli were first used, so in Ionic works the use of dentils was first introduced; for as the mutuli bear a resemblance to the projecting feet of the principal rafters, so, in the Ionic order, the dentils imitate the projection of the common rafters. Hence the Greeks never placed dentils below the mutuli, because the feet of common rafters cannot be below those of principal rafters. For a design must be anomalous, when that which ought to be above the principal rafters is placed below them. The antients, therefore, neither approved nor used mutuli nor dentils in the cornices of their pediments, but coronæ simply; because neither principal nor common rafters tail on the front of a pediment, neither can they project beyond it, their direction being towards the eaves. Their opinion, therefore, evidently was, that a distribution would not be correct in a copy which could not exist in the prototype.

Morgan translation

5The system of triglyphs and mutules was invented for the Doric order, and similarly the scheme of dentils belongs to the Ionic, in which there are proper grounds for its use in buildings. Just as mutules represent the projection of the principal rafters, so dentils in the Ionic are an imitation of the projections of the common rafters. And so in Greek works nobody ever put dentils under mutules, as it is impossible that common rafters should be underneath principal rafters. Therefore, if that which in the original must be placed above the principal rafters, is put in the copy below them, the result will be a work constructed on false principles. Neither did the ancients approve of or employ mutules or dentils in pediments, but only plain coronae, for the reason that neither principal nor common rafters tail into the fronts of pediments, nor can they overhang them, but they are laid with a slope towards the eaves. Hence the ancients held that what could not happen in the original would have no valid reason for existence in the copy.