[260] These appellations appear to have originated from different nations having assumed different notes as the foundation or commencement of their musical scale. The Abbé Barthelemi informs us, that “the Dorians executed the same air a tone lower than the Phrygians, and the latter a tone still higher than the Lydians; hence the denomination of the Dorian, Phrygian, and Lydian modes.” It appears to have been a general practice to employ the lowest modes for the slowest airs; Anacharsis’s Travels, iii. 73, 74.
[261] Hence the passus will be equal to 5 Roman feet. If we estimate the Roman foot at 11·6496 English inches, we shall have the miliare of 8 stadia equal to 1618 English yards, or 142 yards less than an English statute mile. See Adam’s Roman Antiquities, p. 503; also the articles Miliare and Pes in Smith’s Dictionary of Greek and Roman Antiquities; and for the varieties of the stadium, as employed at different periods and in different countries, see the article Stadium. The stadium which Herodotus employed in measurements of Babylon has been supposed to consist of 490 English feet, while that of Xenophon and Strabo has been estimated at 505; see Ed. Rev. xlviii. 190. The Abbé Barthelemi supposes the stadium to be equal to 604 English feet; Anach. Travels, vii. 284.
[262] There appears to have been two individuals of this name, who have been confounded with each other; the one referred to by Pliny was an astronomer of Alexandria, who flourished about 260 years B.C.; the other was a native of Apamea, a stoic philosopher, who lived about two centuries later; see Aikin’s Biog. in loco; also Hardouin’s Index Auctorum, Lemaire, i. 209.
[263] The terms in the original are respectively nubila and nubes. The lexicographers and grammarians do not appear to have accurately discriminated between these two words.
[264] The words in the text are “vicies centum millia” and “quinquies millia.”
[265] Archimedes estimated that the diameter of a circle is to its circumference as 1 to 3·1416; Hutton’s Dict. in loco. Ptolemy states it to be precisely as 1 to 3; Magn. Const. i. 12.
[266] The author’s reasoning is founded upon the supposition of the length of the sun’s path round the earth being twelve times greater than that of the moon’s; the orbit therefore would be twelve times greater and the radius in the same proportion.
[267] “Non inter Lunam et Saturnum, sed inter Lunam et cœlum affixarum stellarum, medium esse Solem modo dixerat. Quam parum sui meminit!” Alexandre in Lem. i. 291.
[268] “Qui computandi modus plurimum habet verecundiæ et modestiæ, quum ibi sistit, nec ulterius progreditur.” Hardouin in Lemaire, i. 292.
[269] “... ad Saturni circulum addito Signiferi ipsius intervallo, ...”