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Clement of Alexandria
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Introductory Note to Clement of Alexandria
[3338] “Triangular numbers are those which can be disposed in a triangle, as 3 ⊠, 6, etc, being represented by the formula (x2 + x)/2” (Liddell and Scott’s Lexicon). Each side of the triangle of courses contains an equal number of units, the sum of which amounts to the number. [Elucidation VI.]
[3339] This number is called equality, because it is composed of eight numbers, an even number; as fifty-six is called inequality, because it is composed of seven numbers, an odd number.
[3340] The clause within brackets has been suggested by Hervetus to complete the sense.
[3341] That is, 1+3+5+7+11+13+15=120; and 1+3=4+5=9+7=16+9=25+11=36+13=49+15=64, giving us the numbers 4, 9, 16, 25, 36, 49, 64, the squares of 2, 3, 4, 5, 6, 7, 8.
[3342] ἐτερομήκεις, the product of two unequal factors, i.e., 2+4+6+8+10+12+14=56; and 2+4=6=3 x 2, 6+4=10=5 x 2, and so on.
[3343] The cross.
[3345] Ex. xxv. 23. The table is said to be two cubits in length, a cubit in breadth, and a cubit and a half in height; therefore it was six cubits round.
[3347] The three styles of Greek music were the ἐναρμονικόν, διάτονον, and χρωματικόν.
[3348] i.e., of Christ.
[3349] 1 Cor. x. 26, etc.
[3350] ψάλλοντες is substituted by Lowth for ψάλλειν of the text; ἐν τῷ ψάλλειν has also been proposed.
[3352] Ps. xlv. 14. [Elucidation VII.]
[3353] διδακτικήν, proposed by Sylburgius, seems greatly preferable to the reading of the text, διδακτήν, and has been adopted above.
[3354] Wisd. vi. 10.
[3355] Wisd. vii. 16.
[3356] Wisd. xiv. 2, 3.
[3357] That is, resurrection effected by divine power.
[3358] Such seems the only sense possible of this clause,—obtained, however, by substituting for συνάλογοι λόγοὐ κ.τ.λ., σύλλογοι λόγον κ.τ.λ.
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