So that the use of numbers by rule was to the Greek mind as much a discovery as the letters of the alphabet, and is even described here as a greater one: much as in later times men have viewed the use of logarithms, or of the method of fluxions or the calculus. In full conformity with this are the superlative terms, in which Plato speaks of number. Number, in fact, seems to be exhibited in great part of the Greek philosophy, as if it had actually been the guide of the human mind in its progress towards realizing all the great and cardinal ideas of order, measure, proportion, and relation. Up to what point human intelligence, in the time of Homer, was able to push the process of simple addition, we do not precisely know. It is not, however, hastily to be assumed that, in any one of his faculties, Homer was behind his age; and it is safer to believe that the poems, even in these points, represent it advantageously. Now, in one place at least, we have a primitive account of a process of addition. The passage is in the Fourth Odyssey, where Menelaus relates, how Proteus counted upon his fingers the number of his seals[793]. That it was a certain particular number is obvious, because when four of them had been killed by Eidothee, their skins were put upon Menelaus and his three comrades, and the four Greeks were then counted into the herd, so that the word ἀριθμὸς here evidently means a definite total. This addition by Proteus, however, was not addition in the proper arithmetical sense, and would be more properly called enumeration: it was probably effected simply by adding each unit singly, in succession, to the others, with the aid of the fingers, (proved through the word πεμπάσσεται,) but not by the aid of any scale or combination of units, either decimal or quinal. In the word δεκὰς we have, indeed, the first step towards a decimal scale; but we have not even that in the case of the number five, there being no πεντὰς or πεμπτάς. The meaning of πεμπάσσεται evidently is, not that he arranged the numeration in fives, but that, by means of the fingers of one hand, employed upon those of the other, he assisted the process of simple enumeration. [793] Od. iv. 412, 451. ~_Highest numerals of the poems._~ Homer’s highest numeral is μύριοι. He describes the Myrmidons as being μύριοι[794], though, if we assume a mean strength of about eighty-five for their crews, the force would but little have exceeded four thousand: and at the _maximum_ of one hundred and twenty for each ship, it would only come to six thousand. Again, Homer uses the expression μύρια ᾔδη, to denote a person of instructed and accomplished mind[795]. [794] Il. xxiii. 29. [795] Od. ii. 16. Next to the μύρια, the highest numerals employed in the poems are those contained in the passage where the Poet says that the howl of Mars, on being wounded by Diomed, was as loud as the shout of an army of nine thousand or ten thousand men[796]: [796] Il. v. 860.