Reference has been made to the convenience which we find in using number as a measure of quantity, and as a means of comparing things of every species in their own kind. But we never meet with this use of it in Homer. He has not even the words necessary to enable him to say, ‘This house is five times as large as that.’ If he had the idea to express, he would say, Five houses, each as large as that, would hardly be equal to this. The word τρὶς may be called an adverb of multiplication; but it is never used for these comparisons. Indeed, Damm observes, that in a large majority of instances it signifies an indefinite number, not a precise one. Τετράκις is found only once, and in a sense wholly indeterminate: the passage is[791] τρισμάκαρες Δαναοὶ καὶ τετράκις. Πεντάκις does not even exist. Ajax lifts a stone, not ‘twice as large as a mortal of to-day could raise’, but so large that it would require two such mortals to raise it. All Homer’s numerical expressions are in the most elementary forms; such forms, as are without composition, and refuse all further analysis.
Greek estimate of the discovery of Number.
His use of number appears to have been confined to simple addition: and it is probable that all the higher numbers which we find in the poems, were figurative and most vaguely conceived. If we are able to make good the proof of these propositions from the Homeric text, we shall then be well able to understand the manner in which Numeration, or the science of number, is spoken of by the Greeks of the historic age as a marvellous invention. It appears in Æschylus, as among the very greatest of the discoveries of Prometheus[792]:
καὶ μὴν ἀριθμὸν, ἔξοχον σοφισμάτων,
ἐξεῦρον αὐτοῖς·
he goes on to add,
γραμμάτων τε συνθέσεις.
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.
Highest numerals of the poems.