Now we must keep clearly before our minds the idea, that this poetical and figurative use of number among the Greeks at least preceded what I may call its calculative use. We shall find in Homer nothing that can strictly be called calculation. He repeatedly gives us what may be termed the factors of a sum in multiplication; but he never even partially combines them, even as they are combined for example in Cowper’s ballad, John Gilpin’s spouse said to her dear, Though wedded we have been These _twice ten_ tedious years, yet we No holiday have seen. 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. [791] Od. v. 306. ~_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]: [792] Æsch. Prom. V. 468. see also Soph. Naupl. Fragm. v. καὶ μὴν ἀριθμὸν, ἔξοχον σοφισμάτων, ἐξεῦρον αὐτοῖς· he goes on to add, γραμμάτων τε συνθέσεις.