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Boeotia, that the Aryans change their policy of usurpation to that of amalgamation, which alone was possible under the circumstances. To these events is ascribed the period included in the centuries between 1500–1000 B.C.

From here the further expansion eastwards could not be in the wholesale fashion as heretofore, but had to be in driblets. This expansion takes the form of a few powerful kingdoms farther east than the Doab. What the Kurus (or Kauravas) and the Pānchālas were to the Doab, the Kōsalas and Vidēhas were to the further east of those times. It is these regions that the Rāmāyana describes. The period taken up in the expansion (or infiltration) into these regions may have been the quarter millennium 1000–750 B.C.

During these periods the Indo-Aryans were rearing those great edifices of learning and religion, which have given this land of ours all its claims to greatness in the various departments of human activity. The pre-Vedic Aryans brought in their traditions, which they could elaborate at leisure in the Punjab. These, in course of time, were put into shape in the hymns of the Veda, which, as time advanced, required to be explained by an elaborate commentary. These commentaries are the Brāhmaṇas. These in their turn led to the further disquisitions called the Āranyakas culminating in the philosophical flights of the Upanishads. This transformation, or rather elaboration, has been going on steadily up to the period we arrived at in the last section. This is not all. Certain scientific inquiries had to be made for the proper understanding of the Vedas and the Vedic ritual. Their need was met by the elaboration of the Vedāngas namely, (1) Kalpa which included geometry so far as it applied to the construction of sacrificial altars, (2) Siksha or phonetics, (3) Chandas or metre, (4) Viyākarana or grammar, (5) Nirukta or study of words, (6) Jyōtisha