we have seen that many new and extensive fields of mathematical investigation were opened up in the seventeenth century making that era an outstandingly productive one in the development of mathematics. unques-tionably the most remarkable mathematical achievement of the period was the invention of the calculus toward the end of the century by isaac newton and gottfried wilhelm leibniz with this invention creative mathematics quite generally passed to an advanced level and the history of elementary mathematics essentially terminates. the present chapter will be devoted to a very brief account of the origins and development of the important concepts of the calculus concepts which are so far-reaching and which have exercised such an impact on the modern world that it is perhaps correct to say that without some knowledge of them a person today can scarcely claim to be well educated.