文档介绍：PrefaceWhat di?erential calculus, and, in general, analysis of the in?nite, might becan hardly be explained to those innocent of any knowledge of it. Nor can wehere o?er a de?nition at the beginning of this dissertation as is sometimesdone in other disciplines. It is not that there is no clear de?nition of thiscalculus; rather, the fact is that in order to understand the de?nition thereare concepts that must ?rst be understood. Besides those ideas monusage, there are also others from ?nite analysis that are much monand are usually explained in the course of the development of the di?erentialcalculus. For this reason, it is not possible to understand a de?nition beforeits principles are su?ciently clearly the ?rst place, this calculus is concerned with variable every quantity can naturally be increased or decreased withoutlimit, still, since calculus is directed to a certain purpose, we think of somequantities as being constantly the same magnitude, while others changethrough all the stages of increasing and decreasing. We note this distinc-tion and call the formerconstant quantitiesand the lattervariables. Thischaracteristic di?erence is not required by the nature of things, but ratherbecause of the special question addressed by the order that this di?erence between constant quantities and variablesmight be clearly illustrated, let us consider a shot ?red from a cannon witha charge of gunpowder. This example seems to be especially appropriate toclarify this matter. There are many quantities involved here: First, there isthe quantity of gunpowder; then, the angle of elevation of the cannon abovethe horizon; third, the distance traveled by the shot; and, fourth, the lengthvi Prefaceof time the shot is in the air. Unless the same cannon is used throughoutthe experiment, we must also bring into our calculations the length of thebarrel and the weight of the shot. Here, we will not consider variations in thecannon or the shot, le