Collier's New Encyclopedia

A complete general encyclopedia of 1921 — the world as it was understood just after the Great War, from Aachen to Zwingli, across twelve volumes and six thousand pages.

HomeC › Calculus

Calculus

the medical term for what is popularly known as stone. Cal- CALCULUS, the medical term for culi vary in size from a pin's head to a pigeon's egg, and even larger, and weigh from a few grains to several ounces.

They derive their special name and character as well from the organs of the body in which they are found as from the constituents of which they are composed. Thus, for example, a calcomposed. Thus, for example, a calcalled renal, in the bladder vesical, and so on; but, acording to its chemical composition, it would also be called either (1) uric (lithic) acid calculus, or (2) position, it would also be called either (1) uric (lithic) acid calculus, or (2) oxalic (mulberry) calculus, or (3) phosthe bile are also found in the gall-bladder, and in the biliary and intestinal ducts, where they receive the name of call-stones, or biliary calculi. Those found in the salivary glands are called salivary calculi. found in the salivary glands are called ical science. The lower or common analysis contains the rules necessary to ical science. The lower or common analnitude whatever. But quantities are sometimes considered as varying in magnitude, or as having arrived at a given state of magnitude by successive variations. This gives rise to the higher analysis, which is of the greatest use in the ph physico-mathematical sciences. Two objects are here proposed: First, to descend from quantities to to their elements. The method of effecting this is called the differential calculus. Second, descend from quantities to their eleties to the quantities themselves. This method is called the integral calculus.

Both of these methods are included under the general name infinitesimal, or ties to the quantities themselves. This method is called the integral calculus. ties which retain the same value are called constant; those whose values are varying are called variable. When variable quantities are so connected that the value of one of them is determined by the value ascribed to the others, that variable quantity is said to be a function of the others. A quantity is infinitely great great or infinitely small, with regard to another, when it is not possible to assign any quantity sufficiently large or sufficiently small to express the ratio of the two.

When we consider a variable quantity as increasing by infinitely small degrees, for any given period, as a second of to determine the value of this quantity increments, the most natural mode is for any given period, as a second of time, and the value of the same for the ference is called the differential of the period immediately following. This difquantity. The integral calculus, as has been already stated, is the reverse of the differential calculus. There is no variable quantity expressed algebraically, of are differential quantities which we cannot find the differential; but there cause they could not have resulted from differentiation; others because means cause they could not have resulted from have not yet been discovered of intehave not yet been discovered of intecoverer of the principles of the infinitesgrating them. Newton was the first disimal calculus, having pointed them out in a treatise written before 1669, but not published till many years after. Leibnitz, meanwhile, made the same diswith a much better notation, which is with a much better notation, which is now universally adopted.

← Calculating MachineCalcutta →