Calculus
Calculus names 2 different subjects across the 6 encyclopedias on this shelf. Each is set out below.
Calculus a branch of mathematical science
Collier's New Encyclopedia (1921)
a branch of mathematical science. The lower or common analysis contains the rules necessary to calculate quantities of any definite magnitude 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, to ascend from the elements of quantities to the quantities themselves. This method is called the integral calculus. Both of these methods are included under the general name infinitesimal, or transcendental analysis. Those quantities 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, if we wish to know the value of those increments, the most natural mode is to determine the value of this quantity for any given period, as a second of time, and the value of the same for the period immediately following. This difference is called the differential of the quantity. The integral calculus, as has been already stated, is the reverse of the differential calculus. There is no variable quantity expressed algebraically, of which we cannot find the differential; are differential quantities but there which we cannot integrate: some because they could not have resulted from differentiation; others because means have not yet been discovered of integrating them. Newton was the first discoverer of the principles of the infinitesimal calculus, having pointed them out in a treatise written before 1669, but not published till many years after. Leibnitz, meanwhile, made the same discovery, and published it before Newton, with a much better notation, which is now universally adopted.
Calculus the medical term for what is popularly known as stone
Collier's New Encyclopedia (1921)
the medical term for what is popularly known as stone. Calculi 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 calculus found in the kidney or ureter is called 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) oxalic (mulberry) calculus, or (3) phosphatic calculus. Calculi derived from the 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.
What Has Changed in the Last Century
The mathematics in Collier's 1921 account still holds: the differential and integral calculus, functions, constants and variables are described much as a modern first-year course describes them, and Newton's unpublished pre-1669 work versus Leibniz's earlier publication with the better notation is still the standard story. What has shifted is the language of "infinitely small" quantities, which teaching had already begun replacing with limits and which Abraham Robinson put on a rigorous footing in the 1960s as non-standard analysis; the remark that some expressions cannot be integrated "because means have not yet been discovered" was answered in 1969 by Risch's algorithm, which decides symbolic integration mechanically, and such work is now done by computer algebra systems. The medical sense has changed far more. Where a stone of any size once meant cutting, extracorporeal shock-wave lithotripsy, introduced clinically in the early 1980s, breaks kidney stones without incision, and gallstones are now usually treated by laparoscopic removal of the gall-bladder, a technique of the late 1980s.
Written for this edition, 2026.