ANALYSIS. The act of decomposing or dissecting a thing, such as a substance, a proc ess, or a logical concept, into its component elements, and of exhibiting its structure. The term is also used for an inventory of the re sults of this dissection such as we often find preceding a long and intricate article on any subject, and also occasionally for the state re sulting from the dissection.
As mathematics is the study of pure struc ture, all mathematics which devotes itself to existing structures is of the nature of analysis. Accordingly, the word analysis, like the words 'calculus* and "algebra,* is often used as a synonym of mathematical discipline, as in the names "Analysis Situs,Il °Combinatory Analy sis,* etc. That phase of mathematics, however, which outs together old elements in new forms is sympathetic in character. Now, though both these phases go hand and hand in the history of every mathematical subject, the usual rep resentation of geometrical entities has made the method of construction or the synthetic method peculiarly easy and universal there.
On the other hand, algebra and, more especially, those sciences whose roots are in the infinitesi mal calculus are characterized by the prom inence which the analytic method possesses in their investigations and are often known by the collective name of analysis. Geometry and analysis usually appeal to different types of mathematicians, who arc known respectively as geometricians or analysists.
Another mathematical use of the term is its application to the method in which you sup pose the theorem you wish to prove demon strated, reason back to some admitted truth, and then try to retrace the steps by which you have attained it. As to analysis in chem istry see CHEMICAL ANALYSIS.