Subtraction

Definition and stakes

Portrait of James Whitbread Lee Glaisher James Whitbread Lee Glaisher,  Encyclopædia Britannica, Ninth Edition (1882)

“ Logarithms were originally invented for the sake of abbreviating arithmetical calculations, as by their means the operations of multiplication and division may be replaced by those of addition and subtraction, and the operations of raising to powers and extraction of roots by those of multiplication and division. For the purpose of thus simplifying the operations of arithmetic, the base is taken equal to 10, and use is made of tables of logarithms in which the values of x, the logarithm, corresponding to values of m, the number, are tabulated. ”
Source: Wikisource

Portrait of William Whewell William Whewell,  Novum organon renovatum (1858)

“ Yet the doctrine that this is so, as well as the law of the force, were established only by this and the like demonstrations. The doctrine which is the hypothesis of the deductive reasoning, is the inference of the inductive process. The special facts which are the basis of the inductive inference, are the conclusion of the train of deduction. And in this manner the deduction establishes the induction. The principle which we gather from the facts is true, because the facts can be derived from it by rigorous demonstration. Induction moves upwards, and deduction downwards, on the same stair. ”
Source: Gutenberg

Portrait of John Stuart Mill John Stuart Mill,  A System of Logic, Ratiocinative and Inductive

“ There are two laws, each possibly acting in the whole hundred cases, and bringing about a common effect by their conjunct operation. If the force which, being the less conspicuous of the two, is called the disturbing force, prevails sufficiently over the other force in some one case, to constitute that case what is commonly called an exception, the same disturbing force probably acts as a modifying cause in many other cases which no one will call exceptions. ”
Source: Gutenberg

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