...which many of them would turn to a good purpose. Even a knowledge of the axioms of Euclid, such as " things which are equal to the same are equal to one another." If equals be added to equals the wholes are equal. If equals be added to unequals, the wholes are unequal,...

...be paid as well as yours, and I should have d£20,000 a-year instead of 4s. a-day; becanse you see things which are equal to the same are equal to one another.' The Spectator, of April 28, 1849, says — '"Genins" consists in a special capacity for some particular...

...uninfluenced by the demonstration of the simplest problem in Euclid, and to which the axiom, " that things which are equal to the same are equal to one another," would be too abstruse for comprehension. The judgment and the note were familiar. and their relation...

...It may be said, indeed, that every step in analysis is a syllogism, in which the major is the Axiom, Things which are equal to the same are equal to one another; and the minor is a proposition that two certain forms of symbols have been proved to be equal to the...

...the basis on which the syllogism is founded. They bear some analogy to the mathematical axioms : — Things which are equal to the same are equal to one another, and things of which one is equal and the other not equal to the same, are not equal to one another....

...to be reared, and the final appeal in argument. They bear some analogy to the mathematical axioms, Things which are equal to the same are equal to one another; and, Things of which one is equal and the other not equal to the same, are not equal to one another....

...similar to that of music termed the declining of a cadence. Again; the mathematical postulate, that "things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term....

...It may be said, indeed, that every step in analysis is a syllogism, in which the major is the Axiom, Things which are equal to the same are equal to one another; and the minor is a proposition that two certain forms of symbols have been proved to be equal to the...

...authority, if not, possibly by the Egyptian documents yet deciphered) — which hypothesis is Euclidean. " Things which are equal to the same are equal to one another." Now, if the " Mundane Egg" be, in the papyric Rituals, the equivalent to Sun, and that, by other hieroglyphical...

...other," it is evidently only another mode of expressing the axiom in geometry, referred to above, " Things which are equal to the same, are equal to one another." These are not peculiar principles of particular sciences, but formulae of the essential laws of thought...