 | Euclides - 1848 - 52 pages
...point. II. That a terminated straight line may be produced to any length in a straight line. HI. And that a circle may be described from any centre at...centre. AXIOMS. I. THINGS which are equal to the same thing are equal to one another. II. If equals be added to equals, the wholes are equal. III. If equals... | |
 | Bengal (India) - 1848 - 520 pages
...but belong to a higher and larger science. As examples of such axioms he gives that of mathematics, " things which are equal to the same are equal to one another," which can equally well be applied to logic, thereby insinuating that the observations of "philosophia... | |
 | Bengal council of educ - 1848 - 394 pages
...but belong to a higher and larger science. As examples of such axioms he gives that of mathematics, " things which are equal to the same are equal to one another," which can equally well be applied to logic, thereby insinuating that the observations of " philosophia... | |
 | Euclid, Thomas Tate - 1849 - 120 pages
...BA: But it has been proved that CA is equal to AB; therefore CA, CB are each of them equal to AB; but things which are equal to the same are equal to one another (Axiom 1.) ; therefore CA is equal to cu; wherefore CA. AB, BC are equal to one another; and the triangle... | |
 | Secularism - 1849 - 424 pages
...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... | |
 | Richard Dawes - Teaching - 1849 - 228 pages
...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,... | |
 | Francis Bacon - 1850 - 620 pages
...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.... | |
 | William Whewell - Education, Higher - 1850 - 432 pages
...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... | |
 | Henry Aldrich - Logic - 1850 - 406 pages
...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.... | |
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Let it be granted that a straight line may be drawn from any one point to any other point. 
