 | William Whewell - 1850 - 416 σελίδες
...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... | |
 | Maria Georgina Shirreff Grey, Emily Anne Eliza Shirreff - 1851 - 496 σελίδες
...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... | |
 | Ephraim George Squier - 1851 - 294 σελίδες
...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... | |
 | Euclides - 1852 - 48 σελίδες
...a circle may be described from any centre, with any distance from that centre as radius. AXIOMS. 1. Things which are equal to the same, are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders... | |
 | 1858 - 422 σελίδες
...have a gayer or gladder aspect. Mr. Smith's only justification here is a mathematical one : that as things which are equal to the same are equal to one another, and both blossoms and tears have been likened to a shower of rain, therefore blossoms may always be... | |
 | 1852 - 588 σελίδες
..."Yes." " And the three baskets three days too?" "Yes." Well, thought I, if it be a true axiom that things which are equal to the same are equal to one another, then a grape vine and a basket are identical ! So, finding the rabbinical logic of this poor deluded... | |
 | Euclides - 1852 - 152 σελίδες
...compasses. Having these, the reader will be able to draw any of the figures in this book.] AXIOMS. I. THINGS which are equal to the same are equal to one another. II. If equals be added to equals, the wholes are equal. III. If equals be taken from equals, the remainders... | |
 | Euclides - 1853 - 176 σελίδες
...equal (15 def.) to ab; and because the point b is the centre of the circle ace, bc is equal to 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 (1 ax.); therefore ca is equal to... | |
 | Royal Military Academy, Woolwich - 1853 - 400 σελίδες
...(15 Definition) to AB; and because the point B is the centre of the circle ACE, EC is equal to 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 (1 Axiom) ; therefore CA is equal... | |
 | Euclides - 1853 - 146 σελίδες
...1. AC is equal to AB; and because the point B is the centre of the circle ACE, 2. BC is equal to 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 (Ax. 1.) ; therefore 3. CA is equal... | |
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AB; but things which are equal to the same are equal to one another... 
