 | Maria Georgina Shirreff Grey, Emily Anne Eliza Shirreff - Self-culture - 1851 - 496 pages
...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... | |
 | Euclides - 1852 - 48 pages
...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... | |
 | Euclides - 1852 - 152 pages
...circle BCD, • isDefini, AC is equal c 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 AC is equal to AB ; therefore AC, BC are each of them equal to AB ; but things which are equal to the... | |
 | 1858 - 422 pages
...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... | |
 | Churches of Christ - 1852 - 588 pages
..."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 - Geometry - 1853 - 176 pages
...the circle bСd, aС is 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...which are equal to the same are equal to one another (1 ax.); therefore ca is equal to cb; wherefore ca, ab, bc are equal to one another; and the triangle... | |
 | Euclides - 1853 - 146 pages
...(Definition 15.) 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...which are equal to the same are equal to one another (Ax. 1.) ; therefore 3. CA is equal to CB. Wherefore CA, AB, BC, are equal to one another ; and therefore... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...ACE, BC is equal to BA. [Definition 15. But it has been shewn that CA is equal to AB; therefore CA and CB are each of them equal to AB. But things which are equal to the same thing are equal to one another. [Axiom 1. Therefore CA is equal to CB. Therefore CA, AB, BCare equal... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...ACE, BC is equal to BA. [Definition 15. But it has been shewn that CA is equal to AB; therefore CA and CB are each of them equal to AB. But things which are equal to the same thing are equal to one another. [Axiom 1. Therefore CA is equal to CB. Therefore CA, AB, BC are equal... | |
 | Religion and science - 1867 - 524 pages
...science. The man who tells me that he cannot believe that " the whole is greater than the part," or " that things which are equal to the same are equal to one another," cannot step over the very threshold of geometry. Nor are these axioms confined to self-evident truths.... | |
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AB; but things which are equal to the same are equal to one another... 
