 | John Campbell - African Americans - 1851 - 566 pages
...Asiatics, the utter destruction of all biblical chronology by this process would be another. " Now, ' things which are equal to the same are equal to one another.' If they are anterior to Shoopho's pyramid in Egypt, then Meroe must have been occupied in the earliest... | |
 | 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 - 152 pages
...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 same are equal to one 4 I Axiom. another d therefore AC is equal to BC ; wherefore AC, AB, BC are equal to one another; and... | |
 | 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... | |
 | 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... | |
 | 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 - 1853 - 146 pages
...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...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... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...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...which are equal to the same are equal to one another (1 Axiom) ; therefore CA is equal to CB ; wherefore CA, AB, BC are equal to one another; and the triangle... | |
 | Euclides - Geometry - 1853 - 176 pages
...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...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... | |
 | sir George Ramsay (9th bart.) - 1853 - 282 pages
...intervention of any general axiom, that the side AB is equal to the side A C. The general axiom, that things which are equal to the same are equal to one another, cannot make the conclusion one whit more evident than it was before. We see at once from the particular... | |
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But things which are equal to the same are equal to one another (Ax. 
