 | Ephraim George Squier - History - 1851 - 294 pages
...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... | |
 | 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... | |
 | Euclides - 1852 - 152 pages
...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... | |
 | 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... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...3. And that a circle may be described from any centre, at any distance from that centre. 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 - 1853 - 146 pages
...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 to CB. Wherefore CA, AB, BC, are equal to one another ; and therefore... | |
 | 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... | |
 | Euclides - Geometry - 1853 - 176 pages
...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 cb; wherefore ca, ab, bc are equal to one another; and the triangle... | |
 | William Somerville Orr - Science - 1854 - 422 pages
...truths — also such propositions as that, when equals are taken from equals, equals remain ; that things which are equal to the same are equal to one another ; that things which are doubles or halves of the same, are equal to one another ; that twice four arc... | |
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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. 
