| Ephraim George Squier - Indian mythology - 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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