Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal to one... The First Six Books with Notes - Page 3by Euclid - 1822 - 179 pagesFull view - About this book
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...means the square-root of the product of A and B. AXIOMS. 1. Things which are equal to the same thing, are equal to one another. 2. If equals be added to equals, the wholes will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added... | |
| 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 - 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... | |
| 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... | |
| 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... | |
| Royal Military Academy, Woolwich - Mathematics - 1853 - 400 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 Axiom) ; therefore CA is equal to CB ; wherefore CA, AB, BC are equal to one another; and the triangle... | |
| 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... | |
| 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... | |
| Charles Davies - Geometry - 1854 - 436 pages
...means the square•root of the product of A and B. AXIOMS. 1. Things which are equal to the same thing, are equal to one another. 2. If equals be added to equals, the wholes will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added... | |
| 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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