| 1858
...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 - 1853 - 147 sider
...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
...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
...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 - 1853
...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... | |
| William Somerville Orr - 1854
...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... | |
| J. Stevenson Bushnan - 1854 - 234 sider
...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 are... | |
| Francis Bacon - 1855 - 385 sider
...of Music called " sliding from the close or cadence." In like manner, the Mathematical Postulate, " **those things which are equal to the same, are equal to one another," is** Conformable to the construction of the Syllogism in Logic; for it unites those Terms which agree in... | |
| Francis Bacon - 1855 - 338 sider
...of Music called "sliding from the close or cadence." In like manner, the Mathematical Postulate, " **those things which are equal to the same, are equal to one another," is** Conformable to the construction of the Syllogism in Logic; for it unites those Terms which agree in... | |
| Robert Potts - 1855
...that the evidence of the conclusion is manifest.—Dr Whewell. 199. 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.—Bacon.... | |
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