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. The London Magazine - Seite 4511827Vollansicht - Über dieses Buch
| 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... | |
| 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... | |
| 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... | |
| Euclides - 1853 - 147 Seiten
...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 - 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 Seiten
...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... | |
| 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.... | |
| Robert Potts - 1855 - 554 Seiten
...that the evidence of the conclusion is manifest.—Dr Whewett. 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.... | |
| 1855
...art equal to ta<A other. (Euclid 11, 5.) This is nothing more than an application of the axiom, that **things which are equal to the same are equal to one another.** And с : d : : m : n 2. If a :.* : : m : я And m : n : : с : d Cor. If a : 6 : : m : я l m : п>... | |
| Edward Tagart - 1855 - 504 Seiten
...of nature and fact. In mathematical reasoning, no axiom is more constantly employed than this — ' **things which are equal to the same are equal to one another.'** Are the ideas of equality and inequality in the mind of a child before things have been observed, measured,... | |
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