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 - Page 455by John Scott, John Taylor - 1827Full view - About this book
| George Ramsay (sir, 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... | |
| Euclides - Geometry - 1853 - 147 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
...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... | |
| John Stevenson Bushnan - Physiology - 1854 - 234 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 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 pages
...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
...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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