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 Elements of Euclid - Página 246por Euclid - 1838 - 416 páginasVista completa - Acerca de este libro
| James Allanson Picton - 1873 - 492 páginas
...believes the axioms of Euclid, but simply because of the impossibility of thinking the contrary. That " **things which are equal to the same are equal to one another " is a** truth clear at once to any mind capable of understanding its terms, without the slightest necessity... | |
| James Allanson Picton - 1873 - 548 páginas
...because the single case is not, and cannot be, adequately presented to it. For the universal truth, that **things which are equal to the same are equal to one another,** cannot be seen in any case until the notion of equality has been acquired. But this notion again never... | |
| Henry Major - 1873 - 592 páginas
...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;** therefore CA is equal to CB ; wherefore CA, AB, BC, are equal to one another; and the triangle ABC... | |
| Herbert Spencer - 1873 - 678 páginas
...knowledge beyond that of the coexistence of an indefinite number of things ; any more than the axiom — **"Things which are equal to the same are equal to one another,"** can, by multiplied application, do more than establish the equality of some series of magnitudes. But... | |
| 1873 - 626 páginas
...than are producible from the deai Now let us turn to the logical and physical side of the question. **Things which are equal to the same are equal to one another,** and if equals be added to equals the whole are equal. Anatomy teaches us that there is no difference... | |
| Victoria Institute (Great Britain) - 1873 - 518 páginas
...Here again the word is psyche, but containing all the attributes of kardia. The inference is obvious : **things which are equal to the same are equal to one another.** While we may freely admit that, in the terms of a language, this principle will not rigidly apply,... | |
| Herbert Spencer - 1873 - 670 páginas
...knowledge beyond that of the coexistence of an indefinite number of things ; any more than the axiom — **"Things which are equal to the same are equal to one another,"** can, by multiplied application, do more than establish the equality of some series of magnitudes. But... | |
| William Hickey - 1874 - 494 páginas
...laws, which they have been taught to believe sacred, and which alone they can possibly comprehend."1 ' **Things which are equal to the same are equal to one another,'** says Euclid. What applies to the part, will apply to the whole. A political agent, the only political... | |
| Charles Lunn - 1874 - 80 páginas
...living subject than are producible from the dead. Let us turn to the logical side of the question. **Things which are equal to the same are equal to one another.** Anatomy teaches us that there is no difference between the male and female larynx save in size, so... | |
| Robert Potts - 1875 - 210 páginas
...the evidence of the conclusion is manifest. — Dr. Whewell. 214. 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. —... | |
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