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
| Euclides - 1852 - 48 páginas
...a circle may be described from any centre, with any distance from that centre as radius. 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... | |
| 1858 - 422 páginas
...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 - 176 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** (1 ax.); therefore ca is equal to cb; wherefore ca, ab, bc are equal to one another; and the triangle... | |
| sir George Ramsay (9th bart.) - 1853 - 282 páginas
...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 - 146 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** (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 - 400 páginas
...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 - 422 páginas
...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 - 268 páginas
...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 - 386 páginas
...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 - 388 páginas
...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... | |
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