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
| Pierce Morton - 1830 - 584 páginas
...the propositions of the following sections, and are therefore here premised : — • AXIOMS.* • 1. **Things, which are equal to the same, are equal to one another.** 2. If equals be added to equals, the wholes arc equal. 3. If equals be taken from equals, the remainders... | |
| William Sewell - 1830 - 371 páginas
...experiment. A child never doubts that the fire which burnt him yesterday, will burn him to-day, or that two **things which are equal to the same, are equal to one another,** where he .has once seen the axiom illustrated by a single example—and hence one great advantage in... | |
| Francis Bacon, Basil Montagu - 1831 - 478 páginas
...similar to that of music termed the declining of a cadence. 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. Lastly;... | |
| Thomas Perronet Thompson - 1833 - 150 páginas
...But it has been shown that BC is equal to BG ; wherefore AL and BC are each of them equal to BG. And **things which are equal to the same, are* equal to one another** ; therefore AL is equal to BC. Wherefore from the point A a straight line AL has been drawn, equal... | |
| Francis Bacon, Basil Montagu - 1831 - 486 páginas
...similar to that of music termed the declining of a cadence. 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. Lastly... | |
| 1834 - 416 páginas
...Proclus, had preceded him in this attempt : we give the demonstration by Apollonius of the axiom, that **things which are equal to the same are equal to one another.** He argues, that if A is equal to B, it occupies (may be made to occupy) the same place as B. And if... | |
| Alexander Smith - 1835
...of mathematical axioms. Take such instances as these, " all the parts are equal to the whole," — " **things which are equal to the same are equal to one another."** Why must we at once affirm that these propositions are true, and that the contrary of them cannot be... | |
| Euclid - 1835 - 540 páginas
...III. And that a circle may be described from any centre, at any distance from that centre. AXIOMS. I. **THINGS which are equal to the same are equal to one another.** II. If equals be added to equals, the wholes are equal. III. If equals be taken from equals, the remainders... | |
| Alexander Smith (M.A.) - 1835 - 750 páginas
...of mathematical axioms. Take such instances as these, " all the parts are equal to the whole," — " **things which are equal to the same are equal to one another."** Why must we at once affirm that these propositions are true, and that the contrary of them cannot be... | |
| 1835
...demonstrating the propositions of the following sections, and are therefore here premised : — 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... | |
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