| Thomas Perronet Thompson - 1833 - 150 sider
...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... | |
| John Claudius Loudon, Edward Charlesworth, John Denson - 1834
...book marks an epoch in the progress of natural history in Britain. One of Euclid's postulates is, " **a circle may be described from any centre, at any distance from that centre:"** so, in nature, there is not an object which may not become the centre of a thousand associating circumstances.... | |
| 1834
...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... | |
| Francis Bacon, Basil Montagu - 1831
...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.... | |
| John Playfair - 1835 - 316 sider
...other point. 2. That a terminated straight line may be produced to any length in a straight line. 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 thing, are equal to one another. 2. If equals be added to equals,... | |
| 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... | |
| 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... | |
| Euclid - 1835 - 513 sider
...magnitudes, to ratios, viz. that a magnitude cannot be both greater and less than another. That those **things which are equal to the same are equal to one another,** is a most evident axiom when understood of magnitudes; yet Euclid does not make use of it to infer,... | |
| Reginald Rabett - 1835
...equal to 500, so must the former (as the representative of the latter,) be equal to 500 ; because ' **things which are equal to the same are equal to one another.'** But as the «ir«nj/*or or stenographical character q is a cypher, and no letter, or letters, of the... | |
| Alexander Smith (M.A.) - 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... | |
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