 | John Playfair - Euclid's Elements - 1832 - 358 pages
...point. II. That a terminated straight line may be produced to any length in a straight line. III. And that a circle may be described from any centre, at any distance from that centre. Axioms. iTHINGS which are equal to the same thing are equal to one another. II. If equals be added to equals,... | |
 | Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...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 - Natural history - 1834 - 698 pages
...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.... | |
 | Francis Bacon, Basil Montagu - 1831 - 486 pages
...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.... | |
 | Education - 1834 - 416 pages
...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... | |
 | Euclid - 1835 - 540 pages
...point. II. That a terminated straight line may be produced to any length in a straight line. III. And that a circle may be described from any centre, at...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 pages
...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... | |
 | Mathematics - 1835 - 684 pages
...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... | |
 | Reginald Rabett - Bible - 1835 - 408 pages
...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 - Ethics - 1835 - 350 pages
...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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Let it be granted that a straight line may be drawn from any one point to any other point. 
