| Euclides - 1834 - 518 páginas
...AC is • is Defi. equal* to AB ; and because the point B is the centre of the uition. circle ACE, **BC is equal to BA : but it has been proved that CA...equal to AB : but things which are equal to the same** thing are ' 1 Axiom, equal* to one another; therefore CA is equal to CB ; wherefore CA, AB, BC are... | |
| 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... | |
| 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.... | |
| Euclid - 1835 - 540 páginas
...AC is c 15. Defi- equal c to AB ; and because the point B is the centre of the nition. circle ACE, **BC is equal to BA : But it has been proved that CA...things which are equal to the same are equal to one** d 1st Axi- another d ; therefore CA is equal to CB ; wherefore CA, AB, om. BC are equal to one another;... | |
| 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... | |
| Reginald Rabett - 1835 - 408 páginas
...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... | |
| 1835 - 684 páginas
...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... | |
| 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... | |
| Euclid - 1837 - 410 páginas
...definition 30.) to AB; and because the point B is the centre of the circle ACE, BC is equal (I. def. 30.) **to BA. But it has been proved that CA is equal to...AB: but things which are equal to the same are equal** (I. axiom 1.) to one another ; therefore CA is equal to CB; wherefore CA, AB, BC are equal to one another;... | |
| John Playfair - 1837 - 332 páginas
...Definition) to AB ; and because the point B is the centre of the cir-' cle ACE, BC is equal to AB : **But it has been proved that CA is equal to AB ; therefore CA, CB are each of them equal to AB** ; now things which are equal to the same are equal to one another. (1. Axiom) ; therefore CA is equal... | |
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