 | Euclides - 1834 - 518 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 - 350 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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, James Thomson - 1837 - 410 σελίδες
...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 σελίδες
...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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AB; but things which are equal to the same are equal to one another... 
