| John Playfair - 1819 - 354 pages
...point. V H. . That a terminated straight line may be produced to any length in a straight line. HI. And that a circle may be described from any centre, at...centre. AXIOMS. I. THINGS which are equal to the same thing are equal to one anotheii II. If equals be added to equals, the wholes are equal. HI. If equals... | |
| George Townsend - 1819 - 156 pages
...circumstance indeed so very surprising, that if I had time to prosecute the inquiry, I might prove, that as things which are equal to the same, are equal to one another, the Patriarchs are the Caesars, and the Caesars the sons of Jacob, because they are both synonymous... | |
| Henry Aldrich - 1821 - 300 pages
...reared, and as the final appeal in argument. They benr some slight analogy to the mathematical axioms, Things which are equal to the same are equal to one another ; and, Things of which one is equal and the other not equal to the same, are not equal to one another.... | |
| Euclid - 1822 - 222 pages
...a circle may be described from any centre, /&, ff, at any distance from that centre. M o 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... | |
| Peter Nicholson - Mathematics - 1825 - 1046 pages
...other point. 2. That a terminated straight line may be produced to any length in a straight line. 3. That a circle may be described from any centre, at any distance from that centre. AXIOMS. 1. Thingi which ate equal to the same are equal to one another. 2. If equals be added to equals the... | |
| Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...from any eentre, at any distanee from that eentre. AXIOMS, I. THlNGS whieh are equal to the same thing are equal to one another, n. If equals be added to equals, the wholes are equal. III. If equals be taken from equal?, the remainders are equal. IV. If equals be added to unequals,... | |
| Euclid - 1826 - 234 pages
...but it has been shown that CA is equal to AB : therefore CA, св, are each of them equal to AB. And things which are equal to the same are equal to one another. Whence CA is equal to св ; wherefore the three, CA, AB, вс, are equal to one another ; and, consequently,... | |
| Euclides - 1826 - 226 pages
...continually produced shall meet on that side where the angles are less than two right angles. 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... | |
| Robert Simson - Trigonometry - 1827 - 546 pages
...point. If. 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...centre. AXIOMS. I. * THINGS which are equal to the same thing, are equal to one another. II. If equals be added to equals, the wholes are equal. III. If equals... | |
| George Bentham - Logic - 1827 - 304 pages
...which a syllogistic conclusion can be founded ? Such may, perhaps, be found the four following : 1. Things which are equal to the same, are equal to one another. 2. When of two things, one only is equal to a third, and the other is not equal to that third, these... | |
| |