| Euclides - 1863
...AL is equal (Ax. 3) to the remainder BG. But it has been shown that BC is equal to BG. Wherefore AL **and BC are each of them equal to BG. And things that are equal to the same** thing are (Ax. 1) equal to one another. Therefore the straight line AL is equal to the straight line... | |
| Thomas Reid - 1863
...certainly than through demonstration, that we know in a. common notion.' .... Such common notions are — ' **Things that are equal to the same are equal to one another,'** — ' If equals be taken from equals the remainders are equal,' — ' Everything must be either affirmed... | |
| Euclides - 1864
...to the remainder BG; (ax. 3.) but it has been shewn that BC is equal to BG, wherefore AL and B Care **each of them equal to BG; and things that are equal to the same** thing are equal to one another ; therefore the straight line AL is equal to BC. (ax. 1.) Wherefore... | |
| Euclides - 1864
...to the remainder BG ; (ax. 3.) but it has been shewn that BCis equal to BG, wherefore AL and .BCare **each of them equal to BG; and things that are equal to the same** thing are equal to one another ; therefore the straight line AL is equal to BC. (ax. 1.) Wherefore... | |
| Francis Bacon - 1864
...whereas in distributive, if unequals be not given to unequals there is the greatest injustice.1 Again " **things that are equal to the same are equal to one another,"** is likewise a rule of mathematics ; but it is at the same time so potent in logic as to be the basis... | |
| Euclides - 1865
...the same thing are equal to one another ; therefore tne straight line AI. is equal to BC. (ax. 1.) **Wherefore from the given point A a straight line AL...drawn equal to the given straight line BC. Which was** to be done. PROP. III.— PROBLEM. From the greater of two given straight lines to cut off a part equal... | |
| John Playfair - 1855 - 317 páginas
...; and things that are equal to the same are equal to one another ; therefore the straight line AL u **equal to BC. Wherefore, from the given point A, a straight line AL** haj been drawn equal to the given straight line BC. a part equal to tht PROP. III. PROB. From the greater... | |
| Sir William Hamilton - 1866 - 530 páginas
...certainly than through demonstration, that we know in a common notion.' .... Such common notions are—' **Things that are equal to the same are equal to one another,'—'** If equals be taken from equals the remainders are equal,'—' Every thing must be either affirmed or... | |
| Euclid, Isaac Todhunter - 1867 - 400 páginas
...to BG. But things which are equal to the same thing are equal to one another. [Axiom 1 . Therefore **AL is equal to BC. "Wherefore from, the given point...has been drawn equal to the given straight line BC.** QEF PROPOSITION 3. PROBLEM. From the greater of two given straight lines to cut off a part equal to... | |
| Euclid, Isaac Todhunter - 1867 - 400 páginas
...equal to BG. But things which are equal to the same thing are equal to one another. [Axiom 1. Therefore **AL is equal to BC. Wherefore from the given point A a straight line** AI, has been drawn equal to the given straight line BC. QEP PROPOSITION 3. PROBLEM. From the greater... | |
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