 | 1838 - 596 σελίδες
...that CA, CB, are each of them equal to AB, we do not in fact believe that CA is equal to CB because things that are equal to the same are equal to one another, although this be the form in which Euclid exhibits the proof. The reception of one truth does not precede... | |
 | Euclides - 1838 - 264 σελίδες
...wherefore AL and BC are each of them equal to BG: and things which are equal to the same thing are equalt to one another; therefore the straight line AL is equal to BC. Where- * * A*' fore, from the given point A, a straight line AL has been drawn equal to the given straight... | |
 | Euclides - 1841 - 378 σελίδες
...them equal to BF; and things that are equal to the same thing are equal * to one another; • 1 Ax. therefore the straight line AL is equal to BC. Wherefore,...has been drawn equal to the given straight line BC. Which was to be done. PROP. III. PROB. From the greater of two given straight lines to cut off a part... | |
 | John Playfair - 1842 - 332 σελίδες
...remainder (3. Ax.) BG: But it has been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to...has been drawn equal to the given straight line BC. ' PROP. III. PROB. From th? greater of two given straight lines to cut off a part equal to the less.... | |
 | Euclides - 1842 - 316 σελίδες
...remainder (3 Ax.) BG: But it has been shown, that вc is equal to BG ; wherefore AL and вc are each of them equal to BG ; and things that are equal to...another ; therefore the straight line AL is equal to в c. Wherefore from the given point A, a straight line AL has been drawn equal to the given straight... | |
 | J. Cypress - 1842 - 268 σελίδες
...argument to prove, that a dog runs on four feet; and so a cat is like a fox, and a dog is like a fox, and things that are equal to the same are equal to one another ; and so a cat is a dog, and a dog is a cat; and so, your Honors, I trust I have established my defence,... | |
 | William Goode - 1842 - 708 σελίδες
...Scripture is obscure. You will have to teach a child or a clown by more or less of explanation that things that are equal to the same are equal to one another, while I suppose no man will deny that if this proposition was in the Bible as a point of faith, the... | |
 | William Goode - 1842 - 706 σελίδες
...Scripture is obscure. You will have to teach a child or a clown by more or less of explanation that things that are equal to the same are equal to one another, while I suppose no man will deny that if this proposition was in the Bible as a point of faith, the... | |
 | Euclid - 1845 - 218 σελίδες
...to the remainder]: BG; But it has been shewn, that BC is equal to BG ; wherefore AL and BC are each of them equal to BG; and things that are equal to...to BC. Wherefore from the given point A a straight tine AL has been drawn equal to the given straight line BC. Which was to be done. PROPOSITION III.... | |
 | Euclides - 1845 - 546 σελίδες
...BG, wherefore AL and BC are each of them equal to BG; and things which are equal to the same thing are equal to one another ; therefore the straight line AL is equal to BC. (ax. 1.) Wherefore from the given point A a straight line AL has been drawn equal to the given straight... | |
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BG; and things that are equal to the same are equal to one another; therefore the straight line AL is equal to BC. Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC. 
