 | Euclid - 1835 - 540 pages
...is equal to the remainder ff 3- AxBG : 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...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 equal to... | |
 | John Playfair - Euclid's Elements - 1835 - 336 pages
...is equal to the 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...has been drawn equal to the given straight line BC. PROP. III. PROB. From the greater of iwo given straight lines to cut. off a part equal to the lest.... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...is equal to the remainder BG (Ax. 3) : 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...Wherefore from the given point A a straight line AL has teen drawn equal to the given straight line BC. PROPOSITION HI. PROBLEM. From the greater of two given... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...is equal to the 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 « !13 to the same are equal to one another ; therefore the straight line AL is equal to BC. Wherefore,... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...things that are equal to the same are equal (I. ax. 1.) to one another; therefore the straight line AF is equal to BC. Wherefore from the given point A a straight line AF has been drawn equal to the given straight line BC : which was to be done. PROP. III. PROB. FROM... | |
 | Joshua Lacy Wilson - Ecclesiastical courts - 1837 - 156 pages
...agrees with DP. Matthews, and that I agree with Dr. Matthews; Ergo, we all agree as "manifest as two things that are equal to the same are equal to one another," and he says, " I challenge man or angel to find any thing like a discrepancy." Can Dr. Beecher point... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...is equal to the remainder (3. Ax.) BG ; but it has been shown, that BC is equal to G, wherefore AL and BC are each of them equal to BG ; and things that are equal to the same aqfcequal to one another ; therefore the straight line AL is equal to EC. Wherefore from the given... | |
 | Euclides - 1838 - 264 pages
...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... | |
 | 1838 - 596 pages
...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... | |
 | Robert Isaac Wilberforce, Samuel Wilberforce - 1838 - 582 pages
...heavy-looking child, but showing at times much thought — used (in fact) in play yesterday Euclid's axiom, Things that are equal to the same are equal to one another." " has far more courage and character than all the other children." " Heard W. read to me for an hour... | |
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DL is equal to DG, and DA, DB, parts of them, are equal ; therefore the remainder AL is equal to the 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... 
