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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. "
Elements of Geometry: Containing the First Six Books of Euclid, with a ... - Side 19
av Euclid, John Playfair - 1826 - 320 sider
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The American Monthly Magazine, Volum 6

1835
...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 Honours, I trust I have established my defence,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 sider
...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 are equal to...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...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 sider
...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 are equal to...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...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 318 sider
...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...has been drawn equal to the given straight line BC. PROP. III. PROB. From the greater of two given straight lines to cut off a part equal to the less....
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 sider
...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...
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The Elements of Euclid

Euclid - 1838 - 416 sider
...BC are each of them equal to BG ; and things that are equal to the BOOK. THE ELEMENTS OF EUCLID. r» same are equal to one another ; therefore the straight...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...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Euclid, Robert Simson - 1838 - 416 sider
...that are equal to the same aqfcequal to one another ; therefore the straight line AL is equal to EC. Wherefore from the given point A a straight line AL...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 oft' a part...
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The Millennial Harbinger

Alexander Campbell, Charles Louis Loos - 1838
...in the East,, bounded by the same designations. These are contemporaneous and correlate events. But "things that are equal to the same, are equal to one another;" and hence we hasten to observe, that the continuance of the sufferings and sustenance of the woman...
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The Life of William Wilberforce: 1801-1811. v. 4. 1812-1818

Robert Isaac Wilberforce, Samuel Wilberforce - 1838
...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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The Edinburgh Review: Or Critical Journal, Volum 67

1838
...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...
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