| Euclides - 1860
...the remainder BG (Ax. 3). 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...equal to one another; therefore the straight line** to BC. Wherefore from the given AL shall line AL BC. AL is equal point A a straight has been drawn... | |
| Robert Potts - 1860 - 361 sider
...the remainder BG; (ax. 3.) but it has been shewn that BCia equal to BG, wherefore AL and BC are 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 - 1861
...distributive, if unequals be not given VOL. IV. Z 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... | |
| SIR WILLIAM HAMILTON - 1861
...Induction, than in establishing his own. 1 " It is by induction that all axioms are known, such as : — * **Things that are equal to the same are equal to one another** ;' * A whole is greater than its parts ;' and all other mathematical axioms." Huyshe, p. 132. The same... | |
| Euclides - 1862
...same thing are equal to one another, therefore AL is equal to BC. (ax. 1.) Conclusion. — Therefore **from the given point A a straight line AL has been drawn equal to the given straight line BC.** Which was to be done. PROPOSITION 3.— PROBLEM. From the greater of two given straight lines to cat... | |
| Euclides - 1862
...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... | |
| 1862
...demonstration, the idea of a First Cause becomes as intuitive as that all the parts are equal to the whole, or **things that are equal to the same are equal to one another.** Facts that may seem to conflict with this may be easily accounted for from the determination of the... | |
| Euclides - 1863
...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
...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... | |
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