| George Henry Lewes - 1858 - 414 páginas
...variation." And Dr Alexander Harvey reminds us on GEMMATION AND GENERATION. 309 this point, that " **things that are equal to the same, are equal to one another** ;" so that if the product of the bud and the product of the seed be in all respects identical, there... | |
| Francis Bacon - 1858
...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... | |
| REV. JAMES CARLILE - 1859
...the axioms of mathematics depend on our cognitions of matter and space. Those that do not, such as " **Things that are equal to the same are equal to one another,"** or more generally, "Things that are like the same in any particular are like one another in that particular,"... | |
| Euclides - 1860
...AL is equal to 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...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 páginas
...AL is equal to 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... | |
| 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... | |
| 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... | |
| 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 of apart... | |
| 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... | |
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