 | Francis Bacon - 1858 - 540 pages
...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... | |
 | George Henry Lewes - Ilfracombe (England) - 1858 - 448 pages
...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 - 516 pages
...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 - 346 pages
...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 - 288 pages
...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 - Geometry, Plane - 1860 - 380 pages
...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 - Education - 1861 - 816 pages
...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 - 578 pages
...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 - 140 pages
...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 - 172 pages
...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... | |
| |
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... 
