 | 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... | |
 | Euclides - 1860 - 288 pages
...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 - Geometry, Plane - 1860 - 380 pages
...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 - 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | Presbyterian church in the U.S.A. - 1862 - 752 pages
...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 - 122 pages
...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 - Philosophy - 1863 - 542 pages
...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... | |
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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. 
