 | Presbyterian church in the U.S.A. - 1862 - 754 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
...AL is equal (Ax. 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... | |
 | Euclides - 1864 - 448 pages
...to 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... | |
 | Euclides - 1864 - 262 pages
...to the remainder BG ; (ax. 3.) but it has been shewn that BCis equal to BG, wherefore AL and .BCare 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 - Philosophy, English - 1864 - 528 pages
...whereas in distributive, if unequals be not given 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 - 1865 - 402 pages
...the same thing are equal to one another ; therefore tne straight line AI. is equal to BC. (ax. 1.) Wherefore from the given point A a straight line AL...drawn equal to the given straight line BC. Which was to be done. PROP. III.— PROBLEM. From the greater of two given straight lines to cut off a part equal... | |
 | Robert Potts - 1865 - 528 pages
...AL is equal to the remainder BG; (ax. 8.) 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 the same thing are equal to one another ; therefore the straight line AL is equal to BC. (ax. 1.) Wherefore... | |
 | John Playfair - Geometry - 1855 - 350 pages
...; and things that are equal to the same are equal to one another ; therefore the straight line AL u equal to BC. Wherefore, from the given point A, a straight line AL haj been drawn equal to the given straight line BC. a part equal to tht PROP. III. PROB. From the greater... | |
 | Sir William Hamilton - Philosophy - 1866 - 548 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,'—' Every thing must be either affirmed or... | |
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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... 
