 | Thomas Harper - Metaphysics - 1881 - 802 pages
...definition by D, according to the whole of extension, we shall have D = A, S = D, /. S = A ; that is to say, Things that are equal to the same are equal to one another. But, first of all, it should be remembered that, although the equality is logical, it is quite accidental... | |
 | Thomas Harper - Metaphysics - 1881 - 798 pages
...definition by D, according to the whole of extension, we shall have D = A, S = D, /. S = A ; that is to say, Things that are equal to the same are equal to one another. But, first of all, it should be remembered that, although the equality is logical, it is quite accidental... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...equal to BG. But things which are equal to the same thing are equal to one another. [Axiom 1. Therefore AL is equal to B'C. Wherefore from the given point...has been drawn equal to the given straight line BC. QEF PROPOSITION 3. PROBLEM. From, the greater of two given straight lines to cut off a part equal to... | |
 | Stephen Thomas Hawtrey - 1880 - 202 pages
...to the same thing, they are equal to one another. Therefore AL is equal to BC (Ax. 1). Wherefore i from the given point A, a straight line AL has been drawn equal to the given straight line BC, which was to be done. Observe here the connection between the endings of the enunciation, construction,... | |
 | T S. Taylor - 1880 - 152 pages
...equal to one another. BC (a) and AL (c) are each equal to C G. .-. AL is equal to B C. Result. — Wherefore from the given point A a straight line AL has been drawn equal to the given line B CQEF EXERCISES. — I. Let A be the A • given point and BC the given line, then draw a line... | |
 | Pupil teachers - 1880 - 1486 pages
...CG, wherefore AL and CB are each of them equal to CG; and things which are equal to the same thing are equal to one another; therefore the straight line AL is equal to BC (ax. i). Wherefore from the given point A, a straight line AL has been drawn equal to the given straight... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...which are equal to the same thing are equal to one another. [Axiom 1. Therefore AL is equal to BO. Wherefore from the given point A a straight line AL...has been drawn equal to the given straight line BC. QEF PROPOSITION 3. PROBLEM. From the greater of two given straight lines to cut off a part equal to... | |
 | Stewart W. and co - 1884 - 272 pages
...equal 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 are equal to one another; therefore AL is equal to BC. Wherefore from the given point A a straight line AL has been drawn equal to the... | |
 | Euclides - 1884 - 182 pages
...EBA, ABD. But the angles CBE, EBD have been proved equal to the same three angles ; and things which are equal to the same are equal to one another ; therefore the angles CBA, ABD are equal to the angles CBE, EBD. ' (Ax. 1) But CBE, EBD are two right angles. (Constr.)... | |
 | John Neville Keynes - Logic - 1884 - 436 pages
...I should say the same in reference to Hansel's remark (Prolegomena Logica, p. i03), that the Axiom "things that are equal to the same are equal to one another" is only another statement of the Principle of Identity. CHAPTER II. SIMPLE EXERCISES ON THE SYLLOGISM.... | |
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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. 
