| Thomas Harper - 1881 - 414 pągines
...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 - 1880 - 400 pągines
...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 - 155 pągines
...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
...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
...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 - 1883 - 400 pągines
...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
...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
...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 - 1884 - 414 pągines
...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.... | |
| Jeremiah Sullivan Black - 1885 - 621 pągines
...and the white men, and therefore yon can not distinguish between the white men themselves, because **things that are equal to the same are equal to one another.** Is not that as certain as mathematics ? If a State Constitution would provide for a Supreme Court,... | |
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