| 1878
...axioms are verbal truths which verify themselves everywhere and always, independently of experience. " **Things that are equal to the same are equal to one another,"** is verified by the meaning of the word equal, which admits no proper definition ; " the whole is greater... | |
| Euclides - 1879
...equal ; (def. 24) /. the rem. AL = the rem. BG ; (ax. 3) but it has been shown that BC = BG, -. AL **and BC are each of them equal to BG ; and things that are equal to the same** thing are equal to one another; (ax. 1) /. AL = BC. Wherefore, from the g1ven pt. A a st. line AL has... | |
| Thomas Harper - 1881
...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 - 1881 - 6 páginas
...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 páginas
...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
...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, and demonstration,... | |
| 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 páginas
...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
...remainder AL, is equal to the remainder BG ; bnt it has been shown that BC is equal to BG ; wherefore AL **and BC are each of them equal to BG ; and things that...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... | |
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