 | Edward Atkins - 1877 - 72 pages
...are equal to the same thing are equal to one another, therefore AL is equal to BC (Ax. 1). 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 cut off a part... | |
 | Euclides - 1877 - 58 pages
...3) Now AL and BC are each of them equal to BG, therefore AL and BC are equal to each other. (ax. 1) Wherefore from the given point A a straight line AL has been drawn equal to the given straight line. QEF Exercises. 1. If the radms of the smaller circle be half that of the larger, how fails the given... | |
 | Great Britain - 1878 - 860 pages
...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 - 146 pages
...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 - 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, and demonstration,... | |
 | 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... | |
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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... 
