| Euclides - 1874
...to BG ; and things which are equal to the same thing are equal to one another (Ax. 1) ; therefore 4. **The straight line AL is equal to BC. Wherefore, from...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... | |
| Euclides - 1874
...are equal to the same thing are equal to one another. [Ax. i.] Therefore AL is equal to BC. Therefore **from the given point A a straight line AL has been drawn equal to the given straight line BC.** QEF This problem admits of eight cases in the figure. 1. The given point may be joined with either... | |
| Charles Lutwidge Dodgson - 1874
...are equal to one another. Show that this needs no demonstration . This is an instance of the Axiom " **Things, that are equal to the same, are equal to one another."** PROP. XII. If any number of magnitudes be proportionals : as one of the antecedents is to its consequent,... | |
| Euclid, Lewis Carroll - 1874 - 62 pągines
...are equal to one another. Show that this needs no demonstration . This is an instance of the Axiom " **Things, that are equal to the same, are equal to one another."** ~" PROP. XII. If any number of magnitudes be proportionals : as one of the antecedents is to its consequent,... | |
| Robert Potts - 1876 - 403 pągines
...BG, wherefore AL and .BC are each of them equal to BG ; •td 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 from the given point A, a straight line AL has been drawn equal to the given straight... | |
| Edward Atkins - 1877
...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... | |
| Euclides - 1877
...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... | |
| 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
...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... | |
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