| Robert Potts - 1868 - 410 páginas
...to the remainder BG; (ax. 3.) but it has been shewn that .BCis equal to BG, wherefore AL and BCaie **each of them equal to BG; and 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... | |
| Euclid, Charles Peter Mason - 1872
...straight line, the adjacent £s so formed are together equal to two right £s. (Prop. XIII.) 2. That **things that are equal to the same are equal to one another.** (Ax. I.) 3. That if the same quantity be taken from two equal quantities the remainders are equal.... | |
| Henry Major - 1873
...equal to the remainder BG; but it has been shown that BC is equal to BG ; wherefore AL and BC are cash **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 - 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...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 - 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 páginas
...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 páginas
...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 off a part... | |
| 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... | |
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