 | Euclid, Isaac Todhunter - 1867 - 424 sider
...to BG. But things which are equal to the same thing are equal to one another. [Axiom 1 . Therefore AL is equal to BC. "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... | |
 | Euclid, Isaac Todhunter - 1867 - 426 sider
...equal to BG. But things which are equal to the same thing are equal to one another. [Axiom 1. Therefore AL is equal to BC. Wherefore from the given point A a straight line AI, has been drawn equal to the given straight line BC. QEP PROPOSITION 3. PROBLEM. From the greater... | |
 | Robert Potts - 1868 - 434 sider
...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 - 216 sider
...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 - 588 sider
...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 - 342 sider
...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 - 120 sider
...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 - 96 sider
...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 - 80 sider
...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 - 446 sider
...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... | |
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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... 
