 | Henry Major - 1873 - 588 σελίδες
...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 σελίδες
...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 - 120 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 - 72 σελίδες
...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 - 58 σελίδες
...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 - 860 σελίδες
...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 σελίδες
...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... | |
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BG; and things that are equal to the same are equal to one another; therefore the straight line AL is equal to BC. Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC. 
