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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. "
Elements of Geometry: Containing the First Six Books of Euclid, with a ... - Side 19
av Euclid, John Playfair - 1826 - 320 sider
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A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C ...

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...
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Euclid, Book V Proved Algebraically So Far as it Relates to Commensurable ...

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,...
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Euclid, Book V. Proved Algebraically, So Far as it Relates to Commensurable ...

Euclid, Lewis Carroll - 1874 - 62 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,...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1876 - 403 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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Elements of geometry, based on Euclid, book i

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...
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Euclid, book i., propositions i. to xxvi., with exercises and alternative ...

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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The Contemporary Review, Volum 33

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...
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Euclid, books i. & ii., with notes, examples, and explanations, by a late ...

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...
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The Metaphysics of the School: Book4. Principles of being; Book 5. Causes of ...

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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The Metaphysics of the School: Book 4. Principles of being; Book 5. Causes ...

Thomas Harper - 1881 - 6 sider
...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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