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" Let it be granted that a straight line may be drawn from any one point to any other point. "
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Side 11
av Euclid, Robert Simson - 1821 - 516 sider
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 352 sider
...Let it be granted, that a straight line may be drawn from any one point, to any other point : f 2. That a terminated straight line may be produced to any length in a straight line : , 3. That a circle may be described from any centre, at any distance from that centre. J AXIOMS....
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The English Journal of Education, Volum 3

1845
...By the whole of any quantity we understand the sum of all its parts ; thus, AB = AD + DC + CB. 70. " Things which are equal to the same are equal to one another " ; that is, if a = m and b = m, a is equal to b. 71. In any arithmetical operation, " quantities which...
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The Quarterly Review

William Gifford, Sir John Taylor Coleridge, John Gibson Lockhart, Whitwell Elwin, William Macpherson, William Smith, Sir John Murray IV, Rowland Edmund Prothero (Baron Ernle) - 1845
...discovery, that both languages admit of the same Erse interpretation, upon the geometrical principle that things which are equal to the same are equal to one another. This argument however depends for its validity on the accuracy of his remaining assumption, that the...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - 1846
...I. Let it be granted, that a straight line may be drawn from any one point to any other point. II. That a terminated straight line may be produced to any length in a straight line. III. AXIOMS. I. Things which are equal to the same or equal things, are equal to one another. II. If equals...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - 1846
...I. Let it be granted, that a straight line may be drawn from any one point to any other point. II. That a terminated straight line may be produced to any length in a straight line. III. AXIOMS. I. Things which are equal to the same or equal things, are equal to one another. II. If equals...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1846 - 317 sider
...POSTULATES. 1. LET it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3. And that a circle may be described from any centre, at any distance from that centre. AXIOMS. 1...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...POSTULATESLet it be granted, i. That a straight line may be drawn from any one point to any other point : n. That a terminated straight line may be produced to any length in a straight line : in. That a circle may be described from any centre, at any distance from that centre. AXIOMS. i....
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A System of Logic, Ratiocinative and Inductive: Being a Connected View of ...

John Stuart Mill - 1846 - 593 sider
...which may bo .so applied to one another as to coincide ;" the three axioms which follow, (Magnitudes which are equal to the same are equal to one another — If equals are added to equals the sums are equal — If equals are taken from equals the remainders are equal,)...
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An Historical and Critical View of the Speculative Philosophy of ..., Volum 1

John Daniel Morell - 1846 - 536 sider
...judgments, as we have seen in our analysis of Locke, are at first particular and concrete. The axiom, " things which are equal to the same are equal to one another," never suggests itself to a child's mind. and yet as soon as reason is developed enough to observe equality,...
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The Biblical review, and Congregational magazine [formerly The ..., Volum 4

1847
...proved by the use of axioms in the form of propositions, that is not itself evident. The axiom, that things which are equal to the same are equal to one another, is not the proof that A and B, being equal to C, are themselves equal. The latter truth, which is particular,...
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