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" Let it be granted that a straight line may be drawn from any one point to any other point. "
The first six books of the Elements of Euclid, with numerous exercises - Σελίδα 4
των Euclides - 1853 - 147 σελίδες
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Educational Review, Τόμος 6

1893
...in its deformity and danger. Euclid says, under the heading " Postulates" : "1. Let it be taken for granted, that a straight line may be drawn from any one point to any other point. "2. And that a finite straight line (a sect) may be produced in a straight line continually. "3. Also...

Educational Review

1893
...in its deformity and danger. Euclid says, under the heading " Postulates" : "l. Let it be taken for granted, that a straight line may be drawn from any one point to any other point. "2. And that a finite straight line (a sect) may be produced in a straight line continually. "3. Also...

The Atlantic Monthly, Τόμος 4

1859
...his hand, before commencing his artistic and scientific achievements upon Jhe black-board, says : " Let it be granted that a straight line may be drawn from any one point to any other point," I invariably answer, " Of course, — by all manner of means," — although you know, dear Don, that,...

Popular Science Monthly, Τόμος 68

1906
...elementfj> 2. Undemonstrated propositions. The postulates of Euclid are as follows. Let it be granted, 1. 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...

Bulletin of the American Mathematical Society

American Mathematical Society - 1896 - 420 σελίδες
...investigate and discover nearly all that lay within their originally unconsciously imposed boundaries. " Let it be granted, that a straight line may be drawn from any one point to any other point," " let it be granted, that a circle may be described from any centre, at any distance from that centre,"...

Poetry Realized in Nature: Samuel Taylor Coleridge and Early Nineteenth ...

Trevor H. Levere, Trevor Harvey Levere - 2002 - 288 σελίδες
...construction of nature, is taken from geometry. Euclid's second postulate in his Elements asks us to grant "that a terminated straight line may be produced to any length in a straight line."21 The indebtedness to geometry is not coincidental. Coleridge stressed it, as Schelling had...
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Logic from a Rhetorical Point of View

Witold Marciszewski - 1994 - 312 σελίδες
...calls 'requirements' and is usually rendered by 'postulates'. In Book One these are as follows. (El) A straight line may be drawn from any one point to any other point. (E2) A terminated straight line may be produced to any length in a straight line. (E3) A circle may...
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George Boole: Selected Manuscripts on Logic and its Philosophy

Ivor Grattan-Guinness, Gerard Bornet - 1997 - 236 σελίδες
...the ordinary translations of the Elements of Euclid the postulates are only three in number, viz 1. Let it be granted that a straight line may be drawn from any one point of space to any other point. 2. And that a terminated straight line may be produced to any length in...
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Imagining Numbers: (particularly the Square Root of Minus Fifteen)

Barry Mazur - 2004 - 270 σελίδες
...Commentaries on Euclid, the relevant discussion (in Thomas Taylor's translation) beginning with the sentence "Let it be granted that a straight line may be drawn from any one point to any other point." See Thomas Taylor, The Philosophical and Mathematical Commentary of Proclus on the First Book of Euclid's...
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