 | Science - 1906 - 600 pages
...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. 3. And that a circle may be described from any center, at any distance from that center. His axioms state : 1. Things which are equal to the same... | |
 | American Mathematical Society - Mathematics - 1896 - 420 pages
...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," these indicate the limitations of elementary geometry as understood by the Greeks, limitations recognized... | |
 | Trevor H. Levere, Trevor Harvey Levere - Science - 2002 - 296 pages
...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... | |
 | Witold Marciszewski - Language Arts & Disciplines - 1994 - 340 pages
...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 be described from any centre, at any distance from that centre. This interpretation... | |
 | Ivor Grattan-Guinness, Gerard Bornet - Mathematics - 1997 - 310 pages
...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...And that a circle may be described from any centre and at any distance from (with any radius about) that centre. But in the Greek text of Peyrard,7 under... | |
 | Ainsworth Rand Spofford, Charles Annandale - Encyclopedias and dictionaries - 1901 - 594 pages
...three following 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...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. 512 END Of VOL. VI.... | |
 | Benjamin Franklin Finkel - Mathematicians - 1894 - 908 pages
...ELEMENTS. By Professor JOHN N- LTLB, Ph. D., Westminister College, Fulton, Missouri "Let it be granted that a terminated straight line may be produced to any length in a straight line." Euclid lays down the statement just quoted as his second postulate regulative of geometrical constructions.... | |
 | Mathematicians - 1896 - 740 pages
...know straight lines may be curves. They begin by doubting the truth of Euclid's second postulate — "That a terminated straight line may be produced to any length in a straight line" — and his Proposition XXXII, Book I. They are believers, also, as well as doubters. They believe... | |
 | Natural history - 1834 - 700 pages
...book marks an epoch in the progress of natural history in Britain. One of Euclid's postulates is, " a circle may be described from any centre, at any distance from that centre:" so, in nature, there is not an object which may not become thecentre of a thousand associating circumstances.... | |
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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... 
