The Foundations of Mathematics: A Contribution to the Philosophy of Geometry - Couverture souple

Carus PH.D., Paul

Couverture souple

ISBN 10 : 1497962870 ISBN 13 : 9781497962873

Editeur : Literary Licensing, LLC, 2014

Synopsis

This Is A New Release Of The Original 1908 Edition.

A propos du livre

Présentation de l'éditeur

Excerpt from The Foundations of Mathematics: A Contribution to the Philosophy of Geometry

Finally, he adds what he calls Common Notions which embody some general principles of logic (of pure reason) specially needed in geometry, such as that things which are equal to the same thing are equal to one another; that if equals be added to equals, the wholes are equal, etc.

I need not mention here perhaps, since it is a fact of no consequence, that the readings of the several manuscripts vary, and that some propositions (e. g., that all right angles are equal to one another) are now missing, now counted among the postulates, and now adduced as common notions.

The commentators of Euclid who did not understand the difference between Postulates and Common Notions, spoke of both as axioms, and even to-day the term Common Notion is mostly so translated.

In our modern editions of Euclid we find a statement concerning parallel lines added to either the Postulates or Common Notions. Originally it appeared in Proposition 29 where it is needed to prop up the argument that would prove the equality of alternate angles in case a third straight line falls upon parallel straight lines.

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Détails de l'édition

• Éditeur: Literary Licensing, LLC
• Date d'édition: 2014
• Langue: anglais
• ISBN 10: 1497962870
• ISBN 13: 9781497962873
• Reliure: Broché
• Nombre de pages: 148
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible