We describe a theory ECG of “Euclidean constructive geometry”. Things that ECG proves to exist can be constructed with ruler and compass. ECG permits us to make constructive distinctions between different forms of the parallel postulate. We show that Euclid’s version, which says that under certain circumstances two lines meet (i.e., a point of intersection exists) is not constructively equivalent to the more modern version, which makes no existence assertion but only says there cannot be two… CONTINUE READING

Foundations of Geometry (Grundlagen der Geometrie). Open Court, La Salle, Illinois (1960), second English edition, translated from the tenth German edition by Leo Unger

D. Hilbert

Original publication date,

1960

1 Excerpt

The Geometry of Rene Descartes, with a facsimile of the first edition, published in 1637 as an appendix to Discours de la Methode