View source for Lambert quadrangle

{{TEX|done}}{{MSC|51-03|01A50}}

A quadrangle with right angles at three of the vertices. It was considered by J.H. Lambert (1766) in attempts to prove Euclid's parallelism postulate (cf. [[Fifth postulate|Fifth postulate]]). Of the three possible assumptions about the size of the fourth angle, that it is a right, an obtuse or an acute angle, the first is equivalent to Euclid's postulate and the second leads to a contradiction with the other axioms and postulates of Euclid. As for the third, Lambert conjectured that it is satisfied on an imaginary sphere.

====References====
<table>
<TR><TD valign="top">[1]</TD> <TD valign="top">  V.F. Kagan,   "Foundations of geometry" , '''1''' , Moscow-Leningrad  (1949)  (In Russian)</TD></TR>
<TR><TD valign="top">[2]</TD> <TD valign="top">  A.V. Pogorelov,   "Lectures on the foundations of geometry" , Noordhoff  (1966)  (Translated from Russian)</TD></TR>
<TR><TD valign="top">[a1]</TD> <TD valign="top">  H. Busemann,   P.J. Kelly,   "Projective geometry and projective metrics" , Acad. Press  (1953)</TD></TR>
<TR><TD valign="top">[a2]</TD> <TD valign="top">  H.S.M. Coxeter,   "Introduction to geometry" , Wiley  (1963) {ZBL|0095.34502}}</TD></TR>
<TR><TD valign="top">[a3]</TD> <TD valign="top">  M. Greenberg,   "Euclidean and non-Euclidean geometries" , Freeman  (1974)</TD></TR>
<TR><TD valign="top">[a4]</TD> <TD valign="top">  N.W. [N.V. Efimov] Efimow,   "Höhere Geometrie" , Deutsch. Verlag Wissenschaft.  (1960)  (Translated from Russian)</TD></TR>
<TR><TD valign="top">[a5]</TD> <TD valign="top">  A.P. Norden,   "Elementare Einführung in die Lobatschewskische Geometrie" , Deutsch. Verlag Wissenschaft.  (1958)  (Translated from Russian)</TD></TR>
<TR><TD valign="top">[a6]</TD> <TD valign="top">  R. Bonola,   "Non-Euclidean geometry" , Dover, reprint  (1955)  (Translated from Italian)</TD></TR>
</table>