Non-Euclidean Geometry: A Critical and Historical Study of Its Development

Acute Angle angle of parallelism applied argument assume axioms BOLYAI bounded called circle clear common complete consider construction contained corresponding define definition demonstration determine direction distance draw elements elliptic equal equation equidistant Euclid's Euclidean existence expression fact Fifth Postulate figures fixed forces formula function fundamental further Gauss geodesic geometry give given hold hyperbolic hypothesis Ideal Length Ideal Line Ideal Points improper independent infinity interpretation intersect inversion LOBATSCHEWSKY Math means meet method metrical Non-Euclidean Geometry obtain opposite ordinary parallel passing pencil perpendicular plane position possible Postulate preceding principle problem projective projective geometry proof proper properties proposition prove quadrilateral question referred regard region relations remains remarkable representative respect result RIEMANN right angles segment sides space sphere straight line surfaces of constant taken theorem theory transformations translation triangle Trigonometry valid