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Common terms and phrasesabsolute affine affine connection al-Tusi analogous angle sum arbitrary axiom called century circle coincides complex numbers conic connection considered coordinates corresponding cross ratio curvature curve defined denoted differential dimensions distance elements elliptic equal equations equidistant Euclid Euclidean geometry Euclidean space Euler extended Figure finite formulas functions Galois Gauss geodesics given group of motions hyperbolic Ibn al-Haytham Ibn Qurra imaginary infinite interpretation intersect isomorphic Jordan algebras Khayyam Leipzig Lie algebra line AC Lobacevskian geometry magnitudes manifold mapping mathematical mathematician matrices multidimensional n-dimensional non-Euclidean geometry numbers obtained orthogonal paper parallel axiom parallel lines parallel postulate perpendicular Poincare points problem projective proof proposition prove the parallel pseudo-Euclidean space quadric quadrilateral quaternions radius rectangle representation respectively Riemann right angles rotation segment side simple Lie groups sine sphere spherical triangle spherical trigonometry straight line subgroup surface tangent term theorem theory of parallel topological treatise trigonometry vectors Popular passagesPage 36 - THINGS which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same, are equal to one another. Page 37 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles. Page 184 - Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external... Page 36 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles. Page 193 - His hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun in the circumference of a circle, the sun lying in the middle of the orbit... Page 70 - A straight line falling on parallel straight lines makes the alternate angles equal to one another, the exterior angle equal to the interior and opposite angle, and the interior angles on the same side equal to two right angles. Page 40 - ... screening the sun's light, and from this would arise the universal. Thus, as we maintain, to know a thing's nature is to know the reason why it is ; and this is equally true of things in so far as they are said without qualification to be as opposed to being possessed of some attribute, and in so far as they are said to be possessed of some attribute such as equal to two right angles, or greater or less. Page 171 - ... lines it is merely necessary to add or subtract other lines; or else, taking one line which I shall call unity in order to relate it as closely as possible to numbers, and which can in general be chosen arbitrarily... Page 216 - ... uncertain. On the other hand it was my idea to write down all this later so that at least it should not perish with me. It is therefore a pleasant surprise for me that I am spared this trouble, and I am very glad that it is just the son of my old friend, who takes the precedence of me in such a remarkable manner... Page 152 - If a straight line be cut at random, the square on the whole is equal to the squares on the segments, and twice the rectangle contained by the segments. References to this bookFrom other books
From Google ScholarGreat Problems of Mathematics: A Course Based on Original SourcesReinhard C Laubenbacher, David J Pengelley - 1992 - American Mathematical Monthly Chaos Theory and Fractal Geometry: Their Potential Impact on the ...Rhonda Roland Shearer - 1992 - Leonardo Mathematics and Her Sisters in Medieval Islam: A Selective Review ...J Lennart Berggren - 1997 - Historia Mathematica Use of four mirrors to rotate linear polarization but preserve ...Luke L Smith, Peter M Koch - 1996 - Journal of the Optical Society of America A References from web pagesNon-Euclidean geometry references A history of non-Euclidean geometry : - / 1988 - Livros Non-Euclidean Geometry: Its Development and Properties Resources for Using History in Teaching Mathematics Richard Delaware Math 444 Expository Writing Notes A History of Non-Euclidean Geometry - Mathematics (general ... Bibliography Related to Geometry <a href="http://aps.arxiv.org/abs/0712.4294v1">arxiv:0712.4294v1 ... Anthony Auerbach: Structural Constellations phd Thesis 2003 boris a rosenfeld libri - I Libri dell'autore: Boris A Rosenfeld ... Bibliographic information
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