Non-Euclidean GeometryCourier Corporation, 15 Αυγ 2012 - 448 σελίδες This is an excellent historical and mathematical view by a renowned Italian geometer of the geometries that have risen from a rejection of Euclid's parallel postulate. Students, teachers and mathematicians will find here a ready reference source and guide to a field that has now become overwhelmingly important. |
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... pencil with a given straight line in the plane of the pencil , one of these lines alone being excepted . It is true that there is a certain Again , if we accept the second or the third Position of the Parallel Postulate . 19.
... of a triangle is equal to two right angles . It is right to remember that SACCHERI was familiar with and had criticised the work of the Arabian Geometer . Fig . 24 . Among the lines of the pencil. Two Hypotheses give Postulate V. 37.
... pencil through A , coplanar with the line b , there exist lines which cut b , as , e . g . , the line AB perpendicular to b ; and lines which have a common I With this result the question raised by the Greeks , as to the possibility of ...
... pencil , which makes a smaller angle with AB than the acute angle BAP , also cuts b . On the other hand , if the line AQ , different from AA ' , has a common perpendicular with b , every other line , which makes with AB a larger acute ...
... pencil of lines through A two lines p and q , asymptotic to b , one towards the right , and the other towards the left , which divide the pencil into two parts . The first of these consists of the lines which intersect b , and the ...
Άλλες εκδόσεις - Προβολή όλων
Non-Euclidean Geometry: A Critical and Historical Study of Its Development Roberto Bonola Περιορισμένη προεπισκόπηση - 1955 |
Non-Euclidean Geometry: A Critical and Historical Study of Its Development Roberto Bonola Προβολή αποσπασμάτων - 1955 |