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Author by : Olivier Faugeras

Languange Used : en

Release Date : 2004

Publisher by : MIT Press

Description :
This book formalizes and analyzes the relations between multiple views of a scene from the perspective of various types of geometries. A key feature is that it considers Euclidean and affine geometrie...

* Note: ebook file has been transmitted via an external affiliate, we can therefore furnish no guarantee for the existence of this file on our servers.*

In its rigorous deductive organization, the Elements remained the very model of scientific exposition until the end of the 19th century, when the German mathematician David Hilbert wrote his famous Foundations of Geometry (1899). The modern version of Euclidean geometry is the theory of Euclidean (coordinate) spaces of multiple dimensions, where distance is measured by a suitable generalization of the Pythagorean theorem . See analytic geometry and algebraic geometry .

Euclid realized that a rigorous development of geometry must start with the foundations. Hence, he began the Elements with some undefined terms, such as “a point is that which has no part” and “a line is a length without breadth.” Proceeding from these terms, he defined further ideas such as angles, circles, triangles, and various other polygons and figures. For example, an angle was defined as the inclination of two straight lines, and a circle was a plane figure consisting of all points that have a fixed distance (radius) from a given centre.

As a basis for further logical deductions, Euclid proposed five common notions, such as “things equal to the same thing are equal,” and five unprovable but intuitive principles known variously as postulates or axioms . Stated in modern terms, the axioms are as follows:

Note:! If the content not Found, you must refresh this page manually or just wait 15 second to this page refresh automatically. As alternative try our Book Search Engine, click here

Author by : Olivier Faugeras

Languange Used : en

Release Date : 2004

Publisher by : MIT Press

Description :
This book formalizes and analyzes the relations between multiple views of a scene from the perspective of various types of geometries. A key feature is that it considers Euclidean and affine geometrie...

* Note: ebook file has been transmitted via an external affiliate, we can therefore furnish no guarantee for the existence of this file on our servers.*

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