Euclidean geometry is an example of synthetic geometry, in that it proceeds logically from axioms to propositions without the use of coordinates.
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From the point of view of synthetic geometry, projective geometry " should be " developed using such propositions as axioms.
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In synthetic geometry, they are traditionally defined as the composition of one or several special homographies called " central collineations ".
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In synthetic geometry, this property, which is a part of the fundamental theory of projective geometry is taken as the definition of homographies.
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:The name " Pythagorean theorem " arises from the geometric interpretation of this result as an analogue of the theorem in synthetic geometry.
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He especially liked Schwarz s lectures on analytic functions and synthetic geometry, not only because of their innovations but also because Schwarz s teaching method.
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Ernst K�tter published a ( German ) report on " " The development of synthetic geometry from Monge to Staudt ( 1847 ) " ";
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So by the rules of classical, synthetic geometry, Diocles did not solve the Delian problem, which actually can not be solved by such means.
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Is there some way to solve it by synthetic geometry that actually gives you a tetrahedron ? Keenan Pepper 21 : 06, 5 April 2008 ( UTC)
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Schr�ter was influenced by Steiner's lectures, which were available only as note sheets, on synthetic geometry ( projective theory of conics ) published in 1867.
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