Geometri proyektif: Perbedaan antara revisi

Sifat-sifat lainnya dari yang memiliki kepentingan mendasar di antaranya [[Teorema Desargues]] dan [[Teorema Pappus]]. Di dalam ruang projektif berdimensi tiga atau lebih besar, terdapat suatu konstruksi yang membolehkan seseorang untuk membuktikan Teorema Desargues. Tetapi untuk dimensi dua, ia mesti dipostulatkan secara terpisah.

 

 

Projective geometry also includes a full theory of [[conic sections]], a subject already very well developed in Euclidean geometry. There are clear advantages in being able to think of a [[hyperbola]] and an [[ellipse]] as distinguished only by the way the hyperbola ''lies across the line at infinity''; and that a [[parabola]] is distinguished only by being tangent to the same line. The whole family of circles can be seen as ''conics passing through two given points on the line at infinity''—at the cost of requiring [[complex number|complex]] coordinates. Since coordinates are not "synthetic", one replaces them by fixing a line and two points on it, and considering the ''linear system'' of all conics passing through those points as the basic object of study. This approach proved very attractive to talented geometers, and the field was thoroughly worked over. An example of this approach is the multi-volume treatise by [[H. F. Baker]].