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PLÜCKER, JULIUS. - [FOUNDING ALGEBRAIC GEOMETRY]

Über ein neues Coordinatensystem. (and the continuation:) Über eine neue Art, in der analytischen Geometrie Puncte und Curven durch Gleichungen darzustellen. (2 Papers).

lyn40444

Berlin, G. Reimer, 1830. 4to. Without wrappers as extracted from "Journal für die reine und angewandte Mathematik. Hrsg. von C.L. Crelle", Bd. 5 u. 6. With titlepage to Bd. 5. Pp. 1-36 and pp. 107-146. One engraved plate. ¶ First printing of Plückers invention of separate homogenous coordinates. Plücker introduced trilinear coordinates, and he "starts with a fixed triangle and takes the coordinates of any point P to be the signed perpendicular distances from P to the sides of the triangle; each distance can be multiplied by the same arbitrary constant...by using homogenous coordinates and Euler's theorem on homogenous functions.....Plücker was able to give elegant algebraic representations of geometric ideas...and his efforts to treat duality algebraically led him to a beautiful idea, line coordinates....With this notion of line coordinates Plücker was able to give an algebraic formulation and proof of the principle of duality. (Morris Kline).

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