‎"PLÜCKER, JULIUS. - FOUNDING A NEW GEOMETRY.‎
‎Über die allgemeinen Gesetze, nach welchen irgend zwei Flächen einen Contact der verschiedenen Ordnungen haben.‎

‎(Berlin, G. Reimer, 1829). 4to. No wrappers. Extracted from ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", Bd. 4. - Plücker's paper pp. 349-370‎

Reference : 41605

‎First edition of a major paper in the arithmetization of geometry introducing the so-called triangular coordinates. ""In 1829 Plücker contributed to Crelle's Journal (the paper offered here) with a revolutionary point of view that broke completely with the old Cartesian view of coordinates as line segments. The equation of a straight line in homogenous coordinates has the form ax + by + ct=0....Plücker saw that one could modify the usual language and call (a,b,c) the homogenous coordinates of a line....Plücker had discovered the immidiate analytic counterpart of the geometric principle of duality, about which Gergonne and Poncelet had quarreled"" it now became clear that the justification that pure geometry had sought in vain was here supplied by the algebraic point of view."" (Boyer, History of Mathematics).‎