‎"BACHARACH, I.‎
‎Ueber den Cayley'schen Schnittpunktsatz. - [THE CAYLEY-BACHARACH THEOREM]‎

‎Leipzig, B. G. Teubner, 1886. 8vo. Bound in recent full black cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 26., 1886. Entire volume offered. Library label pasted on to pasted down front free end-paper. Small library stamp to lower part of title title page and verso of title page. With a marginal tear affecting pp. 275-282 and 2 cm of the text, otherwise very fine and clean. Pp. 275-299. [Entire volume: IV, 606 pp.].‎

Reference : 47134

‎First printing of Bacharach's paper which gave the final solution to what later was to be known as the Cayley-Bacharach Theorem: That when a plane curve of degree r is drawn through the mn points common to two curves of degrees m and n (both less than r), these do not count for mn conditions in the determination of the curve but for mn reduced by (m + n - r - 1) (m + n - r - 2).""Cayley wrote copiously on analytical geometry, touching on almost every topic then under discussion. Although, as explained elsewhere, he never wrote a textbook on the subject, substantial parts of Salmon’s Higher Plane Curves are due to him"" and without his work many texts of the period, such as those by Clebsch and Frost, would have been considerably reduced in size. One of Cayley’s earliest papers contains evidence of his great talent for the analytical geometry of curves and surfaces, in the form of what was often known as Cayley’s intersection theorem (C. M. P., I, no. 5 [1843], 25-27). There Cayley gave an almost complete proof (to be supplemented by Bacharach, in Mathematische Annalen, 26 [1886], 275-299)"" (DSB).‎