members = Glieder See p. 20, s. 12.

combination = Combinirung Mendel is asking his readers to reproduce the preceding formula (p. 20, s. 16) by multiplying the two expressions listed below the sentence. Their vertical arrangement above each other makes it very convenient to carry out the combinatorial exercise “member by member”, as stated in the previous sentence. The procedure is described in the chapter on arithmetics of polynomials in Andreas von Ettingshausen, Die combinatorische Analysis als Vorbereitungslehre zum Studium der theoretischen höhern Mathematik (Vienna: Wallishausser, 1826), p. 85, but in abstract terms, using capital letters with numerical indices. In general, mathematicians seemed to prefer numbers as “indexes” (Zeiger) in presentations of combinatorial analysis. Ettingshausen discusses this explicitly (op. cit., p. 2) and the popular text book by Joseph Salomon (Lehrbuch der Elementar-Mathematik für Ober-Realschulen, Vienna: Carl Gerold und Sohn, 1853), who taught elementary mathematics at the Polytechnikum in Vienna when Mendel studied there, uses numbers instead of letters as well to designate the elements of combinatory series. Vítězslav Orel, Gregor Mendel: The First Geneticist (Oxford: Oxford University Press, 1996), pp. 68–69, cites Christian Doppler, Compendium der Arithmetik und Algebra: Mit besonderer Rücksicht auf die Bedürfnisse des praktischen Lebens und der technischen Wissenschaften, 2nd ed. (Prague: Borrosch and Andrée, 1844) as a likely source for Mendel’s knowledge of combinatorics and probability theory, but we have not been able to consult a copy. Although it is likely that the notation system Mendel developed was inspired by similar systems used in combinatorial analysis — on p. 35, s. 2, Mendel does use capital letters with numerical indices — it is also clear that he adapted these to match the specific purposes of his research. Especially his choice of using the same letter, in upper and lower-case respectively, to represent a pair of dominant and recessive traits reveals his concern with a biological, and not purely mathematical, problem.

expressions = Ausdrücke See p. 17, s. 6.