(1) k_{1}l'_{0} (2) dh'_{0} (3) a_{1}c_{0} (4) b_{1}e'_{0} (5) k'h_{0} (6) b'l_{0} (7) d'_{1}c'_{0} (1) k_{1}l'_{0} (5) k'h_{0} .'. l'h_{0} ... (8) (8) l'h_{0} (2) dh'_{0} .'. l'd_{0} ... (9) (9) l'd_{0} (6) b'l_{0} .'. db'_{0} ... (10) (10) db'_{0} (4) b_{1}e'_{0} .'. de'_{0} ... (11) (11) de'_{0} (7) d'_{1}c'_{0} .'. c'e'_{0} ... (12) (12) c'e'_{0} (3) a_{1}c_{0} .'. a_{1}e'_{0} Note that, in working a Sorites by this Process, we may begin with _any_ Premiss we choose.] pg091 § 3. _Solution by Method of Underscoring._ Consider the Pair of Premisses xm_{0} + ym'_{0} which yield the Conclusion xy_{0} We see that, in order to get this Conclusion, we must eliminate m and m', and write x and y together in one expression. Now, if we agree to _mark_ m and m' as eliminated, and to read the two expressions together, as if they were written in one, the two Premisses will then exactly represent the _Conclusion_, and we need not write it out separately. Let us agree to mark the eliminated letters by _underscoring_ them, putting a _single_ score under the _first_, and a _double_ one under the _second_. The two Premisses now become xm_{0} + ym'_{0} - = which we read as "xy_{0}". In copying out the Premisses for underscoring, it will be convenient to _omit all subscripts_. As to the "0's" we may always _suppose_ them written, and, as to the "1's", we are not concerned to know _which_ Terms are asserted to _exist_, except those which appear in the _Complete_ Conclusion; and for _them_ it will be easy enough to refer to the original list. pg092 [I will now go through the process of solving, by this method, the example worked in § 2. The Data are 1 2 3 4 k_{1}l'_{0} + dh'_{0} + a_{1}c_{0} + b_{1}e'_{0} + 5 6 7 k'h_{0} + b'l_{0} + d'_{1}c'_{0} The Reader should take a piece of paper, and write out this solution for himself. The first line will consist of the above Data; the second must be composed, bit by bit, according to the following directions. We begin by writing down the first Premiss, with its numeral over it, but omitting the subscripts. We have now to find a Premiss which can be combined with this, _i.e._, a Premiss containing either k' or l. The first we find is No. 5; and this we tack on, with a +.