x'm_{0} + m_{1}y_{0} (which ¶ xy'_{1}) m'_{1}x_{0} + m'y'_{0} (which ¶ x'y_{1}) m_{1}x'_{0} + m_{1}y'_{0} (which ¶ xy_{1}).] The Formula, to be remembered, is xm_{0} + ym_{0} + m_{1} ¶ x'y'_{1} with the following Rule (which is merely the Formula expressed in words):-- _Two Nullities, with Like Eliminands asserted to exist, yield an Entity, in which both Retinends change their Signs._ * * * * * In order to help the Reader to remember the peculiarities and Formulæ of these three Figures, I will put them all together in one Table. pg078 TABLE IX. _______________________________________________________ | | | Fig. I. | | | | xm_{0} + ym'_{0} ¶ xy_{0} | | | | Two Nullities, with Unlike Eliminands, yield a | | Nullity, in which both Retinends keep their Signs. | | | | A Retinend, asserted in the Premisses to exist, may | | be so asserted in the Conclusion. | |_______________________________________________________| | | | Fig. II. | | | | xm_{0} + ym_{1} ¶ x'y_{1} | | | | A Nullity and an Entity, with Like Eliminands, | | yield an Entity, in which the Nullity-Retinend | | changes its Sign. | |_______________________________________________________| | | | Fig. III. | | | | xm_{0} + ym_{0} + m_{1} ¶ x'y'_{1} | | | | Two Nullities, with Like Eliminands asserted | | to exist, yield an Entity, in which both Retinends | | change their Signs. | |_______________________________________________________| I will now work out, by these Formulæ, as models for the Reader to imitate, some Problems in Syllogisms which have been already worked, by Diagrams, in Book V., Chap. II. (1) [see p. 64] "No son of mine is dishonest; People always treat an honest man with respect." Univ. "men"; m = honest; x = my sons; y = treated with respect. xm'_{0} + m_{1}y'_{0} ¶ xy'_{0} [Fig. I.