there remains one-fourth less the share. Remove then (85) one-fifth of what remains of the one-fourth, namely, half one-tenth of the capital less one-fifth of the share. Then return to the one-third, and deduct from it half one-tenth of the capital, and four-fifths of a share, and one other share besides. The remainder then is one-third, less half one-tenth of the capital, and less one share and four-fifths. Add hereto one-fourth of the remainder, which was excepted, and assume the one-third to be eighty; subtracting from it half one-tenth of the capital, there remain of it sixty-eight less one share and four-fifths. Add to this one-fourth of it, namely, seventeen parts, less one-fourth of the shares to be subtracted from the parts. Then you have eighty-five parts less two shares and one-fourth. Add this to the other two-thirds of the capital, namely, one hundred and sixty parts. Then you have one and one-eighth of one-sixth of capital, less two shares and one-fourth, equal to six shares. Reduce this, by removing the shares which are to be subtracted, and adding
![{\displaystyle {\begin{aligned}&1-x-y=6v\\&x=v+{\tfrac {1}{5}}[{\tfrac {1}{4}}-v]\;;\;y=v-{\tfrac {1}{4}}[{\tfrac {1}{3}}-x-v]\\&{\text{i.e.}}\;{\tfrac {2}{3}}+{\tfrac {1}{3}}-x-v+{\tfrac {1}{4}}[{\tfrac {1}{3}}-x-v]=6v\\&{\text{or}}\;{\tfrac {2}{3}}+{\tfrac {5}{4}}[{\tfrac {1}{3}}-x-v]=6v\\&{\text{or}}\;{\tfrac {2}{3}}+{\tfrac {5}{4}}[{\tfrac {1}{3}}-{\tfrac {1}{4}}+{\tfrac {1}{4}}-v-{\tfrac {1}{5}}[{\tfrac {1}{4}}-v]-v]=6v\\&{\text{or}}\;{\tfrac {2}{3}}+{\tfrac {5}{4}}[{\tfrac {1}{12}}+{\tfrac {4}{5}}[{\tfrac {1}{4}}-v]-v]=6v\\&\therefore \;{\tfrac {2}{3}}+{\tfrac {5}{4\times 12}}+{\tfrac {1}{4}}=[7+{\tfrac {5}{4}}]v\\&\therefore \;{\tfrac {8}{3}}+{\tfrac {5}{12}}+1=33v\;\therefore \;{\tfrac {49}{12\times 33}}={\tfrac {49}{396}}=v\\&\therefore \;x=v+{\tfrac {10}{396}},\;{\text{and}}\;y=v-{\tfrac {6}{396}}\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8af777b35559f2c90606454b0e4f7d8f43d0c231)
