_Five_ will make five times as many changes as _four_; for there are five times four figures to be had out of five, and not twice four the same figures, which are to be produced as before, by casting away each of the five figures by turns. Cast away 5, and 1234 will remain; cast away way 4, and 1235 will remain; cast away 3, and 1245 will remain; cast away 2, and 1345 will remain; cast away 1, and 2345 will remain. So that here are five times four figures produced, and not twice four the same figures. Now each four may be varied twenty four ways, as in the preceding example; then to the twenty four changes which each four makes, add the fifth figure which is wanting: as to the twenty four changes on 1234, add the 5; to the twenty four changes on 1235, add the 4. to the changes on 1245, add 3. to the changes on 1345, add 2. and to the changes on 2345, add 1. which renders the changes compleat, for then the five figures stand sixscore times together, and not twice alike. 12345│12354│12453│13452│23451 21345│21354│21453│31452│32451 —————│—————│—————│—————│————— 13245│13254│14253│14352│24351 31245│31254│41253│41352│42351 —————│—————│—————│—————│————— 23145│23154│24153│34152│34251 32145│32154│42153│43152│43251 —————│—————│—————│—————│————— 12435│12534│12543│13542│23541 21435│21534│21543│31542│32541 —————│—————│—————│—————│————— 14235│15234│15243│15342│25341 41235│51234│51243│51342│52341 —————│—————│—————│—————│————— 24135│25134│25143│35142│35241 42135│52134│52143│53142│53241 —————│—————│—————│—————│————— 13425│13524│14523│14532│24531 31425│31524│41523│41532│42531 —————│—————│—————│—————│————— 14325│15324│15423│15432│25431 41325│51324│51423│51432│52431 —————│—————│—————│—————│————— 34125│35124│45123│45132│45231 43125│53124│54123│54132│54231 —————│—————│—————│—————│————— 23415│23514│24513│34512│34521 32415│32514│42513│43512│43521 —————│—————│—————│—————│————— 24315│25314│25413│35412│35421 42315│52314│52413│53412│53421 —————│—————│—————│—————│————— 34215│35214│45213│45312│45321 43215│53214│54213│54312│54321 —————│—————│—————│—————│————— And in this manner the compleat numbers of changes on six, seven, eight, nine, ten, eleven, twelve, _&c._ may also be demonstrated.