E4P60D
Demonstration — Part IV
Latin
Ponatur exempli gratia corporis pars A vi alicujus causæ externæ ita corroborari ut reliquis prævaleat (per propositionem 6 hujus); hæc pars vires suas amittere propterea non conabitur ut reliquæ corporis partes suo fungantur officio. Deberet enim vim seu potentiam habere vires suas amittendi, quod (per propositionem 6 partis III) est absurdum. Conabitur itaque illa pars et consequenter (per propositiones 7 et 12 partis III) mens etiam illum statum conservare adeoque cupiditas quæ ex tali affectu lætitiæ oritur, rationem totius non habet. Quod si contra supponatur pars A coerceri ut reliquæ prævaleant, eodem modo demonstratur quod nec cupiditas quæ ex tristitia oritur, rationem totius habeat. Q.E.D.
English (Elwes 1883)
Let it be assumed, for instance, that A, a part of a body, is so strengthened by some external cause, that it prevails over the remaining parts (IV. vi.). This part will not endeavour to do away with its own powers, in order that the other parts of the body may perform its office; for this it would be necessary for it to have a force or power of doing away with its own powers, which (III. vi.) is absurd. The said part, and, consequently, the mind also, will endeavour to preserve its condition. Wherefore desire arising from a pleasure of the kind aforesaid has no utility in reference to a man as a whole. If it be assumed, on the other hand, that the part, A, be checked so that the remaining parts prevail, it may be proved in the same manner that desire arising from pain has no utility in respect to a man as a whole. Q.E.D.
Modern English
Suppose that part A of a body is so strengthened by some external cause that it prevails over the rest (E4P6). This part will not strive to lose its strength so that the other parts of the body can perform their function — for that would require it to have the power to diminish its own power, which (E3P6) is absurd. That part, and consequently (E3P7) the mind also, will strive to preserve that condition. Desire arising from such a joy therefore takes no account of the whole.
Conversely, if part A is checked so that the remaining parts prevail, it can be shown in the same way that the desire arising from this sadness also takes no account of the whole. Q.E.D.