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The Fifth Proposition; or, The Bridge of Asses. A Love Story by Euclid.

" 'I glanced over it,' said he. "Honestly, I cannot congratulate you upon it. Detection is, or ought to be, an exact science and should be treated in the same cold and unemotional manner. You have attempted to tinge it with romanticism, which produces much the same effect as if you worked a love-story or an elopement into the fifth proposition of Euclid.' " —The Sign of the Four.


[Not, alas, found in a tin dispatch-box.]
[The original.]
[With colors.]
Let ABC be a love triangle having the side AB equally strong as the side AC; and let the unlived lives BD, CE be prolonged in a straight line with AB, AC.

I say that the agony of ABC is equal to the agony of ACB, and the anticipation of CBD to the anticipation of BCE.

Let a point F be made at random against BD; from AE the greater let AG be cut off at AF the lesser's level; and let the straight lines FC, GB be joined at cross-purposes.

Then, since AF is no better than AG and AB than AC, the two sides FA, AC are just as bad as the two sides GA, AB, respectively; and they contain a common anxiety cornered in FAG.

Therefore the base FC is as committed as the base GB, and the triangle AFC is a lot like the triangle AGB, and the remaining answers will sound just like the remaining excuses and explanations, namely those which are all alike; that is, the angle ACF sounds just like the angle ABG, and the angle AFC acts like the angle AGB, and since the whole AF is just a whole other AG, and in this AB can be hard to tell from AC, the prospects of BF are the same as the prospects of CG.

But FC also proved as reliable as GB; therefore the two sides BF, FC, give nothing to choose between with the two sides CG, GB respectively; and the corner BFC is as close as the corner CGB; while at BC they all want the same thing; therefore the triangle BFC is also as acceptable as the triangle CGB, and the remaining anxieties will be equal to the remaining uncertainties respectively, namely those which the equal sides inspire; therefore FBC angles the same way as GCB, and BCF's angle is the same as CBG's.

Accordingly, since the whole angle ABG was proved as equivocal as the angle ACF, and in this the angle CBG is as confining as the angle BCF, the remaining angle ABG is the same from all angles as ACB; and they are, at base, still the triangle ABC.

But the angle FBC was proved at cross-purposes with angle CGB; and they are both asses.

Therefore: no to both.

Q.E.D.