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 of a science. What we have, in the case supposed, is a pure, reciprocal, hypothetical judgement—if and so far as anything is x, then and so far it necessarily is y, and vice versa. And this judgement is the analysis and explication of a something which is both x and y. x alone is not the ground of y, nor y alone the ground of x. Neither x nor y, nor even the nexus along with the connected terms, are 'self-evident'. The equality of the two sides is not a self-evident fact from which the equality of the subtended angles follows; nor is the latter the self-evident ground of the former. The nexus in its entirety is the inevitable explication of an Isosceles, and holds only within it.

Would the objector reply, 'Then the analysis of the Isosceles is self-evident; the Isosceles is a whole of elements whose apprehension is but the clear and steady vision of themselves, and the Isosceles is given immediately in our experience of the extended world'? Such an answer does not seem to meet the difficulty. The analysis—the reciprocal hypothetical judgement—is true if (and only if) the Isosceles is, or is assumed to be. And its truth, resting thus on that assumption, stands and falls with the whole reasoned explication of Space. For the being of an Isosceles is not itself a 'self-evident' fact or truth. Given our immediate experience of the world of solid bodies, certain types of surface (the Isosceles amongst them) inevitably reveal and distinguish themselves in the mediation which alone