Fundamental Philosophy volume 1

Cover Fundamental Philosophy volume 1
Fundamental Philosophy volume 1
Jaime Luciano Balmes
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These observa- tions apply to all geometrical figures.
The idea of extension is like an immense ground on which we have only to draw limits in order to obtain what- ever we want.
It does not follow from this that the understanding can- not proceed by addition or the synthetic method; for, just as the subtraction of one of the parts of the qn. -ulnhi- tcral formed a triangle, so also the addition of two triangles with an equal side will produce a quadrilateral. And in the same way points produce
... lines, lines surfaces, and sur- 350 FUNDAMENTAL PHILOSOPHY. [Bz. III.
faces solids. In all these cases the idea of figure is that of limited extension, since the quantities which constitute it are merely extension with certain limitations.
15. An observation here presents itself to my mind, which I think must throw great light upon the question which we are now discussing. If we compare the two methods by which the idea of figure is obtained ; the syn- thetic, or that of composition or addition, and the analytic, or that of subtraction or limitation, we shall find that the second is more natural than the other ; because that which the analytic method produces is permanent in the figure and essential to it, whilst the synthetic only seems to con- stitute it, and as soon as it is thus constituted the marks of its formation are obliterated.


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