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The conic section is submitted to algebra, an 

 obstetrical appliance which brings forth the 

 equation; and behold, entreated now in one 

 direction, now in another, the womb of the 

 formula gives birth to the ellipse, the hyper- 

 bola, the parabola, their foci, their radius 

 vectors, their tangents, their normals, their 

 conjugate axes, their asymptotes and the rest. 

 It is magnificent, so much so that you are 

 overcome by enthusiasm, even when you 

 are twenty years old, an age hardly adapted 

 to the austerities of mathematics. It is su- 

 perb. You feel as if you were witnessing 

 the creation of a world. 



As a matter of fact, you are merely ob- 

 serving the same idea from different points 

 of view, which are illumined by the success- 

 ive phases of the transformed formula. All 

 that algebra unfolds for our benefit was con- 

 tained in the definition of the cone, but it 

 was contained as a germ, under latent forms 

 which the magic of the calculus converts into 

 explicit forms. The gross value which our 

 mind confided to the equation it returns to 

 us, without loss or gain, in coins stamped 

 with every sort of effigy. And here precisely 

 is that which constitutes the inflexible rigour 

 of the calculus, the luminous certainty before 

 which every cultivated mind is forced to bow. 

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