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 yet it will never reach that point in which the horizontal ray carried from the eye to the glass shall fall, so that it will constantly approach it without ever reaching it, unceasingly dividing the space which will remain under this horizontal point without ever arriving at it. From which is seen the necessary conclusion that is drawn from the infinity of the extension of the course of the vessel to the infinite and infinitely minute division of this little space remaining beneath this horizontal point.

Those who will not be satisfied with these reasons, and will persist in the belief that space is not divisible ad infinitum, can make no pretensions to geometrical demonstrations, and although they may be enlightened in other things, they will be very little in this; for one can easily be a very capable man and a bad geometrician.

But those who clearly perceive these truths will be able to admire the grandeur and power of nature in this double infinity that surrounds us on all sides, and to learn by this marvellous consideration to know themselves, in regarding themselves thus placed between infinitude and a negation of extension, between an infinitude and a negation of number, between an infinitude and a negation of movement, between an infinitude and a negation of time. From which we may learn to estimate ourselves at our true value, and to form reflections which will be worth more than all the rest of geometry itself.

I have thought myself obliged to enter into this long discussion for the benefit of those who, not comprehending at first this double infinity, are capable of being persuaded of it. And although there may be many who have sufficient enlightenment to dispense with it, it may nevertheless happen that this discourse which will be necessary to the one will not be entirely useless to the other.

 

respect that we bear to antiquity is at the present day carried to such a point on subjects in which it ought to have less weight, that oracles are made of all its thoughts and 