Spinoza’s Letter 39: Descartes’ Silence

I post Letter 39 here, for reference. 

Letter 39

To the humane and sagacious Jarig Jelles, from B.d.S.

[The Original, written in Dutch, is lost. It may be the text reproduced in the Dutch edition of the O.P. The Latin is a translation.]

Most humane Sir,

Various obstacles have hindered me from replying any sooner to your letter. I have looked at and read over what you noted regarding the Dioptica of Descartes. On the question as to why the images at the back of the eye become larger or smaller, he takes account of no other cause than the crossing of the rays proceeding from the different points of the object, according as they begin to cross one another nearer to or further from to eye, and so he does not consider the size of the angle which the rays make when they cross one another at the surface of the eye. Although this last cause would be principle (sit praecipua ) to be noted in telescopes, nonetheless, he seems deliberately to have passed over it in silence, because, I imagine, he knew of no other means of gathering rays proceeding in parallel from different points onto as many other points, and therefore he could not determine this angle mathematically.

Perhaps he was silent so as not to give any preference to the circle above other figures which he introduced; for there is not doubt that in this matter the circle surpasses all other figures that can be discovered.

For because a circle is everywhere the same, it has the same properties everywhere. If, for example, circle ABCD should have the property that all rays coming from direction A and parallel to axis AB are refracted at its surface in such a way that they thereafter all meet at point B; and also all rays coming from point C and parallel to axis CD are refracted at its surface so that they all meet together at point D, this is something that could be affirmed of no other figure, although the hyperbola and the ellipse have infinite diameters. So the case is as you describe; that is, if no account is taken of anything except the focal lenth of the eye or of the telescope, we should be obliged to manufacture very long telescopes before we could see objects on the moon as distinctly as those on earth. But as I have said, the chief consideration is the size of the angle made by the rays issuing from different points when they cross one another at the surface of the eye. And this angle also becomes greater or less as the foci of the glasses fitted in the telescope differ to a greater or lesser degree. If you desire to see the proof of this I am ready to send it to you whenever you wish.

Voorburg, 3 March 1667

[trans. Samuel Shirley altered]

Benedicti de Spinoza opera quotquot reperta sunt quotquot reperta sunt By Benedictus de Spinoza, Baruch Spinoza, Johannes van Vloten, Jan Pieter Nicolaas Land