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Correspondence, by Benedict de Spinoza, [1883], at



[Answer to the foregoing letter].

Most learned and distinguished Sir,—I have read the paper you were kind enough to send me, and return you many thanks for the communication. I regret that I

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have not been able quite to follow your meaning, though you explain it sufficiently clearly, whether you think that there is any cause for making the apertures of the glasses small, except that the rays coming from a single point are not collected accurately at another single point, but in a small area which we generally call the mechanical point, and that this small area is greater or less in proportion to the size of the aperture. Further, I ask whether the lenses which you call "pandochæ" correct this fault, so that the mechanical point or small area, on which the rays coming from a single point are after refraction collected, always preserves the same proportional size, whether the aperture be small or large. If so, one may enlarge the aperture as much as one likes, and consequently these lenses will be far superior to those of any other shape known to me; if not, I hardly see why you praise them so greatly beyond common lenses. For circular lenses have everywhere the same axis; therefore, when we employ them, we must regard all the points of an object as placed in the optic axis; although all the points of the object be not at the same distance, the difference arising thence will not be perceptible, when the objects are very remote; because then the rays coming from a single point would, as they enter the glass, be regarded as parallel. I think your lenses might be of service in obtaining a more distinct representation of all the objects, when we wish to include several objects in one view, as we do, when we employ very large convex circular lenses. However, I would rather suspend my judgment about all these details, till you have more clearly explained your meaning, as I heartily beg you to do. I have, as you requested, sent the other copy of your paper to Mr. * * * *. He answers, that he has at present no time to study it, but he hopes to have leisure in a week or two.

I have not yet seen the "Prodromo" of Francis Lana, nor the "Physico-Mechanical Reflections" of John Oltius. What I more regret is, that your "Physical Hypothesis" has not yet come to my hands, nor is there a copy for sale here at the Hague. The gift, therefore, which you so liberally promise me will be most acceptable to me; if I can be of use to you in any other matter, you will always

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find me most ready. I hope you will not think it too irksome to reply to this short note.

Distinguished Sir,       
Yours sincerely,    

The Hague, 9 Nov., 1671.

P.S. Mr. Diemerbroech does not live here. I am, therefore, forced to entrust this to an ordinary letter-carrier. I doubt not that you know someone at the Hague, who would take charge of our letters; I should like to hear of such a person, that our correspondence might be more conveniently and securely taken care of. If the "Tractatus Theologico-Politicus" has not yet come to your hands, I will, unless you have any objection, send you a copy. Farewell.


371:1 Francis Lana, of Brescia, 1631-1687. The title of his book is, "Prodromo premesso all’ Arte maestra." He also wrote "Magistræ naturæ et artis."

Next: Letter LIII. From Fabritius