Abstract
A brief 1671 epistolary exchange between the young Leibniz and Spinoza — not on metaphysics but on optics: ‘pandochic’ lenses and the collection of off-axis rays to widen apertures without loss of sharpness. A document of the relation between the two rationalists before the Ethica.
Testo originale inglese · Delphi Classics, 2025 · pubblico dominio
Among your other merits spread abroad by fame, I understand that you have remarkable skill in optics. I have, therefore, wished to forward my essay, such as it is, to you, as I am not likely to find a better critic in this branch of learning. The paper, which I send you, and which I have styled “a note on advanced optics,” has been published with the view of more conveniently making known my ideas to my friends and the curious in such matters. I hear that * * * * * is very clever in the same subject, doubtless he is well known to you. If you could obtain for me his opinion and kind attention, you would greatly increase my obligation to you. The paper explains itself.
I believe you have already received the “Prodromo” of Francis Lana the Jesuit, written in Italian. Some remarkable observations on optics are contained in it. John Oltius too, a young Swiss very learned in these matters, has published “Physico-Mechanical Reflections concerning Vision;” in which he announces a machine for the polishing all kinds of glasses, very simple and of universal applicability, and also declares that he has discovered a means of collecting all the rays coming from different points of an object, so as to obtain an equal number of corresponding points, but only under conditions of a given distance and form of object.
My proposal is, not that the rays from all points should be collected and re-arranged (this is with any object or distance impossible at the present stage of our knowledge); the result I aim at is the equal collection of rays from points outside the optic axis and in the optic axis, so that the apertures of glasses could be made of any size desired without impairing the distinctness of vision. But this must stand according to your skilled verdict. Farewell, and believe me, distinguished Sir, your obedient servant,
Godfrey Leibnitz,
J. U. D. Councillor of the Elector of Mainz.
Frankfort,
5 Oct. 1671
(new style).
Benedict de Spinoza
9 Nov. 1671
The Hague
Godfrey Leibnitz
Spinoza to Leibnitz.
1671, November 9
[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 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 find me most ready. I hope you will not think it too irksome to reply to this short note.
Distinguished Sir, Yours sincerely,
B. de Spinoza.
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.
Lewis Fabritius
16 Feb. 1673
Heidelberg
Benedict de Spinoza