Equipment Needed

The wheel d must be of some very hard material.

After having given it with the file the figure closest to that which it must have that one could have, it will be very easy to finish it, first with the blades cnop, provided that they were at the beginning so well forged that quenching has since deprived them of nothing of their shape, and that they are applied to this wheel in such a way that their cutting edge nop and its axle ee are in the same plane, and finally that there is a spring or counterweight which presses them against it while it is made to turn on its axle.

Then also with the tool Z 89 {Z89}}}, whose iron must be equally cut on both sides; and with that it can have any quasi shape you want, provided that all the parts of its cutting edge 89 are in a plane which intersects the surfaces of the CGEF boards at right angles.

To use it, you have to move the KLM ruler on poles 1, 2, so that it passes immediately from P to N, then vice versa from N to P, while you rotate the wheel on its axle. By means of which the cutting edge of this tool will remove all the inequalities which will be found from one side to the other in the thickness of this wheel, and its point all those which will be found from top to bottom: for it must have a cutting edge and a point.

After this wheel has thus acquired all the perfection it can have, the glass can easily be cut by the two various movements of it and of the lathe on which it is to be attached, provided only that there be some spring or another invention which, without impeding the movement that the turn gives it, always presses it against the wheel, and that the bottom of this wheel is always immersed in a vase which contains the sandstone, or the emery, or the tripoli, or the hotpot, or other such material which it is necessary to use for cutting and polishing glass.

And following the example of this you can quite understand in what way one must give shape to concave glasses, namely by first making blades like cnop with the tool Z 89 {\displaystyle {\rm {Z89}}}, then cutting a wheel both with these blades and with the tool Y 67 {\displaystyle {\rm {Y67}}}, and everything else in the way just explained. Only it must be observed that the wheel used for the convex can be as large as one wishes, but that the one used for the concave must be so small that, when its center is opposite - screw of line 55 of the machine that is used to cut it, its circumference does not pass above line 12 of the same machine. And we must make this wheel move much faster than the lathe to polish these concave glasses, whereas it is better for the convex ones to make the lathe move more quickly;

The reason for which is that the movement of the lathe wears the ends of the glass much more than the middle, and that on the contrary that of the wheel wears them less. As for the utility of these various movements, it is very manifest; for, polishing the glasses with the hand into a form in the manner which alone has hitherto been in use, it would be impossible to do anything good except by chance, though the forms were all perfect; and polishing them with the single movement of the lathe on a model, all the small defects of this model would mark whole circles on the glass.

I do not add here the demonstrations of several things that belong to geometry, because those who are a little versed in this science will be able to understand them enough for themselves, and I am convinced that the others will be more happy to tell me. to believe than to have the trouble of reading them. For the rest, so that everything is done in order, I would like first of all to practice polishing glasses, flat on one side and convex on the other, which had the shape of a hyperbola whose burning points were two or three feet apart: for this length is sufficient for a telescope which serves to see inaccessible objects quite perfectly.

Let us make concave glasses of various shapes, always hollowing them out more and more until we have found by experience the right shape of the one who would make this bezel as perfect as possible and better proportioned to the eye that would have to use it. Because you know that these glasses must be a little more concave for those who are short-sighted than for others.

Having thus found this concave glass, especially as the same can be used for the same eye for any other kind of glasses, there is no longer any need for glasses which are used to see inaccessible objects, but to practice to make other convex lenses which must be placed further from the concave than the first, and to make some also by degrees which must be placed further and further up to the greatest distance possible, and which are also larger in proportion. But note that, as much as these convex glasses must be placed further from the concaves and consequently also from the eye, all the more so must they be cut more exactly, because the same defects there divert the rays of farther from where they need to go.

Diopter figure 67b.jpg

If the glass F[79] deflects the ray CF as much as the glass E deflects AE, so that the angles AEG and CFH are equal, it is clear that CF, going towards H, goes much further from the point D where it would go without that, which AE does from point B going towards G. Finally, the last and main thing I would like us to practice is to polish the convex glasses on both sides for the glasses which are used to see accessible objects, and that, having first practiced making those which make these glasses very short, because they will be the easiest, one should then try, by degrees, to make those which make them longer, until you have reached the longest you can use.

Lest the difficulty you may find in the construction of these last spectacles disgusts you, I want to warn you that even though their use does not at first attract so much as that of those others who seem to promise to elevate us in the heavens, and to show us there on the stars bodies as particular and perhaps as diverse as those which we see on the earth, I nevertheless judge them much more useful, because we will be able to see by means of them the various mixtures and arrangements of the small parts of which the animals and the plants, and perhaps also the other bodies which surround us, are composed, and from this to draw much advantage to come to the knowledge of their nature: because already, according to the opinion of several philosophers, all these bodies are made only of parts of the elements variously mixed together; and, according to mine, their whole nature and essence, at least of those which are inanimate, consists only in the size, shape, arrangement, and motions of their parts.

For the difficulty that is encountered, when vaulting or hollowing these glasses on both sides, in making the vertices of the two hyperbolas directly opposite each other, we can remedy this by rounding off their circumference, and making it exactly equal to that of the handles to which they must be attached for polishing; then, when they are fastened thereto, and the plaster or pitch and cement with which they are joined thereto is still fresh and flexible, passing them with these handles through a ring into which they hardly enter .

I am not speaking to you of several other peculiarities which must be observed in cutting them, nor also of several other things which I have just said are required in the construction of spectacles, for there are none which I consider so difficult that she can stop the good spirits. And I don’t follow the ordinary reach of craftsmen; but I want to hope that the inventions that I have put in this treatise will be considered beautiful enough and important enough to oblige some of the most curious and industrious of our century to undertake their execution.