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in themselves, and two companions of Saturn, besides the one we had discovered, more manifest than the rest.
If we attend to the advances by which this art has continuously grown to such a degree, we will find nothing else but the increased length of the tubes and the glass lenses, as they are called, more diligently shaped into the convexity of a larger sphere. For although very subtle men have investigated certain other methods and shortcuts; now by the prescribed figures of conic sections to be impressed upon the glass, now by gathering rays of light through the reflections of mirrors; it is certain that all these have been either in vain or far less than wishes and expectations, for reasons which it is not the place to explain here; and thus only one method by which one could progress has been left behind until now: the lengthening of the tubes. And indeed, the more I gaze upon the nature of the thing itself, the more I am inclined to think that nothing else can be hoped for by any other path, even in the future.
Therefore, those appear to have placed their efforts most excellently who have devoted themselves to preparing the lenses of a larger tube. The success of their diligence has not been lacking in this regard. But from elsewhere a not insignificant inconvenience was offered: the excessive weight and bulk of longer tubes. To move these, machines necessarily had to be called in for help. These, however, are difficult to construct and handle even for the lengths now existing, of thirty or forty feet; and if one were to progress further, they would present much more trouble. So much so that this has seemed like a fixed barrier for those tending toward greater things. Wherefore I think I will do a thing especially welcome to those who cultivate these studies and are intent on the observation of the stars if I show by what method all that obstacle and weariness is removed, and how, with a great saving of time, labor, and expense, the greatest telescopes may be applied to these spectacles. I know that among other things proposed to this end, this one which we bring here has come to the minds of others many years ago: that lenses might be arranged without a tube. But they were unable to accomplish what they wished except by some excessively difficult mechanism, which for that reason has not yet had a result. We, however, have found what we will teach to be useful in practice, and we experience this daily to our great convenience. These are the facts of the matter.