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I shall thus grosly declare: We might sling a stone with a stick of a yard long, farther than we will do with a stick six yards lengthy, though the movement of the top of the lengthy stick, that is of the stone positioned in the slit thereof, had been more than double as swift as the motion of the tip of the other shorter stick, because it could be if the velocities had been such that the lesser stick ought to flip thrice round within the time while the higher is making one onely conversion. It’s true, that if I examine the velocities of the identical wheel, or of two wheels equal to each other, that which shall be more swiftly flip’d spherical, shall extrude the stone with higher violence; and the velocity encreasing, the cause of the projection shall likewise encrease: however when the velocity is augmented, not by encreasing the velocity in the same wheel, which would be by causing it to make a higher number of revolutions in equal instances; however by encreasing the diameter, and making the wheel better, so as that the conversion taking over the identical time in the lesser wheel, as in the better,The reason for the projection increaseth not in line with the proportion of the velocity, increased by making the wheel greater.
Now, I observe that there is a superb fallacy in this discourse, in that we do compare these velocities indifferently and completely to one another. Salv.I’ve at all times taken great delight in those issues which I have had the fortune to find, and subsequent to that, which is my chief content, I find nice pleasure in imparting them to some pals, that apprehendeth and seemeth to love them: Now, in regard you’re one of those, slacking a little bit the reins of my ambition, which is far happy when i shew my self extra perspicacious, than some other that hath the repute of a sharp sight, I will for a full and true measure of the previous dispute, produce one other fallacy of the Sectators of Ptolomey and Aristotle, which I take from the argument alledged. Salv.Instance then whereby the fallacy of my argument consisteth, if as you say it’s not concluding in the material spheres, but holdeth good in the immaterial and abstracted. Contact in a single point will not be peculiar to the perfect Spheres onely, however belongeth to all curved figures.Salv.If such there be, then in addition they will touch in a single sole level; for this contact in but one level alone is not the only real and peculiar priviledge of the perfect Sphere and perfect aircraft.
What then is its contact? It had been subsequently a less evil, for you to have granted the conclusion, but conditionally, to wit, that if there could be manufactured from matter a sphere and a airplane that have been and will proceed good, they’d touch in a single sole level, and then to have denied that any such could be made. Moreover, it is extremely laborious for that aircraft to be good, if for nothing else, yet a minimum of for that its matter is porous: and maybe will probably be no less difficult to find a sphere so perfect, as that it hath all the traces from the centre to the superficies, exactly equal. Salv.I very readily grant you all this that you’ve got stated; but it is rather a lot beside our function: for whilst you go about to shew me that a fabric sphere toucheth not a cloth airplane in one level alone, you make use of a sphere that’s not a sphere, and of a airplane that is not a aircraft; for that, in line with what you say, both these things can’t be discovered on the earth, or in the event that they could also be found, they are spoiled in making use of them to work the effect.
Salv.I am able to give you the very best satisfaction, that my talents will give depart: And though in my first discourse you thought that I had enquired into things estranged from our goal, yet neverthelesse I imagine that in the sequel of the dispute, you can find that they don’t prove so. Nay, he that should prosecute this point with extra subtil contemplations would finde that it is way more durable to procure two our bodies that touch with part of their snperficies,It’s more difficult to search out Figures that touch with part of their surface, than in a single sole level. Sagr.Then, if of figures which can be irregular, and consequently laborious to be procured, there are yet infinite that are most perfectly obteined, with what motive can or not it’s stated, that essentially the most simple, and consequently probably the most easie of all, is unattainable to be procured? And if such a Sphere was and is unattainable to be procured, it was much besides the aim to say, Quod Sphæra ænea non tangit in puncto.