We will begin these our Inquiries therefore with the Observations of Bodies of the most simple nature first, and so gradually proceed to those of a more compounded one.  In prosecution of which method, we shall begin with a Physical point; of which kind the Point of a Needle is commonly reckon’d for one; and is indeed, for the most part, made so sharp, that the naked eye cannot distinguish any parts of it:  It very easily pierces, and makes its way through all kind of bodies softer then it self:  But if view’d with a very good Microscope, we may find that the top of a Needle (though as to the sense very sharp) appears a broad, blunt, and very irregular end; not resembling a Cone, as is imagin’d, but onely a piece of a tapering body, with a great part of the top remov’d, or deficient.  The Points of Pins are yet more blunt, and the Points of the most curious Mathematical Instruments do very seldome arrive at so great a sharpness; how much therefore can be built upon demonstrations made onely by the productions of the Ruler and Compasses, he will be better able to consider that shall but view those points and lines with a Microscope.

Now though this point be commonly accounted the sharpest (whence when we would express the sharpness of a point the most superlatively, we say, As sharp as a Needle) yet the Microscope can afford us hundreds of Instances of Points many thousand times sharper:  such as those of the hairs, and bristles, and claws of multitudes of Insects; the thorns, or crooks, or hairs of leaves, and other small vegetables; nay, the ends of the stiriae or small parallelipipeds of Amianthus, and alumen plumosum; of many of which, though the Points are so sharp as not to be visible, though view’d with a Microscope (which magnifies the Object, in bulk, above a million of times) yet I doubt not, but were we able practically to make Microscopes according to the theory of them, we might find hills, and dales, and pores, and a sufficient bredth, or expansion, to give all those parts elbow-room, even in the blunt top of the very Point of any of these so very sharp bodies.  For certainly the quantity or extension of any body may be Divisible in infinitum, though perhaps not the matter.

But to proceed:  The Image we have here exhibited in the first Figure[1], was the top of a small and very sharp Needle, whose point aa nevertheless appear’d through the Microscope above a quarter of an inch broad, not round nor flat, but irregular and uneven; so that it seem’d to have been big enough to have afforded a hundred armed Mites room enough to be rang’d by each other without endangering the breaking one anothers necks, by being thrust off on either side.  The surface of which, though appearing to the naked eye