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 _stiriæ_ 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,