Philosophical Transactions of the Royal Society - Vol 1 - 1666: Giving some Accompt of the present Undertakings, Studies, and Labours of the Ingenious in many considerable parts of the WorldVarious
History
Philosophical Transactions of the Royal Society - Vol 1 - 1666: Giving some Accompt of the present Undertakings, Studies, and Labours of the Ingenious in many considerable parts of the World
Various
Science -- Periodicals
And what he now Adds, being to this purpose; That though _Euclid_'s [Greek:
Semeion], which we translate, _a Point_, be not indeed _Nomen Quanti_; yet
cannot this be actually represented by any thing, but what will have some
Magnitude; nor can _a Painter_, no not _Apelles_ himself, draw a _Line_ so
small, but that it will have some Breadth; nor can _Thread_ be spun so
Fine, but that it will have some Bigness; (_pag._ 2, 3, 19, 21.) is nothing
to the Business; For _Euclide_ doth not speak either of such _Points_, or
of such _Lines_.
He should rather have considered of his own Expedient, _pag._ 11. That,
when one of his (_broad_) Lines, passing through one of his (_great_)
Points, is supposed to cut another Line proposed, into two equal parts; we
are to understand, the _Middle of the breadth_ of that Line, passing
through the _middle_ of that Point, to distinguish the Line given into two
equal parts. And he should then have considered further, that _Euclide_, by
a _Line_, means no more than what Mr. _Hobs_ would call _the middle of the
breadth_ of his; and _Euclide_'s _Point_, is but the _Middle_ of Mr.
_Hobs_'s. And then, for the same reason, that Mr. _Hobs_'s _Middle_ must be
said to have no _Magnitude_; (For else, not the _whole Middle_, but the
_Middle of the Middle_, will be _in the Middle_: And, the _Whole_ will not
be equal to its _Two Halves_; but Bigger than _Both_, by so much as the
_Middle_ comes to:) _Euclide_'s _Lines_ must as well be said to have no
Breadth; and his _Points_ no Bigness.
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