Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

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1ſay, but do not well know how to expreſs my ſelf.
SALV. And I alſo perceive that you underſtand the buſineſs,
but that you have not the proper terms, wherewith to expreſs the
ſame.
Now theſe I can eaſily teach you; teach you, that is, as
to the words, but not as to the truths, which are things.
And that
you may plainly ſee that you know the thing I ask you, and onely
want language to expreſs it, tell me, when you ſhoot a bullet out
of a gun, towards what part is it, that its acquired impetus
eth it?
SIMP. Its acquired impetus carrieth it in a right line, which
continueth the rectitude of the barrel, that is, which inclineth
ther to the right hand nor to the left, nor upwards not
wards.
SALV. Which in ſhort is aſmuch as to ſay, it maketh no angle
with the line of ſtreight motion made by the ſling.
SIMP. So I would have ſaid.
SALV. If then the line of the projects motion be to continue
without making an angle upon the circular line deſcribed by it,
whilſt it was with the projicient; and if from this circular motion it
ought to paſs to the right motion, what ought this right line to be?
SIMP. It muſt needs be that which toucheth the circle in the
point of ſeparation, for that all others, in my opinion, being
longed would interſect the circumference, and by that means make
ſome angle therewith.
SALV. You have argued very well, and ſhewn your ſelf half a
Geometrician.
Keep in mind therefore, that your true opinion
is expreſt in theſe words, namely, That the project acquireth an
impetus of moving by the Tangent, the arch deſcribed by the
motion of the projicient, in the point of the ſaid projects
tion from the projicient.
SIMP. I underſtand you very well, and this is that which I
would ſay.
SALV. Of a right line which toucheth a circle, which of its
points is the neareſt to the centre of that circle?
SIMP. That of the contact without doubt: for that is in the
circumference of a circle, and the reſt without: and the points of
the circumference are all equidiſtant from the centre.
SALV. Therefore a moveable departing from the contact, and
moving by the ſtreight Tangent, goeth continually farther and
farther from the contact, and alſo from the centre of the circle.
SIMP. It doth ſo doubtleſs.
SALV. Now if you have kept in mind the propoſitions, which
you have told me, lay them together, and tell me what you gather
from them.
SIMP. I think I am not ſo forgetful, but that I do remember