Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/196

 say, but do not well know how to express my self.

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 carrieth it?

Its acquired impetus carrieth it in a right line, which continueth the rectitude of the barrel, that is, which inclineth neither to the right hand nor to the left, nor upwards nor downwards.

Which in short is asmuch as to say, it maketh no angle with the line of streight motion made by the sling.

So I would have said.

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?

It must needs be that which toucheth the circle in the point of separation, for that all others, in my opinion, being prolonged would intersect the circumference, and by that means make some angle therewith.

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 separation from the projicient.

I understand you very well, and this is that which I would say.

Of a right line which toucheth a circle, which of its points is the nearest to the centre of that circle?

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.

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.

It doth so doubtless.

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.

I think I am not so forgetful, but that I do remember