The Dioptrics in .NET Implementation UPC Code in .NET The Dioptrics

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Appendix generate, create gtin - 12 none for .net projects Web application framework The Dioptrics AT VI Discourse : Of Refraction La .net framework UPCA ter on we shall need to know how to determine this refraction quantitatively, and since the comparison I have just used [between the refraction of light and the penetration of a cloth by a tennis ball] enables this to be understood easily, I believe it is appropriate that I explain it here and now, and so as to make it easier to understand, I shall speak rst about re ection. Suppose a ball [ g.

] is struck from toward , and at point meets the surface of the ground , which prevents it from going further and causes it to be de ected: let us see in what direction it will go. But so that we do not get caught up in new di culties, assume that the ground is perfectly at and hard, and that the ball always travels at a constant speed, both when it descends and rebounds upwards, and let us ignore entirely the question of the power that continues to move it when it is no longer in contact with the racquet, as well as any e ect of its weight, bulk, or shape. For we are not concerned here to examine it closely, and none of these things has a bearing on the action of light, which is what should concern us.

We need only note that the power, whatever it be, which can make the motion of this ball continue, is di erent from that which determines it to move in one direction rather than another. This can be seen readily from the fact that the motion of the ball depends upon the force with which the racquet has impelled it, and this same force could have made it move in any other direction just as easily as toward ; whereas it is the position of the racquet that determines it to tend toward , and which could have determined it to tend there in the same way. Discourse of the Dioptrics Fig. even if a di erent force had moved it. This already shows that it is not impossible for this ball to be de ected by its impact with the ground, and hence that there could be a change in its determination to tend toward without any change in the force of its movement, since these are two di erent things. And as a result, we must not imagine, as many of our Philosophers do, that it is necessary for the ball to stop for a moment at point before being re ected toward ; for if its motion were to be interrupted by its being stopped momentarily, there is nothing that would cause it to begin again.

Moreover, we should note that not only the determination to move in a particular direction but also the motion itself, and in general any sort of quantity, can be divided into all the parts of which we can imagine it to be composed; and we can readily conceive that the determination of the ball to move from toward is composed of two others, one of which makes it descend from line to line , and at the same time the other makes it go from the left, , toward the right, , so that the two joined together direct it to along the line . And then it is easy to understand that its impact with the ground can prevent only one of these determinations, and not the other in any way. For it must certainly prevent the one that made the ball descend from to , for it occupies all the space below .

But why should it prevent the other, which made the ball move to the right, seeing that it does not o er any opposition at all to the determination in that direction In order to discover in exactly what direction the ball must rebound, let us describe a circle with centre passing through point , and let us say that in as much time as the ball will take to move from to , it inevitably returns from . The World and Other Writings visual .net upc barcodes to a certain point on the circumference of this circle, inasmuch as all the points which are the same distance away from as is can be found on this circumference, and inasmuch as we assume the movement of this ball to be always of a constant speed. Next, in order to determine precisely the point on the circumference to which the ball must return, let us draw three straight lines , , and perpendicular to , so that the distance between and is neither greater nor less than that between and .

And let us say that in the same amount of time as the ball took to move toward the right side from one of the points on the line to one of those on the line it must also advance from the line to some point on ; for any point of this line is as distant from in this direction as is any other, as are those on the line ; and the ball has as much determination to move to that side as it had before. Thus the ball cannot arrive simultaneously both at some point on the line and at some point on the circumference of the circle , unless this point is either or , as these are the only two points where the circumference and the line intersect; and, accordingly, since the ground prevents the ball from passing toward , we must of necessity conclude that it inevitably passes toward . And so it is easy for you to see how re ection occurs, namely at an angle always equal to the one we call the angle of incidence; in the same way that, if a ray coming from point descends to point on the surface of a at mirror , it is re ected toward in such a way that the angle of re ection is neither greater nor smaller than the angle of incidence .

Let us come now to refraction. And rst let us suppose that a ball impelled from toward encounters at point , no longer the surface of the earth, but a cloth , which is so thin and nely woven that this ball has the force to rupture it and pass through it, losing only some of its speed: half, for example. Now given this, in order to know what path it must follow, let us consider that its motion is completely di erent from its determination to move in one direction rather than another, from which it follows that the amounts of these two must be examined separately.

And let us also take into account that, of the two parts of which we can imagine this determination to be composed, only the one making the ball tend downwards can be changed in any way as a result of its collision with the cloth, while that making the ball tend to the right must always remain the same as it was, because the cloth o ers no resistance to it. Then, having described the circle with its centre at [ g. ], and.

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