For let A B (in [fig. 2]) represent a ship, whose length from the prow to the poop is A B, and let the wind lie upon it in the strait parallel lines C B, D E and F G; and let D E and F G be cut in E and[and] G by a strait line drawn from B perpendicular to A B; also let B E and E G be equal, and the angle A B C any angle how small soever. Then between B C and B A let the strait line B I be drawn; and let the sail be conceived to be spread in the same line B I, and the wind to fall upon it in the points L, M and B; from which points, perpendicular to B I, let B K, M Q and L P be drawn. Lastly, let E N and G O be drawn perpendicular to B G, and cutting B K in H and K; and let H N and K O be made equal to one another, and severally equal to B A. I say, the ship B A, by the wind falling upon it in C B, D E, F G, and other lines parallel to them, will be carried forwards almost opposite to the wind, that is to say, in a way almost contrary to the way of the movent.
For the wind that blows in the line C B will (as hath been shown in [art. 6]) give to the point B an endeavour to proceed in a strait line perpendicular to the strait line B I, that is, in the strait line B K; and to the points M and L an endeavour to proceed in the strait lines M Q and L P, which are parallel to B K. Let now the measure of the time be B G, which is divided in the middle in E; and let the point B be carried to H in the time B E. In the same time, therefore, by the wind blowing in D M and F L, and as many other lines as may be drawn parallel to them, the whole ship will be applied to the strait line H N. Also at the end of the second time E G, it will be applied to the strait line K O. Wherefore the ship will always go forward; and the angle it makes with the wind will be equal to the angle A B C, how small soever that angle be; and the way it makes will in every time be equal to the strait line E H. I say, thus it would be, if the ship might be moved with as great celerity sideways from B A towards K O, as it may be moved forwards in the line B A. But this is impossible, by reason of the resistance made by the great quantity of water which presseth the side, much exceeding the resistance made by the much smaller quantity which presseth the prow of the ship; so that the way the ship makes sideways is scarce sensible; and, therefore, the point B will proceed almost in the very line B A, making with the wind the angle A B C, how acute soever; that is to say, it will proceed almost in the strait line B C, that is, in a way almost contrary to the way of the movent; which was to be demonstrated.
But the sail in B I must be so stretched as that there be left in it no bosom at all; for otherwise the strait lines L P, M Q and B K will not be perpendicular to the plane of the sail, but falling below P, Q and K, will drive the ship backwards. But by making use of a small board for a sail, a little waggon with wheels for the ship, and of a smooth pavement for the sea, I have by experience found this to be so true, that I could scarce oppose the board to the wind in any obliquity, though never so small, but the waggon was carried forwards by it.
By the same 6th theorem it may be found, how much a stroke, which falls obliquely, is weaker than a stroke falling perpendicularly, they being like and equal in all other respects.
Let a stroke fall upon the wall A B obliquely, as for example, in the strait line C A (in [fig. 3.]) Let C E be drawn parallel to A B, and D A perpendicular to the same A B and equal to C A; and let both the velocity and time of the motion in C A be equal to the velocity and time of the motion in D A. I say, the stroke in C A will be weaker than that in D A, in the proportion of E A to D A. For producing D A howsoever to F, the endeavour of both the strokes will (by [art. 6]) proceed from A in the perpendicular A F. But the stroke in C A is made by the concourse of two motions in C E and E A, of which that in C E contributes nothing to the stroke in A, because C E and B A are parallels; and, therefore, the stroke in C A is made by the motion which is in E A only. But the velocity or force of the perpendicular stroke in E A, to the velocity or force of the stroke in D A, is as E A to D A. Wherefore the oblique stroke in C A is weaker than the perpendicular stroke in D A, in the proportion of E A to D A or C A; which was to be proved.
In a full medium, motion is propagated to any distance.
9. In a full medium, all endeavour proceeds as far as the medium itself reacheth; that is to say, if the medium be infinite, the endeavour will proceed infinitely.
For whatsoever endeavoureth is moved, and therefore whatsoever standeth in its way it maketh it yield, at least a little, namely, so far as the movent itself is moved forwards. But that which yieldeth is also moved, and consequently maketh that to yield which is in its way, and so on successively as long as the medium is full; that is to say, infinitely, if the full medium be infinite; which was to be proved.
Now although endeavour thus perpetually propagated do not always appear to the senses as motion, yet it appears as action, or as the efficient cause of some mutation. For if there be placed before our eyes some very little object, as for example, a small grain of sand, which at a certain distance is visible; it is manifest that it may be removed to such a distance as not to be any longer seen, though by its action it still work upon the organs of sight, as is manifest from that which was last proved, that all endeavour proceeds infinitely. Let it be conceived therefore to be removed from our eyes to any distance how great soever, and a sufficient number of other grains of sand of the same bigness added to it; it is evident that the aggregate of all those sands will be visible; and though none of them can be seen when it is single and severed from the rest, yet the whole heap or hill which they make will manifestly appear to the sight; which would be impossible, if some action did not proceed from each several part of the whole heap.
Dilatation & contraction what they are.