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12 Feb 2025, Wed

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Salv.I’ve both: and after we shall handle the business of motions apart, I’ll talk them: in the interim, that we might haven’t any more events of interrupting our discourse, we are going to suppose, that we’re to make our computation upon a ball of Iron of an hundred (a) pounds, the which by (a) (b) Note that these Calculations are made in Italian weights and measures. Therefore, Simplicius, that house from the concave of the Moon to the centre of the Earth, which your Accomptant said could not be handed beneath greater than six days, you see that (computing by expertise, and not upon the fingers ends) that it shall be passed in much less than 4 hours; and making the computation actual, it shall be handed by the moveable in three hours, 22 min. Now allow us to compleat the whole Parallelogram AMBC, and let us prolong as far as to the facet thereof BM, not onely the Parallels marked in the Triangle, however these infinite others imagined to be drawn from all the factors of the aspect AC; and like as BC, was the greatest of these infinite parallels of the Triangle, representing unto us the best diploma of velocity acquired by the moveable in the speed up motion, and the entire superficies of the said Triangle, was the mass and sum of the whole velocity, wherewith in the time AC it passed such a sure area, so the parallelogram is now a mass and aggregate of a like number of levels of velocity, however every equal to the greatest BC, the which mass of velocities will be double to the mass of the increasing velocities within the Triangle, like because the stated Parallelogram is double to the Triangle: and therefore if the moveable, that falling did make use of the accelerated levels of velocity, answering to the triangle ABC, hath passed in such a time such an area, it is extremely affordable and probable, that making use of the uniform velocities answering to the parallelogram, it shall passe with an excellent motion in the identical time an area double to that handed by the speed up movement.

Khmer Pidan with Scenes from the Jataka Tales (Late 19th century) // Cambodia Now I inform him, that that very same ball falling from the concave unto the centre, will acquire a level of velocity a lot greater than double the velocity of the diurnal motion of the Lunar concave;The falling moveable if it move with a level of velocity acquired in a like time with an uniform movement, it shall paß an area double to that passed with the accelerated movement. 5, all these levels of velocity wherewith the moveable is moved, make the sum of 15;but when the moveable should transfer with as many levels in quantity as these are, and each of them equal to the most important, which is 5, the aggregate of all these last velocities can be double to the others, namely 30. And due to this fact the moveable shifting with a like time, but with uniform velocity, which is that of the best degree 5, must go an area double to that which it passeth within the speed up time, which beginneth at the state of relaxation. You need to know due to this fact that the grave body falling and buying all the best way new velocity in keeping with the proportion already mentioned, hath in any in any respect place of the road of its motion such a degree of velocity, that if it should continue to move therewith, uniformly without farther encreasing it; in another time prefer to that of its descent, it would passe a space double to that handed in the line of the precedent movement of descent.

person in black shirt wearing virtual reality glasses Sagr.That this proposition is most false, I make little doubt on the earth; however but that yours is absolutely true, I can not effectively guarantee my self: nevertheless, I imagine it, seeing that you so resolutely affirm it; which I’m positive you would not do, in case you had not certain expertise, or some clear demonstration thereof. A proposition which you additionally as soon as before supposed as true, but never demonstrated. Let us mark these three numbers with the Letters A first, B second, C third. And thus for instance, if that ball in coming from the concave of the Moon to its centre hath spent three hours, 22 min. Terrestrial Globe had been bored thorow the centre, a Canon bullet descending by means of that Well, would purchase by that time it came to the centre, such an impulse of velocity, that, it having passed past the centre, would spring it upwards the other manner, as great an area, as that was wherewith it had descended, all the way in which past the centre diminishing the velocity with decreasements like to the increasements acquired within the descent: and the time spent in this second motion of ascent, I believe, can be equal to the time of descent.

Four seconds, passe double that house, particularly as a lot as the entire diameter of the Lunar Orb; and because from the Moons concave to the centre are 196000 miles, which the ball passeth in 3 hours 22 prim. Four seconds, an area double to that, particularly 392000 miles; but the same continuing within the concave of the Moon, which is in circuit 1232000 miles, and moving therewith in a diurnal movement, it might make in the same time, that’s in 3 hours 22 min. 10 be supposed the rising velocities, and the others unto one 1, be the rising; and let those of the time of the descent, and the others of the time of the ascent being added all collectively, make as many, as if one of the two sums of them had been all of the best degrees, and therefore the whole house passed by all of the levels of the increasing velocities, and decreasing, (which put collectively is the entire diameter) must be equal to the space handed by the best velocities, which can be in number half the aggregate of the growing and decreasing velocities. Now let us imagine the elements marked in the road AC, to be equal occasions, and let the parallels drawn by the points D, E, F, G, symbolize unto us the levels of velocity accelerated, and increasing equally in equal instances; and let the purpose A be the state of rest, from which the moveable departing, hath v. g.