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Updated: May 20, 2025
Were the earth's pull on the moon to cease, the moon's inertia would cause it to take the tangential course, AB. On the other hand, were the moon's motion to be stopped for an instant, the moon would fall directly towards the earth, along the line AD. The moon's actual orbit, resulting from these component forces, is AC. Let AC represent the actual flight of the moon in one minute.
But the young clergyman saw with amazement the strange little figure with her unbound hair and her arms high and swaying, and as she took some steps of her dance before the gate, he questioned his host with uplifted brows. "A little mad," the doctor said, nodding, "like us all. She sings in the streets of a glad morning, and dances now and then. We take ours out in tangential opinions.
Therefore it is evident that the average pressure on the surface, instead of being normal to the chord, was so far inclined toward the front that all the head resistance of framing and wires used in the construction was more than overcome. In a wind of fourteen miles per hour resistance is by no means a negligible factor, so that tangential is evidently a force of considerable value.
The thought that suggested itself to Newton's mind was this: If we make a diagram illustrating the orbital course of the moon for any given period, say one minute, we shall find that the course of the moon departs from a straight line during that period by a measurable distance that: is to say, the moon has been virtually pulled towards the earth by an amount that is represented by the difference between its actual position at the end of the minute under observation and the position it would occupy had its course been tangential, as, according to the first law of motion, it must have been had not some force deflected it towards the earth.
Arago at Perpignan noticed considerable irregularities in the divergent rays. Some appeared curved and twisted, a few lay across the others, in a direction almost tangential to the moon's limb, the general effect being described as that of a "hank of thread in disorder."
For the purpose of explaining the phenomena of tangential flight, we will assume that the missile was projected with a sufficient force to reach the vertical point D, which is 4000 miles from the starting point B.
I don't think he has enough vanity to make a fool of himself with it, but the simple truth is he cannot help knowing that he has a wide and lively intelligence, and it pleases him to know it, and to be reminded of it, especially in an oblique and tangential sort of way, so as not to look like downright flattery. Yes, yes, I have amused a summer or two with insects, among other things.
A like instance of anticipation is afforded in the beautiful experiment of the freely-suspended ball revolving in an ellipse under the combined influence of the central and tangential forces, which Jeremiah Horrocks devised, when pursuing Kepler's theory of planetary motion, his intuition being, that the motions of the spheres might be represented by terrestrial movements.
From this tangential point of view we try to grasp the genesis of the curve as envelope, or rather, and better still, the birth of successive tangents as instantaneous directions. Speaking non-metaphorically, we cling to genetic methods of conceptualisation and proceed from the generating principle to its conceptual derivatives.
Thus there arose those devious impulses and tangential flights which spoil the works of every would-be schemer who instead of being wholly machine is half heart.
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