Joanna
Chris Doss wrote:
>--- Bill Bartlett <billbartlett at dodo.com.au> wrote:
>
>
>
>>its a class thing. This style of writing, in other
>>words, is a
>>systematic form of exclusion. It could be written in
>>plain English,
>>
>>
>
>It could? Write this in plain English:
>
>Let the spherical bodies A, B be suspended by the
>parallel and equal strings AC, BD, from the centres C,
>D. About these centres, with those intervals, describe
>the semicircles EAF, GBH, bisected by the radii CA,
>DB. Bring the body A to any point R of the arc EAF,
>and (withdrawing the body B) let it go from thence,
>and after one oscillation suppose it to return to the
>point V: then RV will be the retardation arising from
>the resistance of the air. Of this RV let ST be a
>fourth part, situated in the middle, to wit, so as RS
>and TV may be equal, and RS may be to ST as 3 to 2
>then will ST represent very nearly the retardation
>during the descent from S to A. Restore the body B to
>its place: and, supposing the body A to be let fall
>from the point S, the velocity thereof in the place of
>reflexion A, without sensible error will be the same
>as if it had descended in vacuo from the point T. Upon
>which account this velocity may be represented by the
>chord of the arc TA. For it is a proposition well
>known to geometers, that the velocity of a pendulous
>body in the lowest point is as the chord of the arc
>which it has described in its descent. After
>reflexion, suppose the body A comes to the place s,
>and the body B to the place k. Withdraw the body B,
>and find the place v, from which if the body A, being
>let go, should after one oscillation return to the
>place r, st may be fourth part of rv, so placed in the
>middle thereof as to leave rs equal to tv, and let the
>chord of the arc tA represent the velocity which the
>body A had in the place A immediately after reflexion.
>For t will be the true and correct place to which the
>body A should have ascended, if the resistance of the
>air had been taken off. In the same way we are to
>correct the place k to which the body B ascends, by
>finding the place l to which it should have ascended
>in vacuo. And thus everything may be subjected to
>experiment, in the same manner as if we were really
>placed in vacuo. These things being done, we are to
>take the product (if I may so say) of the body A, by
>the chord of the arc TA (which represents its
>velocity), that we may have its motion in the place A
>immediately before reflexion; and then by the chord of
>the arc tA, that we may have its motion in the place A
>immediately after reflexion. And so we are to take the
>product of the body B by the chord of the arc Bl, that
>we may have the motion of the same immediately after
>reflexion. And in like manner, when two bodies are let
>go together from different places, we are to find the
>motion of each, as well before as after reflexion; and
>then we may compare the motions between themselves,
>and collect the effects of the reflexion. Thus trying
>the thing with pendulums of ten feet, in unequal as
>well as equal bodies, and making the bodies to concur
>after a descent through large spaces, as of 8, 12, or
>16 feet, I found always, without an error of 3 inches,
>that when the bodies concurred together directly,
>equal changes towards the contrary parts were produced
>in their motions, and, of consequence, that the action
>and reaction were always equal. As if the body A
>impinged upon the body B at rest with 9 parts of
>motion, and losing 7, proceeded after reflexion with
>2, the body B was carried backwards with those 7
>parts. If the bodies concurred with contrary motions,
>A with twelve parts of motion, and B with six, then if
>A receded with 2, B receded with 8; to wit, with a
>deduction of 14 parts of motion on each side. For from
>the motion of A subducting twelve parts, nothing will
>remain; but subducting 2 parts more, a motion will be
>generated of 2 parts towards the contrary way; and so,
>from the motion of the body B of 6 parts, subducting
>14 parts, a motion is generated of 8 parts towards the
>contrary way. But if the bodies were made both to move
>towards the same way, A, the swifter, with 14 parts of
>motion, B, the slower, with 5, and after reflexion A
>went on with 5, B likewise went on with 14 parts; 9
>parts being transferred from A to B. And so in other
>cases. By the congress and collision of bodies, the
>quantity of motion, collected from the sum of the
>motions directed towards the same way, or from the
>difference of those that were directed towards
>contrary ways, was ever changed. For the error of an
>inch or two in measures may be easily ascribed to the
>difficulty of executing everything with accuracy. It
>was not easy to let go the two pendulums so exactly
>together that the bodies should impinge one upon the
>other in the lowermost place AB; nor to mark the
>places s and k, to which the bodies ascended after
>congress. Nay, and some errors, too, might have
>happened from the unequal density of the parts of the
>pendulous bodies themselves, and from the irregularity
>of the texture proceeding from other causes.
>
>http://members.tripod.com/~gravitee/axioms.htm
>
>Nu, zayats, pogodi!
>
>
>
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