The Mathematical Principles of Natural Philosophy, Band 1,Ausgabe 1H.D. Symonds, 1803 - 231 Seiten |
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Seite xvii
... ratio of the lunar centripetal force itself , which must be the most irregular of them all , will be , indeed , a little greater than the duplicate , but will be near fixty times nearer to that than it is to the triplicate . But we may give ...
... ratio of the lunar centripetal force itself , which must be the most irregular of them all , will be , indeed , a little greater than the duplicate , but will be near fixty times nearer to that than it is to the triplicate . But we may give ...
Seite xviii
... proportion with which the fquare of the dif- tance is augmented . Let us now ... given time at the very beginning of the motion , when the bodies are urged ... ratio holds between the centripetal force of the moon revolving in its orbit ...
... proportion with which the fquare of the dif- tance is augmented . Let us now ... given time at the very beginning of the motion , when the bodies are urged ... ratio holds between the centripetal force of the moon revolving in its orbit ...
Seite xxxix
... ratio of the diftance ; as he had formerly con- jectured . Upon this principle he found the line defcribed by a ... given her likewife fome of Nature's fine features , and painted the reft to a feem- ing likeness of her . On the other ...
... ratio of the diftance ; as he had formerly con- jectured . Upon this principle he found the line defcribed by a ... given her likewife fome of Nature's fine features , and painted the reft to a feem- ing likeness of her . On the other ...
Seite 20
... given ratio , the di viding point will be either at reft , or proceed uniformly in a right line . This is demonftrated hereafter in lem . 23 and its corol . when the points are moved in the fame plane ; and by a like way of arguing , it ...
... given ratio , the di viding point will be either at reft , or proceed uniformly in a right line . This is demonftrated hereafter in lem . 23 and its corol . when the points are moved in the fame plane ; and by a like way of arguing , it ...
Seite 23
... ratio of the velocities . And if a body be projected in any direction , the motion arifing from its projec- tion is ... given time the right line AB , and with its motion of falling alone could defcribe in the fame time the la- titude AC ...
... ratio of the velocities . And if a body be projected in any direction , the motion arifing from its projec- tion is ... given time the right line AB , and with its motion of falling alone could defcribe in the fame time the la- titude AC ...
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Häufige Begriffe und Wortgruppen
ABFD abfolute accelerative alfo alſo angle VCP apfides apfis arifing attracting body axis becauſe body revolving cafe caufes cauſe centre of force centre of gravity centripetal force circle common centre conic fection corpufcle curve line cycloid decreaſe defcend defcribed demonftrated diminiſhed diſtance drawn duplicate ratio ellipfis equal fecond feveral fides figure fimilar fince firft firſt fituate focus folid fome fquare fubduplicate ratio fuch fuperficies fuppofe fyzygies given by pofition given ratio globe greateſt half-fheets hyperbola immovable increaſed interfections inverſely latus rectum lefs LEMMA let fall meaſure moſt motion move muſt obferved ofcillations orbit paffing parabola parallel parallelogram particles perpendicular plane principal vertex prop proportional PROPOSITION quadratures quantity radius reaſoning reciprocally rectangle refiftance reft right line SCHOLIUM ſhall ſhould ſpace ſphere tangent thefe themſelves THEOREM theſe thofe thoſe trajectory triangles velocity whofe Widegate
Beliebte Passagen
Seite 8 - Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year.
Seite 5 - ... line to the distance of two miles before it falls to the ground; the same, if the resistance of the air were taken away, with a double or decuple velocity, would fly twice or ten times as far.
Seite xxxvi - To make an estimate what might be the degree of this diminution, he considered with himself that, if the moon be retained in her orbit by the force of gravity, no doubt the primary planets are carried round the sun by the like power. And, by comparing the periods of the...
Seite xxviii - Therefore the retardation is proportional to the motion communicated, and the communicated motion, when the velocity of the moving body is given, is as the density of the fluid; and therefore the retardation or resistance will be as the same density of the fluid; nor can it be taken away, unless the fluid, coming about to the hinder parts of the body, restore the motion lost.
Seite 12 - A property near akin to the preceding is this, that if a place is moved, whatever is placed therein moves along with it; and therefore a body which is moved from a place in motion partakes also of the motion of its place.
Seite 28 - ... of a hammer) is (as far as I can perceive) certain and determined, and makes the bodies to return one from the other with a relative velocity, which is in a given ratio to that relative velocity with which they met.
Seite 15 - ... to another, as the fixed stars do in our regions, we could not indeed determine from the relative translation of the globes among those bodies, whether the motion did belong to the globes or to the bodies. But if we observed the cord, and found that its tension was that very tension which the motions of the globes required, we might conclude the motion to be in the globes, and the bodies to be at rest...
Seite 48 - From the same demonstration it likewise follows that the arc which a body, uniformly revolving in a circle by means of a given centripetal force, describes in any time is a mean proportional between the diameter of the circle and the space which the same body falling by the same given force would descend through in the same given time.
Seite 15 - And thus we might find both the quantity and the determination of this circular motion, even in an immense vacuum, where there was nothing external or sensible with which the globes could be compared.
Seite 29 - ... both. But the one extreme part HKI will with its whole weight bear upon and press the middle part towards the other extreme part EGF; and therefore the force with which EGI, the sum of the parts HKI and EGKH, tends towards the third part EGF, is equal to the weight of the part HKI, that is, to the weight of the third part EGF. And therefore the weights of the two parts EGI and EGF, one towards the other, are equal, as I was to prove. And indeed if those weights were not equal, the whole earth...