The Mathematical Principles of Natural Philosophy, Band 1,Ausgabe 1H.D. Symonds, 1803 - 231 Seiten |
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... say , a part of fpace ; not the fituation , nor the external furface of the body . For the places of equal folids , are always equal ; but their fuperficies , by reafon of their diffimilar figures , are often unequal . Pofitions ...
... say , a part of fpace ; not the fituation , nor the external furface of the body . For the places of equal folids , are always equal ; but their fuperficies , by reafon of their diffimilar figures , are often unequal . Pofitions ...
Seite 30
... say , that the ultimate ratios which the infcribed figure AKbLcMdD , the circumfcribed figure AalbmcndoE , and curvilinear figure AabcdE , will have to one another , are ratios of equality . For the difference of the infcribed and ...
... say , that the ultimate ratios which the infcribed figure AKbLcMdD , the circumfcribed figure AalbmcndoE , and curvilinear figure AabcdE , will have to one another , are ratios of equality . For the difference of the infcribed and ...
Seite 35
... say , that A and are one to the other in a given ratio . BC Ꭰ LEMMA XI . The evanefcent fubtense of the angle of contact , in all curves which at the point of contact have a finite curvature , is ulti- mately in the duplicate ratio of ...
... say , that A and are one to the other in a given ratio . BC Ꭰ LEMMA XI . The evanefcent fubtense of the angle of contact , in all curves which at the point of contact have a finite curvature , is ulti- mately in the duplicate ratio of ...
Seite 83
... say farther , that if any right line touches the curve line in the first figure , the fame right line transferred the fame way with the curve into the new figure will touch that curve line In the new figure , and vice verfa . For if any ...
... say farther , that if any right line touches the curve line in the first figure , the fame right line transferred the fame way with the curve into the new figure will touch that curve line In the new figure , and vice verfa . For if any ...
Seite 154
... say , that the interior of the two revolving bodies will , by radii drawn to the in- nermoft and greatest , describe round that body areas more proportional to the times , and a figure more approaching to that of an ellipfis having its ...
... say , that the interior of the two revolving bodies will , by radii drawn to the in- nermoft and greatest , describe round that body areas more proportional to the times , and a figure more approaching to that of an ellipfis having its ...
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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
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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...