Elementary Illustrations of the Celestial Mechanics of Laplace: Part the First, Comprehending the First BookJ. Murray, 1821 - 344 páginas |
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Elementary Illustrations of the Celestial Mechanics of Laplace Pierre Simon marquis de Laplace Visualização completa - 1832 |
Termos e frases comuns
absciss agissent angles appliquées axis body c'est-à-dire centre de gravité centre of gravity conséquent consequently constant corde COROLLAIRE corps côtés curve cycloid d'application d'une DEFINITION described deux autres deux forces deux parties diagonale direction distance droite equal equation equilibrium être evanescent fluent fluid fluxion grandeur l'angle l'autre l'axe l'équilibre l'on aura la force la quille la résistance la résultante levier manière menée motion multiplied nombre opposée ordinate parallelepiped parallèles parallelogram particles perpendicular peut plan incliné plane poids point d'appui posé poulie première pressure principal axes proportional qu'elles qu'on quantity quelconque radius rapport ratio résistance respect résultante des deux right line rotatory roue SCHOLIUM sens sera égale seront sin sin sin sine soient somme des momens square supposed surface tangent THEOREM tion tourner triangles trois forces trouver vanish variation velocity vertical verticale whence
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Página 27 - and is described by three letters placed near the lines, the middle letter at the angular point 64. Definition. When a straight line standing on another straight line makes the adjacent angles equal, they are called right angles.
Página 30 - BCD=CBE (86), and L ACD—BCD=ABE—CBE (16), or L ACB=ABC. 88. Theorem. If two angles of a triangle are equal, the sides opposite to them are equal. A Let L ABC=BCD ; then AC=AB. If it be denied, take, in the greater AC, CD equal to the less AB ; then, since
Página 25 - 62. Definition. A plane is a surface, in which if any two points be joined by a straight line, the whole of the straight line will be in the surface. 63. Definition. An angle is the inclination of two lines to each other. Scholium. An angle is sometimes denoted by this mark
Página 15 - 27. Definition. If the quotients of two pairs of numbers are equal, the numbers are proportional, and the first is to the second, as the third to the fourth
Página 14 - must however observe that this proposition does not extend to the case of 0 for a divisor. 19. Theorem. A multiple fraction is equal to the quotient of the numerator divided by the denominator. Or,
Página 21 - sums of all the increments will be to each other in a ratio nearer to that of the fluxions than the assigned difference (35). 48. Theorem. The fluxion of the product of two quantities is equal to the sum of the products of the fluxion of each into the other quantity. Or
Página 319 - elastic medium with a uniform velocity, equal to that which a heavy body would acquire, by falling- through half m, the height of the medium causing the pressure. Tn this case we have to call the density y, instead of the height of an incompressible fluid in article 378, and to imagine the surface of the wave
Página 10 - —b. A debt is a negative kind of property, a loss a negative gain, and a gain a negative loss. 6. Definition. A unit is a magnitude considered as a whole complete within itself. Scholium. When any quantities are enclosed in a parenthesis, or have a line drawn over them, they are considered as one quantity with respect to other
Página 136 - at which they reach the bottom. 285. Theorem. "257." The times of falling through all chords drawn to the lowest point of a circle are equal. The accelerating force in any chord AB is to that of gravity as AC to AB, or as AB to
Página 6 - Definition. A unit is a magnitude considered as a whole complete within itself. Scholium. When any quantities are enclosed in a parenthesis, or have a line drawn over them, they are considered as one quantity with respect to other symbols ; thus a