# Elementary Illustrations of the Celestial Mechanics of Laplace: Part the First, Comprehending the First Book

J. Murray, 1821 - 344 páginas

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Página 31 - 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 34 - 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 29 - 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 19 - 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 18 - 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 25 - 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 323 - 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 12 - —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 140 - 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 8 - 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