The Principles of Fluxions: Designed for the Use of Students in the Universities |
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Common terms and phrases
a+cz a²+x² abscissa acquire the velocity angle arc of radius Assume axis center of force center of gravity chord of curvature circle circular arc circumference constant corr cosine curve cycloid cylinder density described diameter distance draw ellipse equal equation find the center find the fluent fluent of xx force varying geometric progression given fluxion Given the fluent hence hyperbola increment latus rectum logarithm logarithmic spiral maximum ordinate parallel particle perpendicular PROB PROP PROPOSITION quadrant quantity radius of curvature ratio resistance similar triangles sphere spheroid spiral supposed surface taking the fluxion tangent variable versed sine whole x²)¹
Popular passages
Page 212 - The pressure of the fluid on any horizontal surface or plane, is equal to the weight of a column of the fluid, whose base is equal to that plane, and altitude is its depth below the upper surface of the fluid.
Page iii - the mere knowledge of certain truths is, to the great body of literary men, a matter only of secondary importance, when compared with the advantages which result...
Page 3 - Et responsio facilis est; per velocitatem ultimam intelligi earn, qua corpus movetur, ñeque antequam attingit locum ultimum et motus cessât, ñeque postea, sed tune cuín attingit ; id est, illam ipsam velocitatem quacum corpus attingit locum ultimum et quâcum motus cessât.
Page 73 - ... bodies, is that point upon which the body, or system of bodies, acted upon only by the force of gravity, will balance itself in all positions ; hence it follows, that, if a line or plane, passing through the centre of gravity, be supported, the body or system will be also supported. CENTRE OF GYRATION Is that point into which, if the whole mass were collected, a given force, applied at a given distance, would produce the same angular velocity in the same time as if the bodies were disposed at...
Page 402 - Prove that the problem, to describe a circle with its centre on the circumference of a given circle so that the length of the arc intercepted within the given circle shall he a maximum, is reducible to the solution of the equation 0 = cot 0.
Page 184 - Solve the following equation ; z3 - #2 - 8 x + 12 :r0, which has 2 equal roots. 7. Find the respective bearings of London and Constantinople from each other. 8. Compare the velocity of a body at the vertex of a parabola, with the velocity in a circle at the distance of half the latus rectum.
Page 438 - Find the centroid of a solid hemisphere whose density varies as the nth power of the distance from the center.
Page 73 - ... balance itself in all positions ; hence it follows, that, if a line or plane, passing through the centre of gravity, be supported, the body or system will be also supported. CENTRE OF GYRATION Is that point into which, if the whole mass were collected, a given force, applied at a given distance, would produce the same angular velocity in the same time as if the bodies were disposed at their respective distances. This point differs from the Centre of Oscillation only in this, that, in the latter...
Page 461 - The compressing force of the air varying as the density, and the force of gravity varying inversely as the square of the distance from the center of the Earth, find the relation between the density of the air at any altitude and the density at the Earth's surface.
Page 179 - This is the result arrived at by Newton and which, as we have already remarked, was regarded by him and is now generally received as the theoretical formula for the space through which a body must fall to acquire the velocity of sound. But it is evident from our demonstration that the velocity due to that space, instead of being the velocity of any assignable pulse, is simply a limit below which no pulse can be propagated in an elastic fluid whose subtangent is H...