## A Course of Mathematics: For the Use of Academies as Well as Private Tuition : in Two Volumes, Volume 2W. E. Dean, 1831 |

### From inside the book

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**vibrate**in circles , as pendulums , in which case the chords ( c and c ) of the arcs described are known to be proportional to the velo- cities ; then it will be 2m : m + n :: c : c ; hence m : n :: c : 2c - c . So that , by measuring ... Page 202

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**vibrate**in circles , as pendulums , in which case the chords ( c and c ) of the arcs described are known to be proportional to the velo- cities ; then it will be 2m : m + n :: c : c ; hence m : n :: c : 2c - c . So that , by measuring ... Page 228

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**vibration**the same motions hap- pen to this heavy body , as would happen to any body descending by its gravity ...**vibrations**of pendulums would never cease . But from these obstructions , though small , it happens , that the ... Page 229

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**vibration**of a pen dulum of given length , in an indefinitely small arc . Now , in estimating the time of an oscillation in an indefinitely small circular arc , let it be re- collected that the excess of such an arc above its chord ... Page 232

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**vibrations**in a minute . Such a portable pendulum is highly useful in experiments relative to falling bodies , the velocity of sound , & c . For the comparison of the times of oscillation in indefinite- ly small arcs of circles , in ...### Other editions - View all

### Common terms and phrases

abscissas altitude axis ball base beam becomes body centre of gravity circle conic surface consequently Corol cosine curve cylinder denote density descending determine diameter direction distance draw earth equa equal equation equilibrio EXAM expression feet find the fluent fluid force given fluxion given plane ground line Hence horizontal plane hyperbola inches inclined plane intersection length logarithm measure motion moving multiplied nearly ordinates parabola parallel pendulum perpendicular position pressure prob PROBLEM PROP proportional quantity radius ratio rectangle resistance right angles right line roots Scholium side sine solid angle space specific gravity spherical excess spherical triangle square straight line supposed surface tangent theorem theref tion velocity vertex vertical plane vertical projections vibrations weight whole

### Popular passages

Page 467 - Or, by an. 249 of the same, the pressure is equal to the weight of a column of the fluid...

Page 74 - To prove that the exterior angle of a triangle is equal to the sum of the two interior opposite angles (see fig.

Page 203 - VI, its Corollaries and Scholium, for Constant Forces, are true in the Motions of. Bodies freely descending by their own Gravity ; namely, that the Velocities are as the Times, and the Spaces as the Squares of the Times, or as the Squares of the Velocities. FOR, since the force of gravity is uniform, and constantly the same, at all places near the earth's surface, or at nearly the same distance from the centre of the earth ; and since • this is the force by which bodies descend to the surface ;...

Page 247 - BPC) ; or, the pressure of a fluid on any surface is equal to the weight of a column of the fluid...

Page 297 - The workmen thought that substituting part silver was only a proper <perquisite; which taking air, Archimedes was appointed to examine it ; who, on putting...

Page 35 - Two planes are said to have the same or a like inclination to one another which two other planes have, when the said angles of inclination are equal to one another.

Page 83 - Let a, b, c, be the sides, and A, B, c, the angles of a spherical triangle, on the surface of a sphere whose radius is r ; then...

Page 393 - Multiply the number in the table of multiplicands, by the breadth and square of the depth, both in inches, and divide that product by the length, also, in inches; the quotient will be the weight in Jbs.t Example 1.

Page 252 - Weigh the denser body and the compound mass, separately, both in water and out of it ; then find how much each loses in water, by subtracting its weight in water from its weight in air ; and subtract the less of these remainders from the greater. Then...

Page 148 - Body is either Hard, Soft, or Elastic. A Hard Body is that whose parts do not yield to any stroke or percussion, but retains its figure unaltered. A Soft Body is that whose parts yield^to any stroke or impression, without restoring themselves again ; the figure of the body remaining altered.