## 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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**density**, expansion as a measure of heat , a certain function of planetary velocity as a measure of distance from the central body , arcs of the same circle as measures of plane angles ; and it is in conformity with this ge- neral ... Page 87

... , do not proceed in a right line ; but the atmosphere being composed of an infini . tude of strata ( if we may so call them ) whose

... , do not proceed in a right line ; but the atmosphere being composed of an infini . tude of strata ( if we may so call them ) whose

**density**increases = The as they are posited nearer the earth , the GEODESIC OPERATIONS 87. Page 88

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**density**, and are therefore in . flected more and more towards the earth as the**density**aug . ments . In consequence of this it is , that rays from objects , whether celestial or terrestrial , proceed in curves which are concave towards ... Page 150

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**density**of the former ; if it weigh three pounds , its**density**is triple ; and so on . 11. Motion is a continual and successive change of place . -If the body move equally , or pass over equal spaces in equal times , it is called ... Page 151

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**density**of the body . NEWTONIAN AXIOMS . 18. EVERY body naturally endeavours to continue in its present state , whether it be at rest , or moving uniformly in a right line . 19. The change or Alteration of Motion , by any external force ...### 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.