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
Results 1-5 of 39
Page 579
... vertical planes , or the fundamental or primitive planes , or the planes of projection . In the constructions the ... projections on the horizontal and vertical planes are effected by constructions performed on the horizontal plane ...
... vertical planes , or the fundamental or primitive planes , or the planes of projection . In the constructions the ... projections on the horizontal and vertical planes are effected by constructions performed on the horizontal plane ...
Page 580
... vertical plane EFGH , let fall from the perpendicular PP " meeting it in P " ; then r ' and r " are the projections of the point p on the primitive planes : and it is obvious that the projections of any other point besides P cannot be ...
... vertical plane EFGH , let fall from the perpendicular PP " meeting it in P " ; then r ' and r " are the projections of the point p on the primitive planes : and it is obvious that the projections of any other point besides P cannot be ...
Page 581
... vertical projec- tion with two accents , by means of which the several ... projections P ' , r " , must evidently coincide with the point itself as in ... vertical projection p " falls on the ground line : in No. 2 , the point r ...
... vertical projec- tion with two accents , by means of which the several ... projections P ' , r " , must evidently coincide with the point itself as in ... vertical projection p " falls on the ground line : in No. 2 , the point r ...
Page 583
... vertical projection of r , and which is denoted by the point r " . 2. When the point r is above the horizontal plane , and be- hind the vertical plane . In this case the projections r ' and r " both fall behind the ground line Er , in ...
... vertical projection of r , and which is denoted by the point r " . 2. When the point r is above the horizontal plane , and be- hind the vertical plane . In this case the projections r ' and r " both fall behind the ground line Er , in ...
Page 585
... projections of straight lines . D H P " E K L P P C F Q B Let ABCD be the horizontal plane , and EFGH the vertical plane at right angles to the former , and meeting it in their com- mon intersection EF ; and let Pq be any straight line ...
... projections of straight lines . D H P " E K L P P C F Q B Let ABCD be the horizontal plane , and EFGH the vertical plane at right angles to the former , and meeting it in their com- mon intersection EF ; and let Pq be any straight line ...
Other editions - View all
Common terms and phrases
absciss 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 plane ground line Hence horizontal plane hyperbola inches inclined plane intersection length logarithm measure motion moving multiplied nearly ordinate 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 variable velocity vertex vertical plane vertical projections vibrations weight whole
Popular passages
Page 13 - In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 469 - Or, by art. 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 299 - 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 158 - MECHANICAL POWERS are certain simple instruments employed in raising greater weights, or overcoming greater resistance than could be effected by the direct application of natural strength. They are usually accounted six in number; viz. the Lever, the Wheel and Axle, the Pulley, the Inclined Plane, the Wedge, and the Screw.
Page 249 - BPC) ; or, the pressure of a fluid on any surface is equal to the weight of a column of the fluid...
Page 301 - In the doctrine of fluxions, magnitudes or quantities of all kinds are considered as not made up of a number of small parts, but as generated by continued motion, by means of which they increase or decrease ; as a line by the motion of a point ; a surface by the motion of a line ; and a solid by the motion of a surface.
Page 254 - 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 494 - The reason is, all bodies lose some of their weight in a fluid, and the weight which a body loses in a fluid, is to its whole weight, as the specific gravity of the fluid is to that of the body.
Page 461 - ... horizontal *. 2. The theorems just given may serve to show, in what points of view machines ought to be considered by those who would labour beneficially for their improvement. The first object of the utility of machines consists in furnishing the means of giving to the moving force the most commodious direction ; and, when it can be done, of causing its action to be applied immediately to the body to be moved. These can rarely be united : but the former can be accomplished in most instances...