A Course of Mathematics: For the Use of Academies as Well as Private Tuition : in Two Volumes, Volume 2W. E. Dean, 1831 - Mathematics |
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Page 38
... square base of each , with regular octagonal base , pentagonal ; hexagonal - = Im gonal = m- M- decagonal , duodecagonal , · m gonal base . Hence again we may infer , that the sum of all the solid angles of any prism of triangular base ...
... square base of each , with regular octagonal base , pentagonal ; hexagonal - = Im gonal = m- M- decagonal , duodecagonal , · m gonal base . Hence again we may infer , that the sum of all the solid angles of any prism of triangular base ...
Page 39
... square bases , their vertices all meeting at the centre of the circumscribing sphere ; then each of the solid angles made by the four planes meeting at each vertex , will be of the maximum solid angle ; and each of the solid angles at ...
... square bases , their vertices all meeting at the centre of the circumscribing sphere ; then each of the solid angles made by the four planes meeting at each vertex , will be of the maximum solid angle ; and each of the solid angles at ...
Page 40
... square pyramid be bisected . 1st . Let a plane be drawn through the vertex and any two opposite angles of the base , that plane will bisect the solid angle at the vertex ; forming two trilateral angles , each equal to half the original ...
... square pyramid be bisected . 1st . Let a plane be drawn through the vertex and any two opposite angles of the base , that plane will bisect the solid angle at the vertex ; forming two trilateral angles , each equal to half the original ...
Page 59
... square miles . Ex . 16. Determine the solid angles of a regular pyramid with hexagonal base , the altitude of the pyramid being to each side of the base , as 2 to 1 . Ans . Plane angle between each two lateral faces 125 ° 22′35 ...
... square miles . Ex . 16. Determine the solid angles of a regular pyramid with hexagonal base , the altitude of the pyramid being to each side of the base , as 2 to 1 . Ans . Plane angle between each two lateral faces 125 ° 22′35 ...
Page 83
... square of the radius . PROBLEM VIII . It is required to investigate a theorem , by means of which , spherical triangles , whose sides are small compared with the radius , may be solved by the rules for plane trigono- metry , without ...
... square of the radius . PROBLEM VIII . It is required to investigate a theorem , by means of which , spherical triangles , whose sides are small compared with the radius , may be solved by the rules for plane trigono- metry , without ...
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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...