## 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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**surface**be given = s . Demonstrate that AB = √ ( 2s cot A ) ... BC = √ ( 2s tan a ) , Ex . 25. Demonstrate , and AC = 2 ( s sec 2A ) 1 1. That sin a = = cos 2A ) ✓ ( 1 + cot2A ) 2 cottan 1 cot Attan A = 2 sin ( 45 ° ++ A ) - 1 = 1-2 ... Page 26

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**surface**bounded by three arcs of great circles , is called a Spherical Triangle . Def . 2. Spherical Trigonometry is the art of computing the measures of the sides and angles of spherical triangles . Def . 3. A right - angled spherical ... Page 27

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**surface**of the sphere , constitute that triangle . 6. The angle which is contained between the arcs of two great circles , intersecting each other on the**surface**of the sphere , is called a spherical angle ; and its measure is the same ... Page 30

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**surface**of the sphere , three arcs of great circles , which by their intersections form another spherical triangle ; each side of this new triangle will be the sup . plement to the measure of the angle which is at its pole , and the ... Page 32

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**surface**of these triangles , p for that of the triangle BAF , q for that of CAE , and a for that of the proposed triangle ABC . Then a and m ' together ( or their equal a and m togerther ) make up the**surface**of a spheric lune ...### 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...