A Course of Mathematics: For the Use of Academies as Well as Private Tuition : in Two Volumes, Volume 2W. E. Dean, 1831 |
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Page 4
... prop . 4 , pa . 161 , of the Introduction to the Mathematical Tables : then we have b2 + c3 — a2 = 853444 2bc = 899200 • • log . log . · 5.9311751 · = 5.9538080 The remainder being log . cos . A , or of 18 ° 20 ′ = 9.9773671 Again , a ...
... prop . 4 , pa . 161 , of the Introduction to the Mathematical Tables : then we have b2 + c3 — a2 = 853444 2bc = 899200 • • log . log . · 5.9311751 · = 5.9538080 The remainder being log . cos . A , or of 18 ° 20 ′ = 9.9773671 Again , a ...
Page 31
... due to Philip Langsberg . Vide , Simon Stevin , liv . 3 , de la Cos . nographie , prop . 31 , and Alb . Girard in loc . It is often how . ever treated very loosely by authors on trigonometry : some SPHERICAL TRIGONOMETRY . 31.
... due to Philip Langsberg . Vide , Simon Stevin , liv . 3 , de la Cos . nographie , prop . 31 , and Alb . Girard in loc . It is often how . ever treated very loosely by authors on trigonometry : some SPHERICAL TRIGONOMETRY . 31.
Page 35
... See Sim . Euclid , Prop . 33 , Book VI . It ought also to be demonstrated that spherical surfaces are the mea- sures of solid angles . Ed . . sure ; just as circular arcs are assumed for the SPHERICAL TRIGONOMETRY . 35.
... See Sim . Euclid , Prop . 33 , Book VI . It ought also to be demonstrated that spherical surfaces are the mea- sures of solid angles . Ed . . sure ; just as circular arcs are assumed for the SPHERICAL TRIGONOMETRY . 35.
Page 152
... PROP . If to the extremities of an inflexible right line AB , are applied two forces , P and Q , whose directions are parallel and whose actions concur : -1st , The direction of the resultant , R , of those two forces is parallel to the ...
... PROP . If to the extremities of an inflexible right line AB , are applied two forces , P and Q , whose directions are parallel and whose actions concur : -1st , The direction of the resultant , R , of those two forces is parallel to the ...
Page 153
... PROP . Any number of parallel forces , P , Q , R , S , & c . acting in the same sense , and their points of application be- ing connected in an invariable manner ; to determine their resultant . Determining first , by the preceding prop ...
... PROP . Any number of parallel forces , P , Q , R , S , & c . acting in the same sense , and their points of application be- ing connected in an invariable manner ; to determine their resultant . Determining first , by the preceding prop ...
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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...