A Course of Mathematics: In Two Volumes : for the Use of Academies, as Well as Private Tuition, Volume 2Samuel Campbell, Evert Duyckinck, T. & J. Swords, 1816 |
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Page 8
... means of the analytical expres- sions in arts . 4 and 12. Thus , if A be supposed equal to 10 , in equa . v , it will become . cos ( B ) = cos . O cos . B sin . ( B ) = sin .. cos . B - But sin . O rad . = 1 ; and cos . sin . sin . B ...
... means of the analytical expres- sions in arts . 4 and 12. Thus , if A be supposed equal to 10 , in equa . v , it will become . cos ( B ) = cos . O cos . B sin . ( B ) = sin .. cos . B - But sin . O rad . = 1 ; and cos . sin . sin . B ...
Page 17
... means it will be found , that the sums of the cosines of arcs or angles in arithmetical progression will be COS A + COS ( A + B ) + COS ( A + 2B ) + cos ( A + 3B ) + & C .. sin ( A - 3B ) ad infinitum = COS A † COS ( A + B ) ..... ( cos ...
... means it will be found , that the sums of the cosines of arcs or angles in arithmetical progression will be COS A + COS ( A + B ) + COS ( A + 2B ) + cos ( A + 3B ) + & C .. sin ( A - 3B ) ad infinitum = COS A † COS ( A + B ) ..... ( cos ...
Page 21
... So that the sines may be computed to any arc : and the tangents and other trigonometrical lines , by means of the expressions in art . 4 , & c . Ex . Ex 3. Find the sum of all the natural sines ANALYTICAL PLANE TRIGONOMETRY . 21.
... So that the sines may be computed to any arc : and the tangents and other trigonometrical lines , by means of the expressions in art . 4 , & c . Ex . Ex 3. Find the sum of all the natural sines ANALYTICAL PLANE TRIGONOMETRY . 21.
Page 22
... means of equation XXVII , is rendered very easy . Applying that theo- rem to the present case , we have sin ( A + B ) sin 45 ° , sin ( n + 1 ) B = sin 45 ° 0′30 ′′ , and sin B = sin 30 " . Therefore sin 45 ° X sin 45 ° 0 ′ 30 ...
... means of equation XXVII , is rendered very easy . Applying that theo- rem to the present case , we have sin ( A + B ) sin 45 ° , sin ( n + 1 ) B = sin 45 ° 0′30 ′′ , and sin B = sin 30 " . Therefore sin 45 ° X sin 45 ° 0 ′ 30 ...
Page 23
... Any direct solution to this curious problem , except by means of the analytical formulæ employed above , would be exceed- ingly tedious and operese , Solution Solution to the same by R. ADRAIN . D B ANALYTICAL PLANE TRIGONOMETRY . 23.
... Any direct solution to this curious problem , except by means of the analytical formulæ employed above , would be exceed- ingly tedious and operese , Solution Solution to the same by R. ADRAIN . D B ANALYTICAL PLANE TRIGONOMETRY . 23.
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absciss altitude axis ball base beam becomes body centre of gravity circle column consequently Corol cosine cubic curve cycloid cylinder denote density descending determine diameter direction distance earth equa equal equation equilibrio EXAM expression feet find the fluent fluid force given fluxion gives greatest Hence horizontal hyperbola inches inclined plane length lever logarithm measured motion moving nearly oblique ordinate parabola parallel pendulum perpendicular plane pressure prob PROBLEM projectile prop proportion PROPOSITION quantity radius ratio rectangle resistance right angles right line roots Scholium sides sin² sine solid angle space specific gravity spherical excess spherical triangle square supposed surface tangent theorem theref tion trapezium variable velocity vertical vibrations weight whole
Popular passages
Page 437 - Or, by art. 314 of the same, .the pressure is equal to the weight of a column of the fluid...
Page 258 - ... and — . The preceding equation is only of the fourth power or degree ; but it is manifest that the above remark applies to equations of higher or lower dimensions : viz, that in general . an equation of any degree whatever has as many roots as there are units in the exponent of the highest power of the unknown quantity, and that each root has the property of rendering, by its substitution in place of the unknown quantity, the aggregate' of all the terms of the equation equal to nothing.
Page 34 - 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 249 - Vespasian weighed, suppose 10,000 pounds; and was moved, let us admit, with such such a velocity, by strength of hand, as to pass through 20 feet in one second of time ; and this was found sufficient to demolish the walls of Jerusalem. The question is, with what velocity a 32lb ball must move, to do the same execution ? Ans.
Page 209 - As the weight lost in water is to the whole, or absolute weight ; so is the specific gravity of water ' " to "the specific gravity 'of the body . 2.
Page 241 - ... as the greatest product is to the whole weight of the compound, so is each of the other products to the weights of the two ingredients.
Page 31 - ... the triangle DEF, three others might be formed by the intersection of the three arcs DE, EF, DF. But the proposition immediately before us is applicable only to the central triangle, which is distinguished from the other three by the circumstance (see the last figure) that the two angles A and D lie on the same side of BC, the...
Page 167 - The screw is a spiral thread or groove cut round a cylinder, and every where making the same angle with the length of it. So that if the surface of the cylinder, with this spiral thread on it, were unfolded and stretched into a plane, the spiral thread would form a straight inclined plane, whose length would be to its height, as the circumference of the cylinder...
Page 450 - From a general inspection of this second course of these experiments, it appears that all the deductions and observations made on the former course, are here corroborated and strengthened, respecting the velocities and weights of the, balls, and charges of powder, &c. It furt-her appears also that the velocity of the ball increases with the increase of - charge Penetratio>^ of Balls into solid Eln^wpod.
Page 255 - ... ounces, he found by calculation what part of the king's gold had been changed. And you are desired to repeat the process. Ans.