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 - Mathematics |
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Page 33
... length of the radius , in any circle , is equal to the length of 57-2957795 degrees , measured on the circumference of that circle ; if the spherical excess be mul- tiplied by 57 297795 , the product will express the surface of the ...
... length of the radius , in any circle , is equal to the length of 57-2957795 degrees , measured on the circumference of that circle ; if the spherical excess be mul- tiplied by 57 297795 , the product will express the surface of the ...
Page 45
... length becomes , COS A. sin c = cos a . sin B In like manner , we have , - - sin A · cose . cos b . COS B. sin c = cos b . sin a sin B. Cos C Exterminating cos 6 from these , there results So like- COS B = wise cos c = . cos a . : } ( v ...
... length becomes , COS A. sin c = cos a . sin B In like manner , we have , - - sin A · cose . cos b . COS B. sin c = cos b . sin a sin B. Cos C Exterminating cos 6 from these , there results So like- COS B = wise cos c = . cos a . : } ( v ...
Page 46
... length result cos ( a - b ) tan ( A + B ) = cot c.- cos ( a + b ) tan ( A - B ) cot c.- sin ( a + b ) sin ( a + b ) ( VI . ) Cor : Cor . When ab , the first of the above 46 SPHERICAL TRIGONOMETRY . Spherical Trigonometry 5.
... length result cos ( a - b ) tan ( A + B ) = cot c.- cos ( a + b ) tan ( A - B ) cot c.- sin ( a + b ) sin ( a + b ) ( VI . ) Cor : Cor . When ab , the first of the above 46 SPHERICAL TRIGONOMETRY . Spherical Trigonometry 5.
Page 60
... length is very carefully measured on some plane , heath , or marsh , which is so nearly level as to facilitate the ... length of this base , computed as one of the sides of the chain of triangles , com- pared with its length determined ...
... length is very carefully measured on some plane , heath , or marsh , which is so nearly level as to facilitate the ... length of this base , computed as one of the sides of the chain of triangles , com- pared with its length determined ...
Page 61
... length . Here too , the first , side might be found by a base crossing it perpendicu- larly of about half its length , as at H ; and the last side veri- fied by another such base , R , at the opposite extremity . If the respective sides ...
... length . Here too , the first , side might be found by a base crossing it perpendicu- larly of about half its length , as at H ; and the last side veri- fied by another such base , R , at the opposite extremity . If the respective sides ...
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Common terms and phrases
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.