A Course of Mathematics: In Three Volumes : Composed for the Use of the Royal Military Academy ...J. Johnson, 1811 |
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Page 87
... weight as a measure of density , expansion as a measure of heat , a certain function of planetary velocity as a measure of distance from the central body , arcs of the same circle as measures of plane angles ; and it is in conformity ...
... weight as a measure of density , expansion as a measure of heat , a certain function of planetary velocity as a measure of distance from the central body , arcs of the same circle as measures of plane angles ; and it is in conformity ...
Page 242
... weight or resistance w , from the fulcrum F of a straight lever ; then will the velocity of the power and of the weight at the end of any time t be - R2P RrW R2P + 2w RrP - r2w gt , and Rap + wgt , respectively , the weight and inertia ...
... weight or resistance w , from the fulcrum F of a straight lever ; then will the velocity of the power and of the weight at the end of any time t be - R2P RrW R2P + 2w RrP - r2w gt , and Rap + wgt , respectively , the weight and inertia ...
Page 243
... weight , but possesses inertia only , as when a body is moved along a horizontal Pn2 Pn2 + W And plane , the force which accelerates a will be = either of these values may be readily introduced into the in- vestigation . Cor . 5. The ...
... weight , but possesses inertia only , as when a body is moved along a horizontal Pn2 Pn2 + W And plane , the force which accelerates a will be = either of these values may be readily introduced into the in- vestigation . Cor . 5. The ...
Page 244
... weight conclusions of treme not being a this prop . And in the ex- pulley , the he case where the wheel and axle ... weight raised at the extremity of the other arm when the effect is a maximum . In this case + m is the weight of ...
... weight conclusions of treme not being a this prop . And in the ex- pulley , the he case where the wheel and axle ... weight raised at the extremity of the other arm when the effect is a maximum . In this case + m is the weight of ...
Page 245
... weight w shall be raised from the hori- zontal line AB to the point c , in the least time possible , by means of another given weight P descending along the given plane CB : the two weights being connected by an inextensible thread pcw ...
... weight w shall be raised from the hori- zontal line AB to the point c , in the least time possible , by means of another given weight P descending along the given plane CB : the two weights being connected by an inextensible thread pcw ...
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Common terms and phrases
abscissas altitude ANHG asymptotes axis ball base beam becomes bisect CA² CD² CE² centre circle circumscribed coefficients cone conic section consequently Corol cosine CR² cubic equation curve cylinder denote determine diameter distance divided draw drawn equa equal equation expression feet find the fluent fluxion force gives greatest Hence horizontal hyperbola inches length logarithm manner measured meridian motion nearly negative ordinates parabola parallel perimeter perp perpendicular plane polygon prism prob PROBLEM proportional quadrant quantity radius rectangle resistance right angles right line roots Scholium sides sin² sine solid angle sphere spherical angle spherical excess spherical triangle spherical trigonometry square suppose surf surface tangent theor THEOREM theref tion velocity vertical weight whence whole
Popular passages
Page 63 - 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 112 - Since the exterior angle of a triangle is equal to the sum of the two interior opposite angles (th.
Page 247 - Or, by art. 3 14 of the same, the pressure is equal to the weight of a column of the fluid, •whose base is equal to the surface pressed, and...
Page 78 - A solid angle is that which is made by the meeting of more than two plane angles, which are not in the same plane, in one point. X. ' The tenth definition is omitted for reasons given in the notes.
Page 333 - ... to secure uniformity, his trees were all felled in the same season of the year, were squared the day after, and the experiments tried the 3d day.
Page 164 - Cor. 3. An equation will want its third term, if the sum of the products of the roots taken two and two, is partly positive, partly negative, and these mutually destroy each other. Remark.
Page 162 - ... 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 equul to nothing.
Page 72 - Prove that, in any plane triangle, the base is to the difference of the other two sides, as the sine of half the sum of the angles at the base, to the sine of half their difference : also, that the...
Page 259 - And when this is compared with the proportion of the velocity and length of gun in the last paragraph, it is evident that we gain extremely little in the range by a great increase in the length of the gun, with the same charge of powder. In fact the range is nearly as the 5th root of the length of the bore ; which is so small an increase, as to amount only to about a...
Page 72 - Prob. 12. How must three trees, A, B, C, be planted, so that the angle at A may be double the angle at B, the angle at B double the angle at C, and a line of 400 yards may just go round them ? Ans.