A Course of Mathematics: In Three Volumes : Composed for the Use of the Royal Military Academy ...J. Johnson, 1811 |
From inside the book
Page vii
... preceding parts of the Course , the great object kept con- stantly in view has been utility , especially to gentlemen in- tended for the Military Profession . To this end , all such investigations as might serve merely to display ...
... preceding parts of the Course , the great object kept con- stantly in view has been utility , especially to gentlemen in- tended for the Military Profession . To this end , all such investigations as might serve merely to display ...
Page 1
... preceding years , been employed in manuscript , in the education of the cadets in the academy . The first and principal article in the contents of that volume , was an ex- tensive geometrical treatise on Conic Sections , treated in a ...
... preceding years , been employed in manuscript , in the education of the cadets in the academy . The first and principal article in the contents of that volume , was an ex- tensive geometrical treatise on Conic Sections , treated in a ...
Page 34
... preceding quantity is less than the succeeding one : when , on the contrary , the separating character is > , it denotes that the preceding quantity is greater than the succeeding one . 1 THEOREM THEOREM III . Of all Right Lines that ...
... preceding quantity is less than the succeeding one : when , on the contrary , the separating character is > , it denotes that the preceding quantity is greater than the succeeding one . 1 THEOREM THEOREM III . Of all Right Lines that ...
Page 35
... preceding corollary it might easily be shown , that the least triangle which can possibly be described about , and the greatest parallelogram which can be inscribed in , any curve concave to its axis , will be when the subtangent is ...
... preceding corollary it might easily be shown , that the least triangle which can possibly be described about , and the greatest parallelogram which can be inscribed in , any curve concave to its axis , will be when the subtangent is ...
Page 38
... preceding theorem , and may be demonstrated thus : Let R and I be two figures equal in surface and having the same number of sides , of which R is regular , I irregular : let also R be a regular figure similar to R , and having a ...
... preceding theorem , and may be demonstrated thus : Let R and I be two figures equal in surface and having the same number of sides , of which R is regular , I irregular : let also R be a regular figure similar to R , and having a ...
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Common terms and phrases
abscissas altitude ANHG asymptotes axis ball base beam becomes bisect CA² CE² centre circle circumscribed coefficients cone conic section consequently Corol cosine cubic equation curve cylinder DE² denote determine diameter distance divided draw drawn equa equal equation expression feet find the fluent fluxion force greatest Hence horizontal hyperbola inches length logarithm manner measured meridian motion nearly ordinates parabola parallel perimeter 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 trapezium 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 114 - 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 80 - 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.