## A Course of Mathematics: In Three Volumes : Composed for the Use of the Royal Military Academy ...J. Johnson, 1811 |

### From inside the book

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**greatest**magni- tude it can possibly attain ; and , on the contrary , when it has arrived at the least possible magnitude , it is called a minimum . Def . 2. Isoperimeters , or Isoperimetrical figures , are those which have equal ... Page 34

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**Greatest**Surface . Let ABC , ABD , be two triangles of the same base AB and with equal perimeters , of which the one ABC is isosceles , the other is not : then the triangle ABC has a surface ( or an altitude ) greater than the surface ... Page 35

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**greatest**parallelogram which can be inscribed in , any curve concave to its axis , will be when the subtangent is equal to half the base of the triangle , or to the whole base of the parallelogram : and that the two figures will be in ... Page 36

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**greatest**when that perpendicular is the**greatest**; that is to say , when the other side is not in- clined to that perpendicular , but coincides with it : hence the surface is a maximum when the two given sides are perpendi- cular to ... Page 37

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**Greatest**Polygon which can be con- tained under any number of Unequal Sides , does not at all depend on the Order in which those Lines are connected with each other . For , since the polygon is a maximum under given sides , it is ...### 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.