## A Course of Mathematics ...: Composed for the Use of the Royal Military Academy ... |

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abscissas altitude asymptote axis ball base beam becomes bisect centre circle circumscribed coefficients cone conic section consequently Corol cosine cubic equation curve cylinder denote determine diameter distance divided draw drawn equa equal equation expression feet figure find the fluent fluxion force former gives greatest Hence horizontal hyperbola inches length logarithm manner measured meridian motion nearly negative ordinates parabola parallel perimeter perpendicular plane polygon prism prob PROBLEM proportional quadrant quantity radius rectangle resistance right angles right line roots Scholium sides sine solid angle sphere spherical angle spherical excess spherical triangle spherical trigonometry square suppose surf surface tangent theor THEOREM theref tion trapezium velocity vertex vertical weight whence whole

### Popular passages

Page 124 - Since the exterior angle of a triangle is equal to the sum of the two interior opposite angles (th.

Page 261 - 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 its altitude equal to the depth of the centre of gravity below...

Page 86 - 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 145 - D'Alembert, was the Precession of the equinoxes and the Nutation of the earth's axis, according to the theory of gravitation.

Page 176 - 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 80 - Any Two Sides of a Spherical Triangle are together Greater than the Third.

Page 92 - In Every Spherical Triangle, the Sines of the Angles are Proportional to the Sines of their. Opposite Sides. If, from the first of the equations marked...

Page 55 - The COSINE of an arc, is the sine of the complement of that arc, and is equal to the part of the radius comprised between the centre of the circle and the foot of the sine...

Page 174 - ... 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...

Page 76 - 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...