A Course of Mathematics ...: Composed for the Use of the Royal Military Academy ...F. C. and J. Rivington, 1811 - Mathematics |
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Page 188
... abscissas , from a certain point let a line arbi- trarily taken be called the abscissa , and denoted ( commonly ) by at the several points corresponding to the different values of , let straight lines be continually drawn , making a ...
... abscissas , from a certain point let a line arbi- trarily taken be called the abscissa , and denoted ( commonly ) by at the several points corresponding to the different values of , let straight lines be continually drawn , making a ...
Page 189
... abscissa , while referred to different points of the curve , however the axis and the origin of the abscissas , or even the inclination of the co - ordinates in different systems , may vary ; the same curve will never be ranked under ...
... abscissa , while referred to different points of the curve , however the axis and the origin of the abscissas , or even the inclination of the co - ordinates in different systems , may vary ; the same curve will never be ranked under ...
Page 193
... abscissas an angle equal to half a right angle ; and the second is parallel to the axis , and drawn at a distance = a . These two lines , considered together , are comprized in the proposed equation y2 = ay + xy - ax . In like man- ner ...
... abscissas an angle equal to half a right angle ; and the second is parallel to the axis , and drawn at a distance = a . These two lines , considered together , are comprized in the proposed equation y2 = ay + xy - ax . In like man- ner ...
Page 195
... abscissa AB = x , is determined , will always be of this form : viz , -- " " xy2 + ey = ax3 + bx2 + cx + d . . . ( I. ) Here the coefficients e , a , b , c , d , denote given quantities , affected with their signs + and of which terms ...
... abscissa AB = x , is determined , will always be of this form : viz , -- " " xy2 + ey = ax3 + bx2 + cx + d . . . ( I. ) Here the coefficients e , a , b , c , d , denote given quantities , affected with their signs + and of which terms ...
Page 196
... abscissa AB is determined , will always assume this form : viz . xy = ax3 + bx2 + cx + d ( II . ) CASE III . .... 14. If the opposite legs be of the parabolic kind , draw the right line CBC , terminated at both ends ( if possible ) at ...
... abscissa AB is determined , will always assume this form : viz . xy = ax3 + bx2 + cx + d ( II . ) CASE III . .... 14. If the opposite legs be of the parabolic kind , draw the right line CBC , terminated at both ends ( if possible ) at ...
Common terms and phrases
abscissas altitude asymptote axis ball base beam becomes bisect CA² CD² CE² 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 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 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 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...