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 ix
... Parabola • • Equations to the Conic Sections Elements of Isoperimetry 1. For Surfaces 2. For Solids Analytical Trigonometry 37 42 . 53 Spherical Trigonometry 77 • Resolution of Spherical Triangles Geodesic Operations . 91 111 Problems ...
... Parabola • • Equations to the Conic Sections Elements of Isoperimetry 1. For Surfaces 2. For Solids Analytical Trigonometry 37 42 . 53 Spherical Trigonometry 77 • Resolution of Spherical Triangles Geodesic Operations . 91 111 Problems ...
Page 24
... PARABOLA . THEOREM XX ( 7 ) . If an Ordinate be drawn to the Point of Contact of any Tangent , and another Ordinate produced to cut the Tan- gent ; It will be , as the Difference of the Ordinates : Is to the Difference added to the ...
... PARABOLA . THEOREM XX ( 7 ) . If an Ordinate be drawn to the Point of Contact of any Tangent , and another Ordinate produced to cut the Tan- gent ; It will be , as the Difference of the Ordinates : Is to the Difference added to the ...
Page 25
... - ter of that double ordinate produced . And the diameter drawn through the intersection of two tangents , bisects the line connecting the points of contact . Corol Corol . 2. Hence we have another method of drawing OF THE PARABOLA : 25.
... - ter of that double ordinate produced . And the diameter drawn through the intersection of two tangents , bisects the line connecting the points of contact . Corol Corol . 2. Hence we have another method of drawing OF THE PARABOLA : 25.
Page 27
... and the same properties still follow them . So that , EV PV :: PV ' : P. the param . 1 GW : PW : PW : P , EV : GW :: PV2 : Pw2 , EV : GH :: PV2 : CH . HL . THEOREM THEOREM XXIV ( 20 ) . If two Parallels intersect OF THE PARABOLA . 27 .
... and the same properties still follow them . So that , EV PV :: PV ' : P. the param . 1 GW : PW : PW : P , EV : GW :: PV2 : Pw2 , EV : GH :: PV2 : CH . HL . THEOREM THEOREM XXIV ( 20 ) . If two Parallels intersect OF THE PARABOLA . 27 .
Page 30
... parallel to the asymptotes . = 3. For the Parabola . d C AB If a denote any absciss beginning at the vertex , and y its ordinate , also p the parameter . Then , by cor . theorem 1 , AK AK : KD :: KD : p , or xy 30 CONIC SECTIONS .
... parallel to the asymptotes . = 3. For the Parabola . d C AB If a denote any absciss beginning at the vertex , and y its ordinate , also p the parameter . Then , by cor . theorem 1 , AK AK : KD :: KD : p , or xy 30 CONIC SECTIONS .
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...
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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...