A Course of Mathematics: In Three Volumes : Composed for the Use of the Royal Military Academy ... |
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Page 2
The Difference between the Semi - transverse and a Line drawn from the Focus to any Point in the Curve , is equal to ... DI C b --- For , draw AG parallel and equal to ca the semi - conjugate ; and join CG meeting the ordinate de in H.
The Difference between the Semi - transverse and a Line drawn from the Focus to any Point in the Curve , is equal to ... DI C b --- For , draw AG parallel and equal to ca the semi - conjugate ; and join CG meeting the ordinate de in H.
Page 3
And fe FE = 2C1 ; that is , the difference between two lines drawn from the foci , to any point in the curve , is double ... GG FE is a 4th proportional to + F { £ F = 2 For , through the point of contact E draw FE , and ƒɛ meeting FP ...
And fe FE = 2C1 ; that is , the difference between two lines drawn from the foci , to any point in the curve , is double ... GG FE is a 4th proportional to + F { £ F = 2 For , through the point of contact E draw FE , and ƒɛ meeting FP ...
Page 4
Hence also , if two tangents be drawn to the two ends E , и of any diameter EH ; they will be parallel to each other , and will cut the axis at equal angles , and at equal distances from the centre . For , the two CD , CA being equal to ...
Hence also , if two tangents be drawn to the two ends E , и of any diameter EH ; they will be parallel to each other , and will cut the axis at equal angles , and at equal distances from the centre . For , the two CD , CA being equal to ...
Page 4
If from any Point in the Curve there be drawn an Ordinate , and a Perpendicular to the Curve , or to the Tangent at that Point : Then , the Dist . on the Trans , between the Centre and Ordinate , CD : Will be to the Dist .
If from any Point in the Curve there be drawn an Ordinate , and a Perpendicular to the Curve , or to the Tangent at that Point : Then , the Dist . on the Trans , between the Centre and Ordinate , CD : Will be to the Dist .
Page 5
The same being supposed as in the last Proposition ; then any Lines кQ , QG , drawn parallel to the two Tangents ... Then For , draw the ordinate The three sim . triangles CAN , CDE , CGH , CA2 , CD , CG2 ; are to each other as DE : KQG ...
The same being supposed as in the last Proposition ; then any Lines кQ , QG , drawn parallel to the two Tangents ... Then For , draw the ordinate The three sim . triangles CAN , CDE , CGH , CA2 , CD , CG2 ; are to each other as DE : KQG ...
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A Course of Mathematics: In Three Volumes: Composed for the Use of the Royal ... Charles Hutton No preview available - 2016 |
A Course of Mathematics: In Three Volumes: Composed for the Use of the Royal ... Charles Hutton No preview available - 2016 |
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Popular passages
Page 65 - 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 116 - Since the exterior angle of a triangle is equal to the sum of the two interior opposite angles (th.
Page 249 - 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 82 - 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 335 - ... 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 166 - 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 164 - ... 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 74 - 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 261 - 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 74 - 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.
Bibliographic information
| Title | A Course of Mathematics: In Three Volumes : Composed for the Use of the Royal Military Academy ... Volume 3 of A Course of Mathematics: In Three Volumes : Composed for the Use of the Royal Military Academy, Charles Hutton |
| Author | Charles Hutton |
| Edition | 6 |
| Publisher | J. Johnson, 1811 |
| Original from | the New York Public Library |
| Digitized | 2 May 2006 |
| Export Citation | BiBTeX EndNote RefMan |