A Course of Mathematics: In Three Volumes : Composed for the Use of the Royal Military Academy ... |
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Page 3
If at the intersections of any tangent , with the circumscribed circle , perpendiculars to the tangent be drawn , they will meet the transverse axis in the two foci . That is , the perpendiculars PF , pf give the foci F , f .
If at the intersections of any tangent , with the circumscribed circle , perpendiculars to the tangent be drawn , they will meet the transverse axis in the two foci . That is , the perpendiculars PF , pf give the foci F , f .
Page 7
Two Lines , that any where intersect each other , meet the Curve each in Two Points ; then The Rectangle of the Segments of the one : Is to the Rectangle of the Segments of the other :: As the Square of the Diam .
Two Lines , that any where intersect each other , meet the Curve each in Two Points ; then The Rectangle of the Segments of the one : Is to the Rectangle of the Segments of the other :: As the Square of the Diam .
Page 9
Two Lines , that any where intersect each other , meet the Curve each in Two Points ; then The Rectangle of the Segments of the one : Is to the Rectangle of the Segments of the other :: As the Square of the Diam .
Two Lines , that any where intersect each other , meet the Curve each in Two Points ; then The Rectangle of the Segments of the one : Is to the Rectangle of the Segments of the other :: As the Square of the Diam .
Page 10
In like manner , if any other line p'u'd , parallel to cr or to pq , meet PHQ ; since the rectangles PH'a , p'H'Q ' are also in the same ratio of CRP to cra ; therefore rect . PHQ : pHq :: PH'Q : p'H'q . Also , if another line p'ha ' be ...
In like manner , if any other line p'u'd , parallel to cr or to pq , meet PHQ ; since the rectangles PH'a , p'H'Q ' are also in the same ratio of CRP to cra ; therefore rect . PHQ : pHq :: PH'Q : p'H'q . Also , if another line p'ha ' be ...
Page 12
Consequently DH is every where greater than DE ; and so the asymptote CGH never meets the curve , though they be ever so far produced : but DH and DE approach nearer and nearer to a ratio of equality as they recede farther from the ...
Consequently DH is every where greater than DE ; and so the asymptote CGH never meets the curve , though they be ever so far produced : but DH and DE approach nearer and nearer to a ratio of equality as they recede farther from the ...
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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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altitude angle assumed axis ball base beam becomes centre circle consequently construction Corol cosine curve denote determine diameter direction distance divided double draw drawn effect equal equation expression fall feet figure fluent fluxion force former given gives greater greatest half Hence inches known latter length less manner means measured meet motion moving nearly negative obtain opposite parallel perpendicular plane polygon position preceding PROBLEM produced proportional quantity radius ratio resistance respectively right line roots rule sides similar sine solid space sphere spherical square suppose surface tangent theor THEOREM theref third tion triangle velocity vertical weight whole
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 |