A Course of Mathematics: In Three Volumes : Composed for the Use of the Royal Military Academy ...J. Johnson, 1811 |
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Page 2
... consequently DE2 = AG2 DH2 ca2- DH2 . Also FD CF CD , and FD2 - CF2 2CF . CD + CD2 ; but by right - angled triangles , fd2 + de2 = FE2 ; therefore FE2 CF2 + ca2 2CF . CD + CD2 — DH2 . But by theor . 4 , ca + cF2 CA2 and , by supposition ...
... consequently DE2 = AG2 DH2 ca2- DH2 . Also FD CF CD , and FD2 - CF2 2CF . CD + CD2 ; but by right - angled triangles , fd2 + de2 = FE2 ; therefore FE2 CF2 + ca2 2CF . CD + CD2 — DH2 . But by theor . 4 , ca + cF2 CA2 and , by supposition ...
Page 4
... consequently ECH is a right line . Corol . 1. And , conversely , if ECH be a right line passing through the centre ; then shall it be bisected by the centre , or have CE = CH ; also DE will be GH , and CD = CG . Corol . 2. Hence also ...
... consequently ECH is a right line . Corol . 1. And , conversely , if ECH be a right line passing through the centre ; then shall it be bisected by the centre , or have CE = CH ; also DE will be GH , and CD = CG . Corol . 2. Hence also ...
Page 8
... consequently their like sides are equal , or LQ = Lq . Corol . Any diameter divides the ellipse into two equal parts . For , the ordinates on each side being equal to each other , and equal in number ; all the ordinates , or the area ...
... consequently their like sides are equal , or LQ = Lq . Corol . Any diameter divides the ellipse into two equal parts . For , the ordinates on each side being equal to each other , and equal in number ; all the ordinates , or the area ...
Page 11
... consequently Also FD CF CA : AG2 :: CD2 — CA2 : DE2 ; CA2 : AG2 :: CD2 CA2 : DH2 - AG2 ; - DE2 DH2- AG2 DH2 --- ca2 . CD , and FD2 = CF2 · - 2CF . CD + CD2 ; but , by right angled triangles , FD2 + de2 = fe2 ; therefore FE2 CF2 ca2 But ...
... consequently Also FD CF CA : AG2 :: CD2 — CA2 : DE2 ; CA2 : AG2 :: CD2 CA2 : DH2 - AG2 ; - DE2 DH2- AG2 DH2 --- ca2 . CD , and FD2 = CF2 · - 2CF . CD + CD2 ; but , by right angled triangles , FD2 + de2 = fe2 ; therefore FE2 CF2 ca2 But ...
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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abscissas altitude ANHG asymptotes axis ball base beam becomes bisect CA² 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 find the fluent fluxion force greatest Hence horizontal hyperbola inches length logarithm manner measured meridian motion nearly ordinates parabola parallel perimeter perp perpendicular plane polygon prism prob PROBLEM proportional quadrant 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 trapezium velocity vertical weight whence 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 |