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Page 244
Now the distance of the centre of gyration of the beam from * 2R R - The distance of R , the centre of gyration , from c the centre or axis of motion , in some of the most useful cases , is as below : · In a circular wheel of uniform ...
Now the distance of the centre of gyration of the beam from * 2R R - The distance of R , the centre of gyration , from c the centre or axis of motion , in some of the most useful cases , is as below : · In a circular wheel of uniform ...
Page 245
( M + m ) will represent the mass equivalent to the beam or lever when reduced to the point A ; while the weight equivalent to w , when referred to that point , will be w . Hence , proceeding as in the last prop . we ? R2 shall have .
( M + m ) will represent the mass equivalent to the beam or lever when reduced to the point A ; while the weight equivalent to w , when referred to that point , will be w . Hence , proceeding as in the last prop . we ? R2 shall have .
Page 322
( p + w ) x -aw : the accelerating force f ; hence , by the theorems for constant forces , pa . 342 vol . 2 , t = - S ( p + w ) x3 gf ( px - aw ) g must be For , the action of the beam is in the 322 PROMISCUOUS EXERCISES .
( p + w ) x -aw : the accelerating force f ; hence , by the theorems for constant forces , pa . 342 vol . 2 , t = - S ( p + w ) x3 gf ( px - aw ) g must be For , the action of the beam is in the 322 PROMISCUOUS EXERCISES .
Page 327
To determine the position of a bar or beàm AB , being supported in equilibrio by two cords AC , BC , having their two ends fixed in the beam , at A and B. By art . 210 vol . 2 , the position will be such , that its centre of gravity G ...
To determine the position of a bar or beàm AB , being supported in equilibrio by two cords AC , BC , having their two ends fixed in the beam , at A and B. By art . 210 vol . 2 , the position will be such , that its centre of gravity G ...
Page 328
To determine the position of the beam AE , moveable about the end в , and sustained by a given weight g , hanging by a cord Acg , going over a pulley at c , and fixed to the other end A. B E Let the weight of the beam , and G denote the ...
To determine the position of the beam AE , moveable about the end в , and sustained by a given weight g , hanging by a cord Acg , going over a pulley at c , and fixed to the other end A. B E Let the weight of the beam , and G denote 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 |
Common terms and phrases
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 |