## A Course of Mathematics: In Three Volumes : Composed for the Use of the Royal Military Academy ... |

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Page 87

It is thus that mathematicians , with perfect safety and correctness , make use of space as a measure of

It is thus that mathematicians , with perfect safety and correctness , make use of space as a measure of

**velocity**, mass as a measure of inertia , mass and**velocity**conjointly as a measure of force , space as a measure of time , weight ... Page 241

... be to have run over 50 inches in 10 seconds ; and , as the space described in each second is the same , we may compare the effect to that produced by a moveable which moves for 10 seconds with a

... be to have run over 50 inches in 10 seconds ; and , as the space described in each second is the same , we may compare the effect to that produced by a moveable which moves for 10 seconds with a

**velocity**of 5 inches per second . Page 242

The

The

**velocity**of the moving power is the same as the**velocity**of the impelled point ; the**velocity**of the resistance the same as that of the working point . 4. The performance or effect of a machine , or the work done , is measured by ... Page 243

... quantity of matter P + W ; and w ; g +2 R R2 P - T2 PR2 - RTW PR2 + 72W R R2 the accelerating force F = ( P ~~ w ) ÷ ( P + -w ) . α Ft or is = gtr ( g being = 32 feet ) ; gt , the

... quantity of matter P + W ; and w ; g +2 R R2 P - T2 PR2 - RTW PR2 + 72W R R2 the accelerating force F = ( P ~~ w ) ÷ ( P + -w ) . α Ft or is = gtr ( g being = 32 feet ) ; gt , the

**velocity**of P. And , R2P - RTW But ( vol . ii . p . Page 245

Let the angle of elevation CAD be E , while e is the elevation CBD . Then at the end of the time t , P will have a

Let the angle of elevation CAD be E , while e is the elevation CBD . Then at the end of the time t , P will have a

**velocity**v ; and gravity would impress upon it , in the instant following , a new velocityg sin e . t , proP A E W vided ...### What people are saying - Write a review

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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.