## A Course of Mathematics: In Two Volumes. Composed for the Use of the Royal Military Academy, Volume 1Longman, Orme & Company, 1841 - Mathematics |

### From inside the book

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Page 79

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**hence**infer the equality of the ratios g = 44 , or the existence of the proportion 6 : 3 :: 14 : 7 .**Hence**THEOREM II . We may always form a proportion of the factors of two equal products . If the two means are equal , as in the terms ... Page 73

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**hence**a new approximation to R. Continue this series of approximations till the required degree of accuracy is obtained . The number of figures which may be depended on in each successive value of x , is generally equal to the number of ... Page 79

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**hence**infer the equality of the ratios § = = 44 , or the existence of the proportion 6 : 3 :: 14 : 7 .**Hence**THEOREM 11. We may always form a proportion of the factors of two equal products . If the two means are equal , as in the terms ... Page 94

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**hence**, by multiplying extremes and - rb = sx — sa ; then by transposition , ra sa ; and , by division , the number sought , which is the rule when the results are both too little . means , rx a = rb -sa 1-8 - Sierb - If the results be ... Page 106

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**Hence**we learn that ao always signifies 1 , whatever a may be . Indeed a signifying 1 a " , if m = o we have 1 ao = 1 , or 1 × ao = 1 , or 1 time a taken of no power * whatever . The result is therefore perfectly con- sistent with first ...### Other editions - View all

### Common terms and phrases

ABCD algebraic altitude arithmetical arithmetical progression base bisect breadth centre chord circle circumference coefficients common cone cosec cube root decimal denominator denoted diagonal diameter difference dihedral angle distance divided divisor draw drawn equal equation equiangular EXAMPLES expression figure fraction frustum geometrical given line greater hence inscribed integer intersection join length less lineation logarithms mantissa measure meeting method multiplied parallel parallel ruler parallelogram perpendicular plane polygon prism PROBLEM proportional quantity quotient radii radius ratio rectangle Reduce right angles rule Scholium segment sides sine solid angle solution square root straight line subtraction tangent THEOREM third trapezium triangle ABC u₁ vulgar fraction Whence