A Course of Mathematics: In Two Volumes. Composed for the Use of the Royal Military Academy, Volume 1Longman, Orme & Company, 1841 - Mathematics |
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Page 70
... square root . Thus : — L M N 3 x root already found . 3 x square of root already found . Number whose root is to be found . Root . 2. Divide the number into periods of three figures each , by setting a point over the place of units ...
... square root . Thus : — L M N 3 x root already found . 3 x square of root already found . Number whose root is to be found . Root . 2. Divide the number into periods of three figures each , by setting a point over the place of units ...
Page 71
... square ; and we may proceed with them to find a new root figure , and complete the operation as in rules 3 and 4 . Note . After about one - third of the number of figures in the root have been obtained ( or one - third of the number ...
... square ; and we may proceed with them to find a new root figure , and complete the operation as in rules 3 and 4 . Note . After about one - third of the number of figures in the root have been obtained ( or one - third of the number ...
Page 73
... square of the cube root of 1000 , and likewise of · 001 : and the cube of the square root of 100 and '01 ; and determine the product of these four results . TO EXTRACT ANY ROOT WHATEVER * . LET P be the given number , ʼn the index of ...
... square of the cube root of 1000 , and likewise of · 001 : and the cube of the square root of 100 and '01 ; and determine the product of these four results . TO EXTRACT ANY ROOT WHATEVER * . LET P be the given number , ʼn the index of ...
Page 74
... square root , since 5 × 3 × 2 = 30. It will also be always least laborious to commence with the lowest roots , as with the second before the third , and the third before the fifth , in the case just cited . EXAMPLE . Extract the tenth ...
... square root , since 5 × 3 × 2 = 30. It will also be always least laborious to commence with the lowest roots , as with the second before the third , and the third before the fifth , in the case just cited . EXAMPLE . Extract the tenth ...
Page 75
... square root is approximately equal ; then if n be a near integer or fractional value of the root , the fraction n2 + Nd2 2nd will denote one still nearer . Or , for continuing the process , the following is still more convenient . Let ...
... square root is approximately equal ; then if n be a near integer or fractional value of the root , the fraction n2 + Nd2 2nd will denote one still nearer . Or , for continuing the process , the following is still more convenient . Let ...
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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