A Treatise of Algebra: Wherein the Principles are Demonstrated and Applied ... To which is Added, the Geometrical Construction of a Great Number of Linear and Plane Problems; with the Method of Resolving the Same Numerically |
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Page 24
... ftand here independently , are as much im- poffible in one fenfe , as the imaginary furd quantities b . and V ; fince the fign , according to the established Rules of notation , fhews that the quan- tity to which it is prefixed , is to ...
... ftand here independently , are as much im- poffible in one fenfe , as the imaginary furd quantities b . and V ; fince the fign , according to the established Rules of notation , fhews that the quan- tity to which it is prefixed , is to ...
Page 32
... are demonftrated in them : though perhaps the cafe , in Rule 5 , where the exponent comes out negative , may ftand in need of a more particular Explanation . Accord- Moreover , c + y divided by + gives y 2 . ing 32 OF DIVISION .
... are demonftrated in them : though perhaps the cafe , in Rule 5 , where the exponent comes out negative , may ftand in need of a more particular Explanation . Accord- Moreover , c + y divided by + gives y 2 . ing 32 OF DIVISION .
Page 33
... ftand firft wherein the highest power of that letter is involved , and thofe next where the next highest power is involved , and fo on this being done , feek how many times the first term of the divifor is contained in the first term of ...
... ftand firft wherein the highest power of that letter is involved , and thofe next where the next highest power is involved , and fo on this being done , feek how many times the first term of the divifor is contained in the first term of ...
Page 35
... ftand thus : 6 • 3 - 3a3x + \ aε - 3a2x2 + 3a3x * —x® ( a® + 3a2x + 3ax2 + x3 @ 3 — 3a3 x + ) a ° 3ax2 - x3 / a ° -3a3x + 3a2x2 - a3x2 + 3a3x - 6a + x2 + a3 × 3 + 3a2x * + 3a3x —9a + x2 + 9a3x3 — 3a2x2 + 3a2x2 - 8a3x3 + 6a2xa— ; + 3a2x2 ...
... ftand thus : 6 • 3 - 3a3x + \ aε - 3a2x2 + 3a3x * —x® ( a® + 3a2x + 3ax2 + x3 @ 3 — 3a3 x + ) a ° 3ax2 - x3 / a ° -3a3x + 3a2x2 - a3x2 + 3a3x - 6a + x2 + a3 × 3 + 3a2x * + 3a3x —9a + x2 + 9a3x3 — 3a2x2 + 3a2x2 - 8a3x3 + 6a2xa— ; + 3a2x2 ...
Page 42
... ftand for cc , b for xy , and n for 4 ; then , by fubftituting thefe values , inftead of a , b , and n , the general expreffion will become ° + 4c ° xy + 6c + x2y2 + 4c2x3y3 + x4y , the true value fought . 3 From the preceding ...
... ftand for cc , b for xy , and n for 4 ; then , by fubftituting thefe values , inftead of a , b , and n , the general expreffion will become ° + 4c ° xy + 6c + x2y2 + 4c2x3y3 + x4y , the true value fought . 3 From the preceding ...
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A Treatise of Algebra: Wherein the Principles Are Demonstrated ... to Which ... Thomas Simpson No preview available - 2013 |
Common terms and phrases
alfo alſo annuity anſwers arch arifing ax² bafe baſe becauſe bifect cafe circle co-fine coefficient confequently CONSTRUCTION defcribe denoted difference divided divifor draw E. D. Method equal equation expreffed expreffion faid fame manner fecond fegments feries feven fides fign fimilar fimple fince firft firſt fo fhall folution fome fquare root ftand fubftituted fubtracted fuch fuppofing given angle given ratio intereft interfecting laft laſt leaft leffer lefs likewife Method of Calculation moidores muft multiplied muſt number of terms obferved parallel perpendicular pofitive PROBLEM progreffion propofed quantities queftion quotient radius raiſe reafon rectangle refpectively reprefented right-line ſhall tangent thefe thence Theorem theſe thofe thoſe trapezium triangle triangle ABC uſe whence whereof whofe whole number
Popular passages
Page 47 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 229 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, etc.
Page 57 - Quantities is the least involved, and let the Value of that Quantity be found in each Equation by the Rules already given), looking upon all the Rest as known : let the Values thus found be put equal to each other (for they are equal...
Page 19 - We have seen that multiplying by a whole number is taking the multiplicand as many times as there are units in the multiplier.
Page 28 - EXAMPLES. • 1. If the fractions to be divided have a common denominator, take the numerator of the dividend for a new numerator, and the numerator of the divisor for the new denominator.
Page 44 - ... the said numerator or denominator (whichever it is) into two parts, so that the said letter may be found in every term of the one part, and be totally excluded out of the other ; this being done, let the greatest common divisor of these two parts be found, which will evidently be a divisor to the whole, and by which the division of the...
Page 217 - SIMPLE Intereft, is that which is paid for the Loan of any Principal or Sum of Money, lent out for fome Time, at any...
Page 223 - R% the amount of one pound in two years ; and therefore as I to R, fo is R% the fum forborn the third year, to R3, the amount in three years : whence it appears that R", or R raifed to the power whofe exponent is the number of years, will be the amount of one pound in thofe years. But >as i A is to its amount R", fo is P to ( a) its amount, in the fame time ; whence we have PX R" =r a. Moreover, becaufe the amount of one pound, in nyears, is R", its increafe in that time will be R...
Page 230 - BI, the sine of its complement HB. The tangent of an arc, is a right line touching the circle in one extremity of that arc, continued from thence to meet a line drawn from the...
Page 66 - ... the product of the extremes divided by either mean will give the other mean, and the product of the means divided by either extreme will give the other extreme.