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 4
... ( because the line which feparates the numerator from the denominator is drawn below ✓ ) fignifies that the fquare ... because 4 × 4 × 4 is 64 ) , and✓ab + cd the cube root of ab + cd ; alfo 16 denotes the biquadratic root of 16 ( which ...
... ( because the line which feparates the numerator from the denominator is drawn below ✓ ) fignifies that the fquare ... because 4 × 4 × 4 is 64 ) , and✓ab + cd the cube root of ab + cd ; alfo 16 denotes the biquadratic root of 16 ( which ...
Page 14
... ( because the multiplicand is b times as great ) it must therefore be equal to Ix a ( or a ) , repeated b times , that is , equal to a xb , by the definition of multiplication . In the fame manner , the equality of all the variations , or ...
... ( because the multiplicand is b times as great ) it must therefore be equal to Ix a ( or a ) , repeated b times , that is , equal to a xb , by the definition of multiplication . In the fame manner , the equality of all the variations , or ...
Page 15
... first example ) , therefore the product of a by 3b , which must be three times as great ( because the multiplier is here three times as great ) , In the preceding examples all the products are affir mative will OF MULTIPLICATION . IS.
... first example ) , therefore the product of a by 3b , which must be three times as great ( because the multiplier is here three times as great ) , In the preceding examples all the products are affir mative will OF MULTIPLICATION . IS.
Page 18
... because its divifor is D times as great as that of AC : therefore these two quanti- B A C AC ties , X and being the fame part of one and B BD the fame quantity , they must neceffarily be equal to each other ; which was to be proved . As ...
... because its divifor is D times as great as that of AC : therefore these two quanti- B A C AC ties , X and being the fame part of one and B BD the fame quantity , they must neceffarily be equal to each other ; which was to be proved . As ...
Page 19
... because , by what has been already fhewn , 3 x3 isx : and , in the fame manner , will c + y be expressed by x2 ; because 2 × x2 × x2 is | 3 likewifex . Therefore c + y X I I 1 2 c + y 3 is = 3⁄43 × x2 = x2 = the fifth power of c + y + y ...
... because , by what has been already fhewn , 3 x3 isx : and , in the fame manner , will c + y be expressed by x2 ; because 2 × x2 × x2 is | 3 likewifex . Therefore c + y X I I 1 2 c + y 3 is = 3⁄43 × x2 = x2 = the fifth power of c + y + y ...
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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.