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 NumericallyF. Wingrave, 1800 - 400 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 10.
Σελίδα 69
... substitution , a x ah - fa2 bx ab - fc + 2 fb - ag fb - ag + c = 0 , This , by uniting the two laft terms , and ... substituted in the equation ah - fe + fb ag x bb igo , it thence becomes 0 , - -10 + yy2 + y ― 10 ; 3y x 10y + 3y3o ...
... substitution , a x ah - fa2 bx ab - fc + 2 fb - ag fb - ag + c = 0 , This , by uniting the two laft terms , and ... substituted in the equation ah - fe + fb ag x bb igo , it thence becomes 0 , - -10 + yy2 + y ― 10 ; 3y x 10y + 3y3o ...
Σελίδα 121
... substituted for r , in the preceding equation , we have sta s 2 4s3 b . This , folved , gives 25 + a S = aa - b bb b + : whence every thing elfe 2 4aa 2a is readily found . PROBLEM LXXI . The fum ( a ) and the fum of the fquares ( b ) ...
... substituted for r , in the preceding equation , we have sta s 2 4s3 b . This , folved , gives 25 + a S = aa - b bb b + : whence every thing elfe 2 4aa 2a is readily found . PROBLEM LXXI . The fum ( a ) and the fum of the fquares ( b ) ...
Σελίδα 131
... substituted instead of x , the whole ex- preffion vanishes . Hence it appears , that an equation may have as many roots as it has dimenfions , or as are expreffed by the number of the factors , whereof it is fup- pofed to be produced ...
... substituted instead of x , the whole ex- preffion vanishes . Hence it appears , that an equation may have as many roots as it has dimenfions , or as are expreffed by the number of the factors , whereof it is fup- pofed to be produced ...
Σελίδα 137
... substituted for x , the business fuc- ceeds , the positive and negative terms destroying each other . Moreover , if the equation x + x3 - 29x2 - 9x + 180 o were proposed , the work will ftand as follows : • · 5.7.10.14 · 35 · 70 • · 2 ...
... substituted for x , the business fuc- ceeds , the positive and negative terms destroying each other . Moreover , if the equation x + x3 - 29x2 - 9x + 180 o were proposed , the work will ftand as follows : • · 5.7.10.14 · 35 · 70 • · 2 ...
Σελίδα 156
... substituted , alternately , for each other , without producing a new equation , are always capable of being reduced to others of lower dimenfions . In order to fuch a reduction let the equation , if it be of an even dimenfion , be firft ...
... substituted , alternately , for each other , without producing a new equation , are always capable of being reduced to others of lower dimenfions . In order to fuch a reduction let the equation , if it be of an even dimenfion , be firft ...
Άλλες εκδόσεις - Προβολή όλων
A Treatise of Algebra: Wherein the Principles Are Demonstrated ... to Which ... Thomas Simpson Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2013 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 47 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Σελίδα 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.
Σελίδα 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...
Σελίδα 19 - We have seen that multiplying by a whole number is taking the multiplicand as many times as there are units in the multiplier.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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...
Σελίδα 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...
Σελίδα 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...
Σελίδα 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.