A Treatise of Algebra: In Three Parts. Containing. The fundamental rules and operations. The composition and resolution of equations of all degrees, and the different affections of their roots. The application of algebra and geometry to each other. To which is added an appendix concerning the general properties of geometrical lines. I.. II.. III.A. Millar & J. Nourse, 1748 - 431 páginas |
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Página 7
... Unit is understood to be the Coefficient . Thus I is the Coefficient of a or of b . Quantities are faid to be like or fimilar , that are reprefented by the fame Letter or Letters equally repeated . Thus + 3a and like ; but a and b , or ...
... Unit is understood to be the Coefficient . Thus I is the Coefficient of a or of b . Quantities are faid to be like or fimilar , that are reprefented by the fame Letter or Letters equally repeated . Thus + 3a and like ; but a and b , or ...
Página 12
... Units in ; and the Product is evi- dently na . Cafe II . When a is multiplied by n , then - -a is to be taken as often as there are Units in , and the Product must be na . Cafe III . Multiplication by a positive Number implies a ...
... Units in ; and the Product is evi- dently na . Cafe II . When a is multiplied by n , then - -a is to be taken as often as there are Units in , and the Product must be na . Cafe III . Multiplication by a positive Number implies a ...
Página 13
... Units in n ; but ( by § 10. ) to fubtracta is equivalent to adding + a , confequently the Product is + na . The IId and IVth Cafes may be illustrated in the following Manner . + By the Definitions , aao ; therefore , if we multiply + aa ...
... Units in n ; but ( by § 10. ) to fubtracta is equivalent to adding + a , confequently the Product is + na . The IId and IVth Cafes may be illustrated in the following Manner . + By the Definitions , aao ; therefore , if we multiply + aa ...
Página 24
... Unit . If Ъ the Numerator is greater than the Denominator , then the Fraction is greater than Unit . In both thefe Cafes , the Fraction is called Improper . But if the Numerator is less than the Denominator , then the Fraction is less ...
... Unit . If Ъ the Numerator is greater than the Denominator , then the Fraction is greater than Unit . In both thefe Cafes , the Fraction is called Improper . But if the Numerator is less than the Denominator , then the Fraction is less ...
Página 27
... . ) And if an Integer is to be multiplied by a Frac- tion , you may reduce it to the Form of a Frac- tion by placing Unit under it . EXAMPLES . 51 X × 3 = 1⁄2 - 1 ; 9x 12 18 bx x = = = = 6 : 6 Chap . 6 . ALGEBRA . 27.
... . ) And if an Integer is to be multiplied by a Frac- tion , you may reduce it to the Form of a Frac- tion by placing Unit under it . EXAMPLES . 51 X × 3 = 1⁄2 - 1 ; 9x 12 18 bx x = = = = 6 : 6 Chap . 6 . ALGEBRA . 27.
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Términos y frases comunes
adeoque æqualis affumed Afymptote alfo arife autem becauſe Biquadratic Cafe cafu Coefficient common Meaſure confequently Conic Section contactus contingentes Corol Cube Root Cubic Equation curvæ curvam curvaturæ Curve Dimenfions divided Divifor ducantur ducta ductæ enim Equa equal erit eritque ex puncto Exponent expreffed Expreffions faid fame Manner fecabit fecet fecond Term fegmenta femper fhall fimple Equations fince firft Term firſt flexus fome fquare Root Fraction fubftituting fubtract fuch funt fuppofe give greater greateſt hæc impoffible integer Interfection itſelf laft Term laſt leaft lefs Linea Locus multiplied muſt mutuo negative Number occurrat Parabola parallela pofitive Power Product Progreffion propofed Equation punctum Quadratic Equations quæ Quotient recta recta quævis rectæ recte rectis refolved refpect Refult reprefent Rule ſhall Signs Square ſuppoſe Surd tangentes thefe theſe thofe thoſe tion unknown Quantity Value vaniſh whofe Roots
Pasajes populares
Página 98 - AB there be taken more than its half, and from the remainder more than its half, and so on ; there shall at length remain a magnitude less than C.
Página 135 - ... -{-24, equal to nothing, according to the propofed equation. And it is certain that there can be no other values of x...
Página 82 - Where the numerator is the difference of the products of the opposite coefficients in the order in which y is not found, and the denominator is the difference of the products of the opposite coefficients taken from the orders that involve the two unknown quantities. Coefficients are of the same order which either affect no unknown quantity, as c anil ci ; or the same unknown quantity in the different equations, as a and o'.
Página 24 - Fractions ; and the dividend or quantity placed above the line is called the Numerator of the fraction, and the divifor or quantity placed under the line is called the Denominator...
Página 19 - If there is a remainder, you are to proceed after the fame manner till no remainder is left ; or till it appear that there will be always fome remainder. Some Examples will illuftrate this operation. EXAMPLE I.
Página 144 - Xx + bXx+cxx + d, &c. = o, will exprefs the equation to be produced ; all whofe terms will plainly be pofitive ; fo that " -when all the roots of an equation are negative, it is plain there will be no changes in the Jigns of the iermt of that equation
Página 121 - B, the Sum of the Terms in the even Places, each of which involves an odd Power of y will be a rational Number multiplied into the Quadratic Surd I/?2.
Página 134 - And after the same manner any other equation admits of as many solutions as there are simple equations multiplied by one another that produce it, or as many as there are units in the highest dimensions of the unknown quan tity in the proposed equation.
Página 1 - BRA is a general Method of Computation by certain Signs and Symbols which have been contrived for this Purpofe, and found convenient. It is called an UNIVERSAL ARITHMETICK, and proceeds by Operations and Rules fimilar to thofe in Common A* rithmetick, founded upon the fame Principles.
Página 10 - ... more than two quantities to be added together, firft add the pofitive together into one fum, and then the negative (by Cafe I.) Then add thefe two fums together (by Cafe II.) to A TREATISE of EXAMPLE. Parti. -f 8a - 7" + 100 . — 124 Sum of the pofitive . . . + 1 8a Sum of the negative ... — iga Sum of all — a Cafe III.