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 sider |
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Side i
... Rules and Operations . II . The Compofition and Refolution of Equa tions of all Degrees ; and the different Affections of their Roots : III . The Application of Algebra and Geo- metry to each other . To which is added an APPENDIX ...
... Rules and Operations . II . The Compofition and Refolution of Equa tions of all Degrees ; and the different Affections of their Roots : III . The Application of Algebra and Geo- metry to each other . To which is added an APPENDIX ...
Side vi
... Rules of the Science , in the shorteft , and , at the fame time , the most clear and comprehenfive Man- ner that was poffible . Agreeable to this , though every Rule is properly exemplified , yet he does not launch out into what we may ...
... Rules of the Science , in the shorteft , and , at the fame time , the most clear and comprehenfive Man- ner that was poffible . Agreeable to this , though every Rule is properly exemplified , yet he does not launch out into what we may ...
Side ix
... Rules concerning the Impoffible Roots of Equations , our Author had very fully confi- dered , as appears from his Manufcript Papers : But as ... Rule , which pre- Supposes fuppofes only what the Reader has been taught in a To the READER . ix.
... Rules concerning the Impoffible Roots of Equations , our Author had very fully confi- dered , as appears from his Manufcript Papers : But as ... Rule , which pre- Supposes fuppofes only what the Reader has been taught in a To the READER . ix.
Side xiii
In Three Parts. Containing. The fundamental rules and operations. The composition and resolution of equations of all ... Rule , and others of that Kind , 223 IX . Of the Methods by which you may ap proximate to the Roots of Numeral ...
In Three Parts. Containing. The fundamental rules and operations. The composition and resolution of equations of all ... Rule , and others of that Kind , 223 IX . Of the Methods by which you may ap proximate to the Roots of Numeral ...
Side xiv
... Rules for finding the Number of impoffible Roots in an Equation , 275 XII . Containing a general Demonftration of Sir Ifaac Newton's Rule for finding the Sums of the Powers of the Roots of an Equation , PART III . 286 Of the Application ...
... Rules for finding the Number of impoffible Roots in an Equation , 275 XII . Containing a general Demonftration of Sir Ifaac Newton's Rule for finding the Sums of the Powers of the Roots of an Equation , PART III . 286 Of the Application ...
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A Treatise of Algebra,: In Three Parts. Containing I. The Fundamental Rules ... Colin MacLaurin Uten tilgangsbegrensning - 1796 |
A Treatise of Algebra: In Three Parts. Containing. The fundamental rules and ... Colin MacLaurin Uten tilgangsbegrensning - 1796 |
A Treatise of Algebra, in Three Parts: Containing I. The Fundamental Rules ... Colin MacLaurin Uten tilgangsbegrensning - 1748 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 135 - ... -{-24, equal to nothing, according to the propofed equation. And it is certain that there can be no other values of x...
Side 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'.
Side 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...
Side 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.
Side 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
Side 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.
Side 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.
Side 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.
Side 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.