Elementary algebra: with brief notices of its historyLongmans & Company, 1879 - Algebra |
From inside the book
Results 1-5 of 68
Page 6
... equations . The Arabians held a less general notion of equations than the Hindus , as they only knew equals to be the equality of two or more absolute positive quantities . They had no conception of the equation x2 + px + q = 0 , the ...
... equations . The Arabians held a less general notion of equations than the Hindus , as they only knew equals to be the equality of two or more absolute positive quantities . They had no conception of the equation x2 + px + q = 0 , the ...
Page 20
... equation = 2x + 21 has only one negative root , the other two being impossible , or involving the square root of a negative quantity . In this manner he shows how a cubic equation may have one , two , or three roots , according to the ...
... equation = 2x + 21 has only one negative root , the other two being impossible , or involving the square root of a negative quantity . In this manner he shows how a cubic equation may have one , two , or three roots , according to the ...
Page 32
... equation , three a cubic , four a biquadratic , & c . , with all the terms on one side made equal to zero . From this it is obvious , on inspection , what relations subsist between the roots and the coefficients of any equation . Since ...
... equation , three a cubic , four a biquadratic , & c . , with all the terms on one side made equal to zero . From this it is obvious , on inspection , what relations subsist between the roots and the coefficients of any equation . Since ...
Page 12
... equation being given expressing the relation of two or more lines x , y , z , & c . , described in the same time by two or more moving bodies , A , B , C , & c . , to find the relation of their velocities , P , 4 , r , & c . Resolution ...
... equation being given expressing the relation of two or more lines x , y , z , & c . , described in the same time by two or more moving bodies , A , B , C , & c . , to find the relation of their velocities , P , 4 , r , & c . Resolution ...
Page 40
... equation to the same side as the other terms which involve the unknown quantity , he was enabled to show that an equation of any degree could be formed with simple equations ; and conversely , that every equation has as many roots as ...
... equation to the same side as the other terms which involve the unknown quantity , he was enabled to show that an equation of any degree could be formed with simple equations ; and conversely , that every equation has as many roots as ...
Other editions - View all
Elementary Algebra: With Brief Notices of Its History, Volumes 1-12 Robert Potts No preview available - 2016 |
Common terms and phrases
a+b+c a²+b² Algebra arithmetical progression binomial Binomial Theorem biquadratic calculus coefficients common difference consist contains cube root cubic equation decimal denominator denote the number determined digits divided dividend divisible Eliminate equal Euclid Euclid's Elements expression extract factors find the number find the value fluxions four fourth fraction geometrical progression given equations greater Hence highest common divisor involving jebr least common multiple Leibnitz less letters mathematical means method method of fluxions multiplied natural numbers negative quantity Newton notation number of terms positive integer published quadratic equation quotient ratio reduced remainder respectively result second equation shew side signs solution square numbers square root substituted subtraction surd symbols theorem third tion treatise unity unknown quantities whence
Popular passages
Page 29 - This most beautiful system of the sun, planets, and comets could only proceed from the counsel and dominion of an intelligent and powerful Being.
Page iv - The sluggard is wiser in his own conceit than seven men that can render a reason.
Page 30 - We know him only by his most wise and excellent contrivances of things, and final causes; we admire him for his perfections; but we reverence and adore him on account of his dominion: for we adore him as his servants; and a god without dominion, providence, and final causes, is nothing else but Fate and Nature.
Page 32 - Théorie des fonctions analytiques, contenant les principes du calcul différentiel, dégagés de toute considération d'infiniment petits ou d'évanouissans, de limites ou de fluxions, et réduits à l'analyse algébrique des quantités finies; par JL Lagnuige.
Page 32 - Les plus grandes âmes sont capables des plus grands vices aussi bien que des plus grandes vertus ; et ceux qui ne marchent que fort lentement peuvent avancer beaucoup davantage , s'ils suivent toujours le droit chemin, que ne font ceux qui courent et qui s'en éloignent.
Page 6 - WHEN I wrote my treatise about our system, I had an eye upon such principles as might work with considering men for the belief of a Deity ; and nothing can rejoice me more than to find it useful for that purpose.
Page 5 - To make an estimate, what might be the degree of this diminution, he considered with himself, that if the moon be retained in her orbit by the force of gravity, no doubt the primary planets are carried round the sun by the like power. And by comparing the periods of the several planets with their distances from the sun, he found, that if any power like gravity held them in their courses, its strength must decrease in the duplicate proportion of the increase of distance.
Page 59 - If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.