Elementary algebra: with brief notices of its historyLongmans & Company, 1879 - Algebra |
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Page 5
... remainder is one dirhem equal to half a thing . Double it ; then you have thing , equal to two dirhems . This is one of the two numbers , and the other is four . " In modern notation , = = 1 , 2x = x + 2 , x = 2 and x + 2 = 4 . from ...
... remainder is one dirhem equal to half a thing . Double it ; then you have thing , equal to two dirhems . This is one of the two numbers , and the other is four . " In modern notation , = = 1 , 2x = x + 2 , x = 2 and x + 2 = 4 . from ...
Page 7
... remainder is three . This is the root of the square you sought for ; the square itself is nine . In modern notation , the equation is x2 + 10x = 39 . The following is another example from M. Rosen's translation : - " I have divided ten ...
... remainder is three . This is the root of the square you sought for ; the square itself is nine . In modern notation , the equation is x2 + 10x = 39 . The following is another example from M. Rosen's translation : - " I have divided ten ...
Page 10
... square number is that which being increased or diminished by ten , the sum and remainder are both square numbers ? 3. A person said he owed Zaid ten all but the square root of what he owed translator remarks : - " By order of the Emperor ...
... square number is that which being increased or diminished by ten , the sum and remainder are both square numbers ? 3. A person said he owed Zaid ten all but the square root of what he owed translator remarks : - " By order of the Emperor ...
Page 42
... remainder or an endless addition of terms to be made to it , one after another . Hence we may conceive it as a whole of its own kind ; and therefore the infinite series may be said to have a real value determinable or not . Now , in ...
... remainder or an endless addition of terms to be made to it , one after another . Hence we may conceive it as a whole of its own kind ; and therefore the infinite series may be said to have a real value determinable or not . Now , in ...
Page 38
... remainder of Taylor's series after a finite number of terms has been found . La Grange devised a formula that bears his name , which is use- ful for the development of implicit functions . It first appeared in the Berlin Memoirs for the ...
... remainder of Taylor's series after a finite number of terms has been found . La Grange devised a formula that bears his name , which is use- ful for the development of implicit functions . It first appeared in the Berlin Memoirs for the ...
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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.