## Elementary algebra: with brief notices of its history |

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added addition Algebra appears applied arithmetical assumed becomes calculus called coefficients combinations common considered consist contains continued cube cubic denominator denote determined difference digits divided divisible divisor edition employed equal equation example expansion explained expression extraction factors figures four fourth fraction geometrical given gives greater Hence increased infinite integral involving jebr known language least length less letters manner mathematical means method multiplied nature negative Newton operations original positive principles progression prove published quadratic quotient ratio reduced relation remainder remarks respectively result rule shew shows side signs solution square root substituted subtraction successive supposed symbols taken taking things third tion translated treatise units unity unknown quantity volume writings written

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Page 33 - 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 34 - 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 3 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when...

Page 36 - 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 34 - 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 4 - ... if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...

Page 8 - 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 7 - 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 63 - 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.