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

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added addition Algebra appears arithmetical assumed becomes biquadratic called chance coefficients combinations common considered consist contains continued cube cubic denominator denote determined difference digits divided divisible divisor Eliminate employed equal equation example expansion expression extract factors figures four fourth fraction geometrical give given given equation greater harmonical Hence increased integer interest involving known least length less letters limit manner mathematical means method multiplied named nature negative points positive possible probability problems progression proportion prove published quadratic equation quotient ratio reduced relation remainder respectively result rule shew side signs solution Solve square root substituted subtraction successive Suppose taken taking things third tion transformed treatise units unity unknown quantity volume write

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Page 36 - ... la diversité de nos opinions ne vient pas de ce que les uns sont plus raisonnables que les autres, mais seulement de ce que nous conduisons nos pensées par diverses voies, et ne considérons pas les mêmes choses. Car ce n'est pas assez d'avoir l'esprit bon, mais le principal est de l'appliquer bien.

Page 36 - Le bon sens est la chose du monde la mieux partagée ; car chacun pense en être si bien pourvu , que ceux même qui sont les plus difficiles à contenter en toute autre chose n'ont point coutume d'en désirer plus qu'ils en ont.

Page 57 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any...

Page 30 - As a blind man has no idea of colors, so have we no idea of the manner by which the all-wise God perceives and understands all things. He is utterly void of all body and bodily figure, and can therefore neither be seen, nor heard, nor touched ; nor ought he to be worshipped under the representation of any corporeal thing. We have ideas of his attributes, but what the real substance of anything is, we know not.

Page 18 - The number of square units in the area of a rectangle...

Page 13 - But the answer is easy; for by the ultimate velocity is meant that with which the body is moved, neither before it arrives at its last place and the motion ceases, nor after, but at the very instant it arrives; that is, that velocity with which the body arrives at its last place, and with which the motion ceases.

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. And if the fixed stars are the centers of other like systems, these being formed by the like wise counsel, must be all subject to the dominion of One...

Page 52 - Prove that if any number of quantities be in continued proportion, as one of the antecedents is to its consequent so is the sum of all the antecedents to the sum of all the consequents.

Page 19 - Collins, dated between the years 1669 and 1677, inclusive; and showed them to such as knew and avouched the hands of Mr. Barrow, Mr. Collins, Mr. Oldenburg, and Mr. Leibnitz ; and compared those of Mr. Gregory with one another, and with copies of some of them taken in the hand of Mr. Collins...

Page 13 - ... instant it arrives ; that is, that velocity with which the body arrives at its last place, and with which the motion ceases. " And in like manner, by the ultimate ratio of evanescent quantities...