Elementary algebra, with brief notices of its history1879 |
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Page 3
... unity to the mind , and every assemblage of objects or units suggests the idea of numbers , or of a greater or a less assemblage of units . The idea of a simple number is an abstraction , and from the fact of men having five fingers on ...
... unity to the mind , and every assemblage of objects or units suggests the idea of numbers , or of a greater or a less assemblage of units . The idea of a simple number is an abstraction , and from the fact of men having five fingers on ...
Page 28
... unity , Bhascara gives this rule of Sridhara : " Multiply both sides of the equation by a number equal to four times the coefficient of the square , and add to each side a number equal to the original coefficient of the first power of ...
... unity , Bhascara gives this rule of Sridhara : " Multiply both sides of the equation by a number equal to four times the coefficient of the square , and add to each side a number equal to the original coefficient of the first power of ...
Page 29
... unity , the product of ach two roots will be unity , and therefore the number of units , or the oefficient itself , shows the number of different twos that can be taken in n things . Again , because the fourth term is the sum of the ...
... unity , the product of ach two roots will be unity , and therefore the number of units , or the oefficient itself , shows the number of different twos that can be taken in n things . Again , because the fourth term is the sum of the ...
Page 6
... unity , where it was necessary . The next step was to relieve the equation of negative quantities by the operation of al jebr . This name was given to the operation because it was only after negative terms had been removed that the ...
... unity , where it was necessary . The next step was to relieve the equation of negative quantities by the operation of al jebr . This name was given to the operation because it was only after negative terms had been removed that the ...
Page 23
... unity , the exponents of the powers will , after 0 , become negative numbers , and be still the true exponents of the powers which are less than unity . He exemplifies in the following two series the relation between the order of the ...
... unity , the exponents of the powers will , after 0 , become negative numbers , and be still the true exponents of the powers which are less than unity . He exemplifies in the following two series the relation between the order of the ...
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Common terms and phrases
a+b+c a²+b² Algebra arithmetical progression binomial biquadratic calculus coefficients consist contains cube numbers cube root cubic equation decimal denominator determined digits divided dividend divisible equal Euclid Euclid's Elements expression extraction factors find the number find the value fluxions four fourth fraction geometrical progression given equation greater harmonical means Hence highest common divisor involving jebr least common multiple Leibnitz less letters mathematical means method method of fluxions multiplied natural numbers negative quantity Newton number ends number of terms positive integer published quadratic equation quotient ratio reduced remainder respectively result second equation second term shew shewn side signs solution square numbers square root substituted subtraction symbols theorem things third tion treatise unity unknown quantities
Popular passages
Page 34 - ... 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 34 - 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 61 - 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 28 - 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 16 - The number of square units in the area of a rectangle...
Page 11 - 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 27 - 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 56 - 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 17 - 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 11 - ... 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...