Elementary algebra, with brief notices of its history1879 |
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Page 21
... root and the cube root . The fifth chapter of the Lilavati treats of progressions , arithme- tical and geometrical ... square of the difference between the first term and half that increase , the square root being extracted , this root ...
... root and the cube root . The fifth chapter of the Lilavati treats of progressions , arithme- tical and geometrical ... square of the difference between the first term and half that increase , the square root being extracted , this root ...
Page 24
... square and cube , are employed to denote the second and third powers , and these are combined to denote the higher powers , which are reckoned by the products , and not by the sums of the lower powers , as in the modern algebra . A surd ...
... square and cube , are employed to denote the second and third powers , and these are combined to denote the higher powers , which are reckoned by the products , and not by the sums of the lower powers , as in the modern algebra . A surd ...
Page 27
... square root and the cube root are given by reversing the direct process . Also rules are given for the addition and subtraction , multiplication and division , of quadratic surd numbers , as also for their involution and evolution . It ...
... square root and the cube root are given by reversing the direct process . Also rules are given for the addition and subtraction , multiplication and division , of quadratic surd numbers , as also for their involution and evolution . It ...
Page 28
... root of a square formed by a line expressing 5 may be found , though the root of 5 cannot be numerically expressed ; but the numbers 1 , 4 , 9 , & c . , may be expressed both ways . The square roots of the numbers 2 , 3 , 5 , & c ...
... root of a square formed by a line expressing 5 may be found , though the root of 5 cannot be numerically expressed ; but the numbers 1 , 4 , 9 , & c . , may be expressed both ways . The square roots of the numbers 2 , 3 , 5 , & c ...
Page 29
... roots , there- fore in the nth power of 1 + 1 , where every root is unity , the coefficient ... root is unity , the product of ach two roots will be unity , and therefore ... square and of 200 times the simple umber , is a myriad less one ...
... roots , there- fore in the nth power of 1 + 1 , where every root is unity , the coefficient ... root is unity , the product of ach two roots will be unity , and therefore ... square and of 200 times the simple umber , is a myriad less one ...
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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...