On the study and difficulties of mathematics [by A. De Morgan]. |
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Side 4
... defining a term ; and here we may say a few words on defini- tions in general , which will apply equally to all sciences . Definition is the explaining a term by means of others , which are more easily understood , and thereby fixing ...
... defining a term ; and here we may say a few words on defini- tions in general , which will apply equally to all sciences . Definition is the explaining a term by means of others , which are more easily understood , and thereby fixing ...
Side 13
... definition . should recollect that is 1 divided into 6 parts and five of them taken , or the sixth part of 5 , and he should reason upon these suppositions , neglecting all rules until he has established them in his own mind by ...
... definition . should recollect that is 1 divided into 6 parts and five of them taken , or the sixth part of 5 , and he should reason upon these suppositions , neglecting all rules until he has established them in his own mind by ...
Side 23
... definition still some- times given of the quantity a , that it is less than nothing . It is astonishing that the human intellect should ever have tolerated such an absurdity as the idea of a quantity less than nothing ; above all , that ...
... definition still some- times given of the quantity a , that it is less than nothing . It is astonishing that the human intellect should ever have tolerated such an absurdity as the idea of a quantity less than nothing ; above all , that ...
Side 24
... definition of a α fraction , the same as the fraction , and all that remains is to see whether that fraction can be represented by a simple algebraical expression without fractions or not ; just as in arithmetic the division of 200 by ...
... definition of a α fraction , the same as the fraction , and all that remains is to see whether that fraction can be represented by a simple algebraical expression without fractions or not ; just as in arithmetic the division of 200 by ...
Side 27
... definition of these operations . Such is also the con- tinual use of 0 as a quantity , the addition and subtraction of it from other quanti- ties , and the multiplication of it by others , neither of which were contem plated when these ...
... definition of these operations . Such is also the con- tinual use of 0 as a quantity , the addition and subtraction of it from other quanti- ties , and the multiplication of it by others , neither of which were contem plated when these ...
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absurd algebra algebraical quantity apply arithmetic asserted ax² axioms beginner called circle coefficient connexion contained cube root cyphers decimal fraction deduced definition denominator difficulties divided division divisor equal equation Euclid evident exact number example expres expression factors figure frac geometry gisms give given greater greatest common measure inch least common multiple less letter linear unit logarithms mA-nB magnitude manner mathematics meaning merator method metic middle term multiplied negative sign notion positive premises principles problem proceed proportion proposition proved quantity quotient reasoning recollect reduced remain represent result right angles rule shew shewn sides simple sion solution species square root stand straight line student subtraction suppose supposition symbol taken term theorem tion treatise triangle true truth whole numbers written
Populære avsnitt
Side 75 - XIII. •All parallelograms on the same or equal bases and between the same parallels...
Side 76 - Thus, that the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the other two sides, was an experimental discovery, or why did the discoverer sacrifice a hecatomb when he made out its proof ?
Side 25 - To divide a term of the second series by one which comes before it, subtract the exponent of the divisor from the exponent of the dividend, and make this difference the exponent of c.
Side 30 - Four persons purchased a farm in company for 4755 dollars ; of which B paid three times as much as A ; C paid as much as A and B ; and D paid as much as C and B. What did each pay 1 Prob. 32. It is required to divide the number...
Side 12 - A'H'C'D' contains ^ of G. Here then appears a connexion between the multiplication of whole numbers, and the formation of a fraction whose numerator is the product of two numerators, and its denominator the product of the corresponding denominators. These operations will always come together, that is whenever a question occurs in which, when whole numbers are given, those numbers are to be multiplied together ; when fractional numbers are given, it will be necessary, in the same case, to multiply...
Side 13 - J., and is found by multiplying the numerator of the first by the denominator of the second for the numerator of the result, and the denominator of the first by the numerator of the second for the denominator of the result. That this process does give the same result as ordinary division in all cases where ordinary division is applicable, we can easily shew from any two whole numbers, for example, 12 and 2, whose quotient is 6. Now 12 is...
Side 71 - ... what has just been observed; since in the comparison of two things with one and the same third thing, in order to ascertain their connexion or discrepancy, consists the whole of reasoning. Thus, the deduction without further process of the equation...
Side 90 - When it is said that the angle = — ^r- — , it is only meant that, on one particular supradius position, (namely, that the angle 1 is that angle whose arc is equal to the radius,) the number of these units in any other angle is found by dividing the number of linear units in its arc by the number of linear units in the radius. It only remains to give a formula for finding the number of degrees, minutes, and seconds in an angle, whose theoretical measure is given. It is proved in geometry that...
Side 25 - A fraction is not altered by multiplying or dividing both its numerator and denominator by the same quantity.
Side 3 - ... faculties which would otherwise never have manifested their existence. It is, therefore, as necessary to learn to reason before we can expect to be able to reason, as it is to learn to swim or fence, in order to attain either of those arts. Now, something must be reasoned upon, it matters not much what it is, provided that it can be reasoned upon with certainty.