On the Study and Difficulties of MathematicsOpen Court Pub., 1898 - 288 sider |
Inni boken
Resultat 1-5 av 24
Side 13
... numbers , is taught so early , that the method by which we began is hardly recollected . Few , therefore , reflect ... natural and obvious does it seem , that it came with our language , and is a part of it ; and that we are not much indebted ...
... numbers , is taught so early , that the method by which we began is hardly recollected . Few , therefore , reflect ... natural and obvious does it seem , that it came with our language , and is a part of it ; and that we are not much indebted ...
Side 16
... whole num- ber of ways being 24. But this is more than we want ; one certain method of representing a number is suffi- cient . The most natural way is to place them in order of magnitude , either putting the largest collection first or ...
... whole num- ber of ways being 24. But this is more than we want ; one certain method of representing a number is suffi- cient . The most natural way is to place them in order of magnitude , either putting the largest collection first or ...
Side 23
... whole of the rules consist of processes intended to shorten and simplify that which would otherwise be long and complex . For example , multiplication is continued addition of the same number ... numbers by taking away any part of the first ...
... whole of the rules consist of processes intended to shorten and simplify that which would otherwise be long and complex . For example , multiplication is continued addition of the same number ... numbers by taking away any part of the first ...
Side 25
... number except 1. When the process of di- vision can be performed , it can be ascertained whether a given number is divisible by any other number , that is , whether it is prime or not . This can be done by dividing it by all the numbers ...
... number except 1. When the process of di- vision can be performed , it can be ascertained whether a given number is divisible by any other number , that is , whether it is prime or not . This can be done by dividing it by all the numbers ...
Side 34
... number , not only our first notion of it , but also the extended one , of which the first is only a part . Those to which our first notions applied we call whole numbers , the others fractional numbers , but still the name number is ...
... number , not only our first notion of it , but also the extended one , of which the first is only a part . Those to which our first notions applied we call whole numbers , the others fractional numbers , but still the name number is ...
Andre utgaver - Vis alle
On the study and difficulties of mathematics [by A. De Morgan]. Augustus De Morgan Uten tilgangsbegrensning - 1831 |
Vanlige uttrykk og setninger
absurd algebra algebraical quantity apply arithmetic asserted AUGUSTUS DE MORGAN axioms beginner binomial theorem called circle connexion contained cube root cyphers decimal fraction deduced definition denominator difficulties divided division divisor elementary equa equal equation Euclid evident exact number example expression factors figure geometry give given greater greatest common measure inch least common multiple less letter linear unit logarithms mA-nB magnitude manner mathematics meaning method metic multiplied notion operations premisses principles problem proceed proportion proposition proved quantity quotient reasoning recollect rectangle reduced remainder represented result right angles rule sides simple solution species square root stand straight line student subtraction suppose supposition syllogism symbol taken term theorem theory of equations tion treatise triangle true truth whole numbers written
Populære avsnitt
Side 225 - ... equal angles in each ; then shall the other sides be equal, each to each; and also the third angle of the one to the third angle of the other.
Side 225 - XIII. •All parallelograms on the same or equal bases and between the same parallels...
Side 230 - 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 78 - 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 36 - 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 the numerator by the numerator,...
Side 8 - So it is with our reasoning faculties: it is desirable that their powers should be exerted upon objects of such a nature, that we can tell by other means whether the results which we obtain are true or false, and this before it is safe to trust entirely to reason. Now the mathematics are peculiarly well adapted for this purpose, on the following grounds: 1. Every term is distinctly explained, and has but one meaning, and it is rarely that two words are employed to mean the same thing. 2. The first...
Side 8 - When the conclusion is attained by -reasoning, its truth or falsehood can he ascertained, in geometry by actual measurement, in algebra by common arithmetical calculation. This gives confidence, and is absolutely necessary, if, as was said before, reason is not to be the instructor, but the pupil. 5. There are no words whose meanings are so much alike that the ideas which they stand for may be confounded. Between the meanings of terms there is no distinction, except a total distinction, and all adjectives...