On the Study and Difficulties of MathematicsOpen Court Pub., 1898 - 288 sider |
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Side
... greater advantage than in the present work , which was conceived and written with the full natural freedom , and with all the fire , of youthful genius . For the contents and purpose of the book the reader may be referred to the ...
... greater advantage than in the present work , which was conceived and written with the full natural freedom , and with all the fire , of youthful genius . For the contents and purpose of the book the reader may be referred to the ...
Side 4
... greater than either of those parts . II . Two straight lines cannot inclose a space . III . Through one point only one straight line can be drawn , which never meets another straight line , or which is parallel to it . It is on such ...
... greater than either of those parts . II . Two straight lines cannot inclose a space . III . Through one point only one straight line can be drawn , which never meets another straight line , or which is parallel to it . It is on such ...
Side 6
... greater than its part , " no useful re- sult can possibly be derived , and that we might as well expect to make use of " two and two make four . " This observation , which is common enough in the mouths of those who are commencing ...
... greater than its part , " no useful re- sult can possibly be derived , and that we might as well expect to make use of " two and two make four . " This observation , which is common enough in the mouths of those who are commencing ...
Side 7
... greater is the ordinary light the more will occa- sional darkness be felt . To remove some of these difficulties is the principal object of this Treatise . We shall now make a few remarks on the advan- tages to be derived from the study ...
... greater is the ordinary light the more will occa- sional darkness be felt . To remove some of these difficulties is the principal object of this Treatise . We shall now make a few remarks on the advan- tages to be derived from the study ...
Side 9
... greater than B , " but it is entirely unimportant whether A is very little or very much greater than B. Any proposition which includes the foregoing asser- tion will prove its conclusion generally , that is , for all cases in which A is ...
... greater than B , " but it is entirely unimportant whether A is very little or very much greater than B. Any proposition which includes the foregoing asser- tion will prove its conclusion generally , that is , for all cases in which A is ...
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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...