On the Study and Difficulties of MathematicsOpen Court Pub., 1898 - 288 sider |
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Side
... fact that in algebra the different species of contradictions in problems are attended with distinct absurdities , resulting from them as necessarily as different numerical results from different numerical data . This being granted , the ...
... fact that in algebra the different species of contradictions in problems are attended with distinct absurdities , resulting from them as necessarily as different numerical results from different numerical data . This being granted , the ...
Side 2
... fact related in history , such as the murder of Cæsar , whence did we derive the certainty ? how came we to feel sure of the general truth of the circum- stances of the narrative ? The ready answer to this question will be , that we ...
... fact related in history , such as the murder of Cæsar , whence did we derive the certainty ? how came we to feel sure of the general truth of the circum- stances of the narrative ? The ready answer to this question will be , that we ...
Side 3
... fact ; and , if we allow that there is still a possibility of its falsehood , it is because this supposition does ... facts asserted in these sciences are of a nature totally distinct from those of history ; so much so , that a ...
... fact ; and , if we allow that there is still a possibility of its falsehood , it is because this supposition does ... facts asserted in these sciences are of a nature totally distinct from those of history ; so much so , that a ...
Side 4
... fact , of the truth of which our eyes and hands convince us . In geometry , of the principles alluded to , those which are most commonly used are- I. If a magnitude be divided into parts , the whole is greater than either of those parts ...
... fact , of the truth of which our eyes and hands convince us . In geometry , of the principles alluded to , those which are most commonly used are- I. If a magnitude be divided into parts , the whole is greater than either of those parts ...
Side 5
... fact in history or an asserted truth of meta- physics . In reality , our senses are our first mathe- matical instructors ; they furnish us with notions . which we cannot trace any further or represent in any other way than by using ...
... fact in history or an asserted truth of meta- physics . In reality , our senses are our first mathe- matical instructors ; they furnish us with notions . which we cannot trace any further or represent in any other way than by using ...
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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...