On the Study and Difficulties of MathematicsOpen Court Pub., 1898 - 288 sider |
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Side 1
... length the nature without going into the routine of the operations . No person commences the study of mathematics without soon discovering that it is of a very different nature from those to which he has been accustomed . The pursuits ...
... length the nature without going into the routine of the operations . No person commences the study of mathematics without soon discovering that it is of a very different nature from those to which he has been accustomed . The pursuits ...
Side 23
... length , hardly sensible of their presence , are the foundation of the arithmetical rules : I. We do not alter the sum of two numbers by taking away any part of the first , if we annex that part to the second . This may be expressed by ...
... length , hardly sensible of their presence , are the foundation of the arithmetical rules : I. We do not alter the sum of two numbers by taking away any part of the first , if we annex that part to the second . This may be expressed by ...
Side 31
... length will be obtained if we divide 1 into 8 parts , and take 5 of them , or find 5. To prove this let each of the lines drawn be- low represent of an inch ; repeat five times , and repeat the same line eight times . In each column is ...
... length will be obtained if we divide 1 into 8 parts , and take 5 of them , or find 5. To prove this let each of the lines drawn be- low represent of an inch ; repeat five times , and repeat the same line eight times . In each column is ...
Side 32
... length by dividing 1 inch into 20 parts , and taking 12 of them , which we get by dividing 1 inch into 5 parts and taking 3 of them . This hardly needs demonstration . Taking 12 out of 20 is taking 3 out of 5 , since for every 3 which ...
... length by dividing 1 inch into 20 parts , and taking 12 of them , which we get by dividing 1 inch into 5 parts and taking 3 of them . This hardly needs demonstration . Taking 12 out of 20 is taking 3 out of 5 , since for every 3 which ...
Side 35
... length to one inch , and the square G , each of whose sides is one inch . If the lines AB and BC contain an exact number of inches , the rect- angle ABCD contains an exact number of squares , E F G each equal to G , and the number of ...
... length to one inch , and the square G , each of whose sides is one inch . If the lines AB and BC contain an exact number of inches , the rect- angle ABCD contains an exact number of squares , E F G each equal to G , and the number of ...
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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...