On the Study and Difficulties of MathematicsOpen Court Publishing Company, 1898 - 288 pàgines |
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On the study and difficulties of mathematics [by A. De Morgan]. Augustus De Morgan Visualització completa - 1831 |
Frases i termes més freqüents
absurd algebra algebraical quantity apply arithmetic asserted AUGUSTUS DE MORGAN ax² 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 observe 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
Passatges populars
Pàgina 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.
Pàgina 225 - XIII. •All parallelograms on the same or equal bases and between the same parallels...
Pàgina 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 ?
Pàgina 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.
Pàgina 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,...
Pàgina 80 - ... any previous one. Rules were afterwards deduced for the addition and subtraction of the total result of several expressions in which these signs occur, as follows : To add two expressions, form a third, which has all the quantities in the first two, with the same signs. To subtract one expression from another, change the sign of each term of the subtrahend, and proceed as in the last rule. The only terms in which these rules do not apply are those which have no sign, viz. the first of each. But...
Pàgina 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...
Pàgina 213 - ... others, such as that any angles in the same segment of a circle are equal. The third class contains those theorems in which areas are asserted to be equal to other areas, differing in form from themselves, though not in magnitude, such as Book I. 47, in which it is asserted that the sum of the squares on the sides of a right-angled triangle, is equal to the square on the hypothenuse. The first class of...