On the Study and Difficulties of MathematicsOpen Court Pub., 1898 - 288 sider |
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Side 4
... sides and the included angle respectively equal are equal in all respects , by proving that , if they are not equal , two straight lines will inclose a space , which is impossible . In other treatises on geometry , the ON THE STUDY OF ...
... sides and the included angle respectively equal are equal in all respects , by proving that , if they are not equal , two straight lines will inclose a space , which is impossible . In other treatises on geometry , the ON THE STUDY OF ...
Side 11
... assumption of some fact or other which ought to be proved . Thus , when it is said that a square is " a four sided figure , all whose sides are equal , and all whose angles are right angles , " though no more On Arithmetical Notation II.
... assumption of some fact or other which ought to be proved . Thus , when it is said that a square is " a four sided figure , all whose sides are equal , and all whose angles are right angles , " though no more On Arithmetical Notation II.
Side 12
... sides equal , and one only of its angles a right angle , all the other angles must be right angles also . Therefore ... sides of the figure are straight lines or curves . should be , " a square is a four - sided rectilinear figure , all ...
... sides equal , and one only of its angles a right angle , all the other angles must be right angles also . Therefore ... sides of the figure are straight lines or curves . should be , " a square is a four - sided rectilinear figure , all ...
Side 35
... sides AB and BC in inches . Draw the B C D line EF equal in 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 ...
... sides AB and BC in inches . Draw the B C D line EF equal in 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 ...
Side 59
... side by side , and inclosing each of them in brackets . Thus , if a + b + c is to be multiplied by d + e + ƒ , the product is written in any of the following ways : ( a + b + c ) ( d + e + f ) , [ a + b + c ] [ d + e + f ] , { a + b + c } ...
... side by side , and inclosing each of them in brackets . Thus , if a + b + c is to be multiplied by d + e + ƒ , the product is written in any of the following ways : ( a + b + c ) ( d + e + f ) , [ a + b + c ] [ d + e + f ] , { a + b + c } ...
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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...