On the study and difficulties of mathematics [by A. De Morgan]. |
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Página 2
... equal are equal in all respects , by proving that , if they are not equal , two straight lines will inclose a space , which is im- possible . In the Treatise on Geometry , Prop . 4 , the same thing is proved in the same way , only the ...
... equal are equal in all respects , by proving that , if they are not equal , two straight lines will inclose a space , which is im- possible . In the Treatise on Geometry , Prop . 4 , the same thing is proved in the same way , only the ...
Página 4
... equal , and all whose angles are right angles , " though no more is said than is true of a square , yet more is said than is necessary to define it , because it can be proved that if a four - sided figure have all its sides equal , and ...
... equal , and all whose angles are right angles , " though no more is said than is true of a square , yet more is said than is necessary to define it , because it can be proved that if a four - sided figure have all its sides equal , and ...
Página 10
... equal parts , and one of these parts is called the quo- tient . In this case the quotient is 7. But it is equally possible to divide 57 into 8 equal parts ; for example , we can divide 57 feet into 8 equal parts , but the eighth part of ...
... equal parts , and one of these parts is called the quo- tient . In this case the quotient is 7. But it is equally possible to divide 57 into 8 equal parts ; for example , we can divide 57 feet into 8 equal parts , but the eighth part of ...
Página 11
... 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 rectan- gle ABCD contains an exact number of E G F squares , each equal to G , and the ...
... 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 rectan- gle ABCD contains an exact number of E G F squares , each equal to G , and the ...
Página 13
... equal parts , each of which will be , and take 15 of these parts , we shall get 15 , or 3. The fraction whose numerator is 15 , and whose de- nominator is 8 , or 15 , will in these pro- blems take the place of the quotient of the two ...
... equal parts , each of which will be , and take 15 of these parts , we shall get 15 , or 3. The fraction whose numerator is 15 , and whose de- nominator is 8 , or 15 , will in these pro- blems take the place of the quotient of the two ...
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Términos y frases comunes
absurd algebra algebraical quantity apply arithmetic asserted ax² axioms beginner called circle coefficient connexion contained cube root cyphers decimal fraction deduced definition denominator difficulties divided division divisor equal equation Euclid evident exact number example expres expression factors figure frac geometry gisms give given greater greatest common measure inch least common multiple less letter linear unit logarithms mA-nB magnitude manner mathematics meaning merator method metic middle term multiplied negative sign notion positive premises principles problem proceed proportion proposition proved quantity quotient reasoning recollect reduced remain represent result right angles rule shew shewn sides simple sion solution species square root stand straight line student subtraction suppose supposition symbol taken term theorem tion treatise triangle true truth whole numbers written
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Página 75 - XIII. •All parallelograms on the same or equal bases and between the same parallels...
Página 76 - 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 ?
Página 25 - 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.
Página 30 - Four persons purchased a farm in company for 4755 dollars ; of which B paid three times as much as A ; C paid as much as A and B ; and D paid as much as C and B. What did each pay 1 Prob. 32. It is required to divide the number...
Página 12 - A'H'C'D' contains ^ of G. 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...
Página 13 - J., and is found by multiplying the numerator of the first by the denominator of the second for the numerator of the result, and the denominator of the first by the numerator of the second for the denominator of the result. That this process does give the same result as ordinary division in all cases where ordinary division is applicable, we can easily shew from any two whole numbers, for example, 12 and 2, whose quotient is 6. Now 12 is...
Página 71 - ... what has just been observed; since in the comparison of two things with one and the same third thing, in order to ascertain their connexion or discrepancy, consists the whole of reasoning. Thus, the deduction without further process of the equation...
Página 90 - When it is said that the angle = — ^r- — , it is only meant that, on one particular supradius position, (namely, that the angle 1 is that angle whose arc is equal to the radius,) the number of these units in any other angle is found by dividing the number of linear units in its arc by the number of linear units in the radius. It only remains to give a formula for finding the number of degrees, minutes, and seconds in an angle, whose theoretical measure is given. It is proved in geometry that...
Página 25 - A fraction is not altered by multiplying or dividing both its numerator and denominator by the same quantity.
Página 3 - ... faculties which would otherwise never have manifested their existence. It is, therefore, as necessary to learn to reason before we can expect to be able to reason, as it is to learn to swim or fence, in order to attain either of those arts. Now, something must be reasoned upon, it matters not much what it is, provided that it can be reasoned upon with certainty.