Library of Useful Knowledge: Mathematics I.Baldwin and Cradock, 1836 |
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Side 2
... means obtain of a fact in history or an asserted truth of metaphysics . In reality , our senses are our first mathematical instructors ; they furnish us with notions which we cannot trace any further or re- present in any other way than ...
... means obtain of a fact in history or an asserted truth of metaphysics . In reality , our senses are our first mathematical instructors ; they furnish us with notions which we cannot trace any further or re- present in any other way than ...
Side 3
... means , such as measure- ment and ocular demonstration of all sorts , whether the results are true or not . When the guiding property of the load stone was first ascertained , and it was necessary to learn how to use this new discovery ...
... means , such as measure- ment and ocular demonstration of all sorts , whether the results are true or not . When the guiding property of the load stone was first ascertained , and it was necessary to learn how to use this new discovery ...
Side 4
... means of others , which are more easily understood , and thereby fixing its mean- ing , so that it may be distinctly seen what it does imply , as well as what it does not . Great care must be taken that the definition itself is not a ...
... means of others , which are more easily understood , and thereby fixing its mean- ing , so that it may be distinctly seen what it does imply , as well as what it does not . Great care must be taken that the definition itself is not a ...
Side 8
... than its half . This process would be laborious when the given number is large ; still it may be done , and by this means the number itself may be reduced to its prime fac- above stated , the product of those two fractions , 8 STUDY OF.
... than its half . This process would be laborious when the given number is large ; still it may be done , and by this means the number itself may be reduced to its prime fac- above stated , the product of those two fractions , 8 STUDY OF.
Side 10
... mean that 56 is to be divided into 8 equal parts , and one of these parts is called the quo- tient . In this case the ... means that 5 is to be divided into 8 parts , and stands for one of these parts . The same length I will be obtained ...
... mean that 56 is to be divided into 8 equal parts , and one of these parts is called the quo- tient . In this case the ... means that 5 is to be divided into 8 parts , and stands for one of these parts . The same length I will be obtained ...
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algebra algebraical quantities answer arithmetic ax² becomes binomial theorem called ciphers coefficient common logarithms contained cube root decimal fraction decimal places decimal point digits divided dividend division divisor equa equal equation example exponent expression factors figure frac geometry given gives greater inches instance least common multiple less letters loga logarithm magnitude means metical multiply negative nth root observe operations permutations positive preceding proceed proportion proposition proved quotient reasoning reduced remainder result right angles rithm rule shillings solution square root student subtract suppose theorem things taken third tion triangle true unit unity unknown quantities vulgar fraction whole number write yards
Populære avsnitt
Side 69 - Parallelograms on the same or equal bases, and between the same parallels, are equal. The explanation of this is as follows : the whole proposition is divided into distinct assertions, which are placed in separate consecutive paragraphs, which paragraphs are numbered in the first column on the left ; in the second column on the left we state the reasons for each paragraph, either by referring to the preceding paragraphs from which they follow, or the preceding propositions in which they have been...
Side 12 - D' contains £T 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 the...
Side 53 - ... with one another. This cannot be attained by a mere reading of the book, however great the attention which may be given. It is impossible, in a mathematical work, to fill up every process in the manner in which it must be filled up in the mind of the student before he can be said to have completely mastered it. Many results must be given, of which the details are suppressed, such are the additions, multiplications, extractions of the square root, etc., with which the investigations abound.
Side 70 - 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 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. The properties of mind...
Side 84 - When it is said that the angle = arc , it is only meant that, 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 the ratio of the circumference of a circle to its diameter, or that of half the circumference to...
Side 13 - This process is then, by extension, called division : y is called the quotient of £ divided by 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...
Side 80 - In each succeeding term the coefficient is found by multiplying the coefficient of the preceding term by the exponent of a in that term, and dividing by the number of the preceding term.
Side 3 - ... thought advisable to make many passages between ports that were well known before attempting a voyage of discovery. 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...
Side 74 - ... number of combinations of n things r at a time is the same as the number of combinations of n things n — r at a time ; This result is frequently useful in enabling us to abridge arithmetical work.