Library of Useful Knowledge: Mathematics I.Baldwin and Cradock, 1836 |
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Side 1
... answer to this question will be , that we have not abso- lute certainty upon this point ; but that we have the relation of historians , men of credit , who lived and published their accounts in the very time of which they write ; that ...
... answer to this question will be , that we have not abso- lute certainty upon this point ; but that we have the relation of historians , men of credit , who lived and published their accounts in the very time of which they write ; that ...
Side 2
... - mencement , for it is evident that every student will feel a claim to have his ob- jections answered , not by authority , but by argument , and that the intelligent student will perceive more readily than another the force of STUDY OF.
... - mencement , for it is evident that every student will feel a claim to have his ob- jections answered , not by authority , but by argument , and that the intelligent student will perceive more readily than another the force of STUDY OF.
Side 8
... answer with a key to the book , printed for the preceptor's private use , to save the trouble which he ought to bestow upon his pupil , is not teaching arithmetic any more than pre- senting him with a grammar and dic- tionary is ...
... answer with a key to the book , printed for the preceptor's private use , to save the trouble which he ought to bestow upon his pupil , is not teaching arithmetic any more than pre- senting him with a grammar and dic- tionary is ...
Side 15
... answered that they cannot . It is a principle which is demonstrated in the science of algebra , —that if a number be not divisible by a sidered as of any consequence , as in all probability the expense of a more accu- rate measurement ...
... answered that they cannot . It is a principle which is demonstrated in the science of algebra , —that if a number be not divisible by a sidered as of any consequence , as in all probability the expense of a more accu- rate measurement ...
Side 15
... answered that they cannot . It is a principle which is demonstrated in the science of algebra , —that if a number be not divisible by a example , in measuring land for sale , an error of an inch in five hundred yards is not worth ...
... answered that they cannot . It is a principle which is demonstrated in the science of algebra , —that if a number be not divisible by a example , in measuring land for sale , an error of an inch in five hundred yards is not worth ...
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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.