An Introduction to Algebra: Being the First Part of a Course of Mathematics : Adapted to the Method of Instruction in the American CollegesHowe & Spalding, 1820 - 332 σελίδες |
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... Euclid . It may be thought , by some , to be unwise to form our gen- eral habits of arguing , on the model of a science in which the inquiries are accompanied with absolute certamty ; while the common business of life must be conducted ...
... Euclid . It may be thought , by some , to be unwise to form our gen- eral habits of arguing , on the model of a science in which the inquiries are accompanied with absolute certamty ; while the common business of life must be conducted ...
Σελίδα
... Euclid and others have given to the geometrical part , a degree of clearness and precision which would be very desirable , but is hardly to be expected , in algebra . " For the reasons which have been mentioned , the manner in which the ...
... Euclid and others have given to the geometrical part , a degree of clearness and precision which would be very desirable , but is hardly to be expected , in algebra . " For the reasons which have been mentioned , the manner in which the ...
Σελίδα
... Euclid . That is sufficient for the purposes of pure geometrical demonstration . But it is important that the propositions should also be pre- sented , under the algebraic forms . In addition to this , great assistance may be derived ...
... Euclid . That is sufficient for the purposes of pure geometrical demonstration . But it is important that the propositions should also be pre- sented , under the algebraic forms . In addition to this , great assistance may be derived ...
Σελίδα 89
... of these is equal to the other . ( Art . 212. ) The cube of axb + d , is ( axb + d ) 3 , or g3 × ( b + d } 3 « * Euclid's Elements , Book Ir . Prop . 4 . 217. When a quantity whose power has been expressed by 13 INVOLUTION . 89.
... of these is equal to the other . ( Art . 212. ) The cube of axb + d , is ( axb + d ) 3 , or g3 × ( b + d } 3 « * Euclid's Elements , Book Ir . Prop . 4 . 217. When a quantity whose power has been expressed by 13 INVOLUTION . 89.
Σελίδα 173
... Euclid's Elements , Book 5 , 7 , 8. Euler's Algebra , Part I , Sec . 3 . Emerson on Proportion . Camus ' Geometry , Book III . Ludlam's Mathe- matics . Wallis ' Algebra , Chap . 19 , 20. Saunderson's Algebra , Book 7 . Barrow's ...
... Euclid's Elements , Book 5 , 7 , 8. Euler's Algebra , Part I , Sec . 3 . Emerson on Proportion . Camus ' Geometry , Book III . Ludlam's Mathe- matics . Wallis ' Algebra , Chap . 19 , 20. Saunderson's Algebra , Book 7 . Barrow's ...
Συχνά εμφανιζόμενοι όροι και φράσεις
12 rods abscissa added algebraic antecedent applied arithmetical become binomial calculation co-efficients common difference Completing the square compound quantity consequent contain cube root cubic equation curve Divide the number dividend division divisor dollars equa errour Euclid exponents expression extracting factors fourth fraction gallons geometrical geometrical progression given quantity greater greatest common measure Hence inches infinite series inverted last term length less letters manner mathematics Mult multiplicand multiplied or divided negative quantity notation nth power nth root number of terms ordinate parallelogram perpendicular positive preceding prefixed principle Prob proportion proposition quadratic equation quan quotient radical quantities radical sign ratio reciprocal Reduce the equation remainder rule sides square root substituted subtracted subtrahend supposed supposition third tion tity Transp Transposing triangle twice unit unknown quantity varies α α
Δημοφιλή αποσπάσματα
Σελίδα 298 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Σελίδα 186 - Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.
Σελίδα 199 - If three quantities are proportional, the first is to the third, as the square of the first, to the square of the second ; or as the square of the second, to the square of the third.
Σελίδα 231 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient.
Σελίδα 203 - What two numbers are those, whose difference, sum, and product, are as the numbers 2, 3, and 5, respectively ? Ans.
Σελίδα 42 - As the product of the divisor and quotient is equal to the dividend, the quotient may be found, by resolving the dividend into two such factors, that one of them shall be the divisor. The other will, of course, be the quotient. Suppose abd is to be divided by a. The factors a and Id will produce the dividend.
Σελίδα 215 - THE EXTREMES IS EQUAL TO THE SUM OF ANY OTHER TWO TERMS EQUALLY DISTANT FROM THE EXTREMES.
Σελίδα 81 - ... of this part. At the end of the third year, his original stock was doubled. What was that stock ? Ans.
Σελίδα 237 - Divide one of the quantities by the other, and the preceding divisor by the last remainder, till nothing remains ; the last divisor will be the greatest common measure.