The Academic AlgebraThompson, Brown, 1889 - 414 páginas |
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Página
... become more familiar with algebraic reasoning . The adjective , Arithmétic , is used by recent writers on Algebra , and in referring to a series of numbers , as it corre- sponds with the adjectives , Geometric and Harmonic , it has been ...
... become more familiar with algebraic reasoning . The adjective , Arithmétic , is used by recent writers on Algebra , and in referring to a series of numbers , as it corre- sponds with the adjectives , Geometric and Harmonic , it has been ...
Página 1
... become concrete . - NOTE 1. Quantity , the subject of all mathematical investigation , has been variously used to mean not only anything which can be meas- ured , as time , distance , etc. , but also the abstract number arising from its ...
... become concrete . - NOTE 1. Quantity , the subject of all mathematical investigation , has been variously used to mean not only anything which can be meas- ured , as time , distance , etc. , but also the abstract number arising from its ...
Página 21
... become : ( 1 ) + a + ( + b ) = a + b ( 2 ) + a + ( -b ) = a -b ( 3 ) + a ( + b ) = a -b ( 4 ) + a ( b ) = a + b ) ( C ) 50. To prove the above laws true for all negative values , let cb , where b is any positive number ; then c is any ...
... become : ( 1 ) + a + ( + b ) = a + b ( 2 ) + a + ( -b ) = a -b ( 3 ) + a ( + b ) = a -b ( 4 ) + a ( b ) = a + b ) ( C ) 50. To prove the above laws true for all negative values , let cb , where b is any positive number ; then c is any ...
Página 30
... becomes in each 3 less , the remainder in each is 3 greater than in the preceding . ( 12. ) ( 12. ) ( 13. ) ( 14. ) - ( 8. ) ( 9. ) ( 10. ) ( 11. ) ( 11. ) Min . 9 6 3 0 - Sub . 9 9 9 9 3 9 - 9 9 Rem . 0 3 6 -9 - 12 15 - 18 - 6 9 In ...
... becomes in each 3 less , the remainder in each is 3 greater than in the preceding . ( 12. ) ( 12. ) ( 13. ) ( 14. ) - ( 8. ) ( 9. ) ( 10. ) ( 11. ) ( 11. ) Min . 9 6 3 0 - Sub . 9 9 9 9 3 9 - 9 9 Rem . 0 3 6 -9 - 12 15 - 18 - 6 9 In ...
Página 42
... becomes ax + bx + ay + by + az + bz , and this equals by the Commu- tative Law for Addition ( § 56 ) , a x + ay + a z + b x + b y + b z . Hence , for the multiplication of a polynomial by a polyno- mial , we have the following Rule ...
... becomes ax + bx + ay + by + az + bz , and this equals by the Commu- tative Law for Addition ( § 56 ) , a x + ay + a z + b x + b y + b z . Hence , for the multiplication of a polynomial by a polyno- mial , we have the following Rule ...
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Términos y frases comunes
9 a² a b c a² b² a² b³ a²b² a²x² algebraic expressions arithmetical progression b² c² binomial Binomial Theorem bracket cents coefficient cube root denominator digits divided dividend equal examples exponent figures Find the factors Find the greatest Find the number Find the square Find the sum Find the value following Rule geometrical progression given greatest common divisor Hence integral last term least common multiple less logarithm miles an hour mixed number monomial Multiply negative number number of hours number of terms polynomial positive number quadratic equation quotient radical ratio remainder second term simplest form Simplify square root subtracted Theorem Transposing trial divisor unknown number x y z x² y² x²y x³ y² yards
Pasajes populares
Página 53 - 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. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Página 317 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Página 317 - In a proportion the antecedents and consequents of the two ratios are respectively the antecedents and consequents of the proportion. The first and fourth terms are called the extremes, and the second and third the means.
Página 152 - The first term of a ratio is called the antecedent, and the other the consequent ; and the two terms together are called a couplet.
Página 228 - Multiply the true divisor by this neiv root figure, subtract the product from the dividend, and to the remainder annex the next period, for a new dividend.
Página 330 - Any three of the five following things being given, the other two may be found : 1. The first term. 2. The last term. 3. The number of terms. 4. The common difference. 5. The sum of all the terms.
Página 61 - The square of the sum of two numbers is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Página 152 - Three quantities are said to be proportional when the ratio of the first to the second is equal to the ratio of the second to the third.
Página 227 - Subtract the square of this figure from the left-hand period, and to the remainder annex the next period for a dividend.
Página 250 - Resolve the quantity under the radical sign into two factors, one of which is the greatest perfect power of the same degree as the radical.