An Introduction to Algebra: With Notes and Observations; Designed for the Use of Schools and Places of Public EducationJoseph Crukshank, 1806 - 208 σελίδες |
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Σελίδα 40
... furd , and over this new quantity place the radical fign , and it will be of the form requir- ed . EXAMPLES . 1. It is required to reduce 3 to the form of the fquare root . Firft 3 × 3 = 32 = 9 ; whence 9 the answer . 2. It is required ...
... furd , and over this new quantity place the radical fign , and it will be of the form requir- ed . EXAMPLES . 1. It is required to reduce 3 to the form of the fquare root . Firft 3 × 3 = 32 = 9 ; whence 9 the answer . 2. It is required ...
Σελίδα 42
... furd , and fet its root before the remaining quantities , with the proper radical fign between them . When the given furd contains no exact power , it is already in its moft fimple terms . EXAMPLES . 1. It is required to reduce 48 to 42 ...
... furd , and fet its root before the remaining quantities , with the proper radical fign between them . When the given furd contains no exact power , it is already in its moft fimple terms . EXAMPLES . 1. It is required to reduce 48 to 42 ...
Σελίδα 44
... furd part be the fame in them all , an- nex it to the fum of the rational parts , with the sign of multiplication , and it will give the total fum required . But if the furd part be not the fame in all the quan- tities , they can only ...
... furd part be the fame in them all , an- nex it to the fum of the rational parts , with the sign of multiplication , and it will give the total fum required . But if the furd part be not the fame in all the quan- tities , they can only ...
Σελίδα 45
... furd , give the difference of the furds required . will But if the quantities have no common furd , they can only be fubtracted by means of the fign E 2 EXAMPLES . 1. It is required to find the difference SURDS .
... furd , give the difference of the furds required . will But if the quantities have no common furd , they can only be fubtracted by means of the fign E 2 EXAMPLES . 1. It is required to find the difference SURDS .
Σελίδα 50
... furd A + B , or A - B , may be found thus : take A2-2 ) = D ; then √ ( A + Bi = √A + D + v A - D 2 > and ( AB ) = √ = A + D - 2 A - D 2 Thus the fquare root of 8 + 27 = 1 + √7 , and the fquare root of 3 — √8√2—1 : but for the cube ...
... furd A + B , or A - B , may be found thus : take A2-2 ) = D ; then √ ( A + Bi = √A + D + v A - D 2 > and ( AB ) = √ = A + D - 2 A - D 2 Thus the fquare root of 8 + 27 = 1 + √7 , and the fquare root of 3 — √8√2—1 : but for the cube ...
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An Introduction to Algebra; With Notes and Observations: Designed for the ... John Bonnycastle Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
Συχνά εμφανιζόμενοι όροι και φράσεις
affigned affirmative alſo anſwering arife becauſe co-efficient common denominator completing the square cube numbers cube root cubic equation decimal Diophantus dividend divifor equal EXAMPLES fame fecond term fide fimple equation fince find the fum find the value find three numbers find two numbers find x firſt fome fquare numbers fquare root fraction fubftituted fubtracted fum fhall fuppofe furd geometrical feries geometrical progreffion given equation given number greateſt impoffible improper fraction increaſe infinite feries laft term laſt leaft lefs Let the number logarithm moidores moſt multiplied muſt natural numbers negative number of terms number required pofitive PROBLEM propoſed publiſhed quadratic equation queſtion quotient Reduce remainder Required the difference Required the fquare Required the fum Required the product required to find root required RULE ſeries ſhall ſquare ſum sum required surd thefe theſe thofe thoſe unknown quantity uſe Whence whole numbers whoſe
Δημοφιλή αποσπάσματα
Σελίδα 86 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.
Σελίδα 84 - His head weighed as much as his tail and half his body, and his body weighed as much as his head and tail together.
Σελίδα 85 - A hare is 50 leaps before a greyhound, and takes 4 leaps to- the greyhound's 3, but 2 of the greyhound's leaps are as much as 3 of the hare's ; how many leaps must the greyhound take to catch the hare ? Ans. 300.
Σελίδα 85 - ... and the chaise to twice the price of the horse and harness ; what did he give for each ? Ans. 13/.
Σελίδα 34 - Note. The whole number of terms will be one more than the index of the given power ; and when both terms of the root are +, all the terms of the power will be...
Σελίδα 198 - Multiply the log. thus found, by the index of the power proposed. -Find the number answering to the product, and it will be the power required. Note. In multiplying a logarithm with a negative index, by an affirmative number, the product will be negative. But what is to be carried from the decimal part of the logarithm, will always be affirmative.
Σελίδα 84 - A post is I in the mud, ~ in the water, and 10 feet above the water : what is its whole length ? Ans. 24 feet.