First Lessons in Algebra: Being an Easy Introduction to that Science, Designed for the Use of Academies and Common SchoolsJenks & Palmer, 1847 - 252 σελίδες |
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Σελίδα 11
... . 212 Of Fractions ... • 213 Of Surds .... 215 CHAP . XI . EQUATIONS OF THE SECOND DEGREE . SECT . I. Pure Equations Rule for solving Pure Equations 216 218 II . Affected Equations .. 223 Common Method of Completing CONTENTS . 11.
... . 212 Of Fractions ... • 213 Of Surds .... 215 CHAP . XI . EQUATIONS OF THE SECOND DEGREE . SECT . I. Pure Equations Rule for solving Pure Equations 216 218 II . Affected Equations .. 223 Common Method of Completing CONTENTS . 11.
Σελίδα 12
... Completing the Square .... 226 Rule for solving Affected Equations .... Another Way to Complete the Square ... 229 230 III . Questions producing Affected Equations ...... 234 To find the Second Power of a Surd .... 238 CHAP . XII ...
... Completing the Square .... 226 Rule for solving Affected Equations .... Another Way to Complete the Square ... 229 230 III . Questions producing Affected Equations ...... 234 To find the Second Power of a Surd .... 238 CHAP . XII ...
Σελίδα 98
... complete : and a - ( a + b ) 2 = a2 + 7 a® b + 21 a5 b2 + 35 a4 b3 + 35 a3 b4 + 21 a2 b5 + 7 a bε + 67 . - ( a - b ) 7 = a7 — 7 a b + 21 a5 b2 — 35 a4 b3 + 35 a3 b4 — 21 a2 b5 +7 a b¤ — b7 . It will be observed , that the coefficients ...
... complete : and a - ( a + b ) 2 = a2 + 7 a® b + 21 a5 b2 + 35 a4 b3 + 35 a3 b4 + 21 a2 b5 + 7 a bε + 67 . - ( a - b ) 7 = a7 — 7 a b + 21 a5 b2 — 35 a4 b3 + 35 a3 b4 — 21 a2 b5 +7 a b¤ — b7 . It will be observed , that the coefficients ...
Σελίδα 100
... the required power will be complete . m2 = a2 + 2 a b + b2 . n2 = c2 + 2 c d + d2 . ANS . a2 + 2 a b + b2 + 2 a c + 2 b c + 2 ad + 2bd + c2 + 2 c d + d2 . In this way , any quantity whatever can be raised 100 FIRST LESSONS IN ALGEBRA .
... the required power will be complete . m2 = a2 + 2 a b + b2 . n2 = c2 + 2 c d + d2 . ANS . a2 + 2 a b + b2 + 2 a c + 2 b c + 2 ad + 2bd + c2 + 2 c d + d2 . In this way , any quantity whatever can be raised 100 FIRST LESSONS IN ALGEBRA .
Σελίδα 197
... complete power , that is , if its root cannot be ex- actly found , it is called a Surd , or Irrational Quantity . Thus , 35 , 3x2 , 5 / a3 , & c . , are surd quantities . 2 Express the roots of the following quantities by means of the ...
... complete power , that is , if its root cannot be ex- actly found , it is called a Surd , or Irrational Quantity . Thus , 35 , 3x2 , 5 / a3 , & c . , are surd quantities . 2 Express the roots of the following quantities by means of the ...
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First Lessons in Algebra: Being an Easy Introduction to That Science ... Ebenezer Bailey Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
First Lessons in Algebra: Being an Easy Introduction to That Science ... Ebenezer Bailey Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
a b c a b x A's share a² b² a² b³ acres added Algebra algebraic quantity amount answer asked the age barrels binomial bought bushels cents coefficient common denominator completing the square compound quantity contain cost cube root debt difference Divide 18 dividend divisor equal exponent expressed Extract the square farmer fourth power gain gallons gentleman give given quantity horse improper fraction less Let x A's letter miles an hour negative quantity obtain oranges peaches positive quantity quan question quotient Reduce remainder Required the number Required the square rods root of a² second power second term SECTION shillings Simple Quantities sold square root subtracted third power tion tity transposition twice unknown quantity worth x y z yards
Δημοφιλή αποσπάσματα
Σελίδα 68 - 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 120 - A man driving his geese to market, was met by another, who said, good morrow, master, with your hundred geese ; says he, I have not a hundred ; but if I had half as many more as I now have, and two geese and a half, I should have a hundred ; how many had he ? /C s"~
Σελίδα 68 - Then divide the first term of the remainder by the first term of the divisor...
Σελίδα 242 - Several gentlemen made an excursion, each taking the same sum of money. Each had as many servants attending him as there were gentlemen ; the number of dollars which each had was double the number of all the servants, and the whole sum of money taken out was 3456 dollars.
Σελίδα 235 - A square court yard has a rectangular gravel walk round it. The side of the court wants 2 yards of being 6 times the breadth of the gravel walk ; and the number of square yards in the walk exceeds the number of yards in the periphery of the court by 164. Required the area of the court ? All equations of the second degree may be reduced to one of the following forms.
Σελίδα 136 - A gentleman invested -J of his property in a canal. When he sold out, he lost f of the sum invested, receiving only $1,446. What was the value of his property when he began ? Ans., $11,568. 29. A gentleman leaves $315 to be divided among four servants in the following manner : B is to receive as much as A, and |- as much more; C is to receive as much as A and B, and ^ as much more ; D is to receive as much as the other three, and £ as much more. What is the share of each ? price of the chaise, the...
Σελίδα 164 - 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 129 - There is a fish whose head weighs 9 lb. his tail weighs as much as his head and half his body, and his body weighs as much as his head and tail both.
Σελίδα 123 - The distance from A to D is 34 miles. The distance from A to B is to the distance .from C to D as 2 to 3. And ± of the distance from A to B, added to half the distance from C to D, is three times the distance from B to C. What are the respective distances ? Ans.
Σελίδα 220 - Each man received one third as many shillings as there were persons relieved ; and each woman received twice as many shillings as there were women more than men. The men received all together 18s.