Elements of Algebra. For the Use of Students in UniversitiesWilliam Creech, and sold, 1796 - 311 pages |
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Page 105
... positive quantity may be either pofitive or negative , according to the most extenfive use of the figns , every quadratic equation will have two roots , except fuch of the third form , whofe roots become im- poffible 0 of ( 105 )
... positive quantity may be either pofitive or negative , according to the most extenfive use of the figns , every quadratic equation will have two roots , except fuch of the third form , whofe roots become im- poffible 0 of ( 105 )
Page 106
William Trail. of the third form , whofe roots become im- poffible . 2. It is obvious that , in the two first forms , one of the roots must be positive , and the other negative . 3 . In the third form , if a2 , or the square 4 of half of ...
William Trail. of the third form , whofe roots become im- poffible . 2. It is obvious that , in the two first forms , one of the roots must be positive , and the other negative . 3 . In the third form , if a2 , or the square 4 of half of ...
Page 112
... the fquare of half the given fum of the num- bers fought . This limitation can easily be fhewn from other principles ; for , the great- eft poffible product of two parts , into which any any number may be divided , is when each of ( 112 )
... the fquare of half the given fum of the num- bers fought . This limitation can easily be fhewn from other principles ; for , the great- eft poffible product of two parts , into which any any number may be divided , is when each of ( 112 )
Page 116
... poffible . If the fquare be completed , and the roots extract- 3a + b = √3a + b2 — 8a2 ed , they become - and 39 + b 4 4 -x = √3a + b2 Z = 3a + b2 — 8a2 . cafe z is the leaft of the three 4 But in this . terms , and a is great- 2 er ...
... poffible . If the fquare be completed , and the roots extract- 3a + b = √3a + b2 — 8a2 ed , they become - and 39 + b 4 4 -x = √3a + b2 Z = 3a + b2 — 8a2 . cafe z is the leaft of the three 4 But in this . terms , and a is great- 2 er ...
Page 117
... poffible 3a- only when is not lefs than 2 , that , 4 is , when a2 + b2 is not lefs than 6ab , or when a - b is not lefs than 2 ab . When the roots are poffible , & may be either great- ≈ er or less than 3a - b > and hence each root 4 ...
... poffible 3a- only when is not lefs than 2 , that , 4 is , when a2 + b2 is not lefs than 6ab , or when a - b is not lefs than 2 ab . When the roots are poffible , & may be either great- ≈ er or less than 3a - b > and hence each root 4 ...
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Elements of Algebra. for the Use of Students in Universities. Third Edition ... William Trail No preview available - 2018 |
Elements of Algebra. for the Use of Students in Universities William Trail No preview available - 2018 |
Common terms and phrases
abfolute term affumed alfo algebra algebraical quantities alſo anſwer arifing cafe called Chap coefficient cofine conftruction continued fraction correfponding cubic equation curve deduced denominator denote dimenfions divided dividend divifible divifion divifor diviſible eaſily equa equal example exponents expreffed expreffion faid fecond term feries fides fimple equations fince firft term firſt folution fome fquare root fraction ftraight line fubftituted fubtracted fuch fuppofed furds geometrical given equation greateſt hence impoffible inferted integer intereft interfection itſelf laft laſt lefs leſs logarithms meaſure moſt muft multiplied muſt neceffary negative notation number of terms obferved odd number phyfical poffible pofitive poſitive powers preceding Prob problem Prop propofition proportional equation quadratic quadratic equation quan queftion quotient radical fign reaſoning refolved refult remainder repreſent rule SCHOLIUM ſign ſquare thefe theorem theſe thofe thoſe tion tities Tranfp unknown quantity uſed