A Synopsis of the Principal Formulae and Results of Pure MathematicsJ. & J.J. Deighton, 1829 - 358 σελίδες |
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Αποτελέσματα 1 - 5 από τα 19.
Σελίδα 1
... n is not a positive integer , the signification of a " is conventional , being merely such as to satisfy equation ( 1 ) . - n = aman . am a = n a M - m = 1 . 1 = & = A a2 = √ a TM = ( am ) 2 Definitions and rules Powers and roots 53, 54.
... n is not a positive integer , the signification of a " is conventional , being merely such as to satisfy equation ( 1 ) . - n = aman . am a = n a M - m = 1 . 1 = & = A a2 = √ a TM = ( am ) 2 Definitions and rules Powers and roots 53, 54.
Σελίδα 40
... separate systems of values that satisfy the given equations . If the last remainder is independent of the unknown quan- tities , the equations are incompatible . Further observations , and their application to particular ( Bour 40 ALGEBRA .
... separate systems of values that satisfy the given equations . If the last remainder is independent of the unknown quan- tities , the equations are incompatible . Further observations , and their application to particular ( Bour 40 ALGEBRA .
Σελίδα 53
... values of y and that satisfy the equations A = 0 , B = 0 ; let these be a1 , α , & c . B1 , B. , & c . then a , + B1√ - 1 , a2 + B2 - 1 , & c . are the required roots . - - The series of quantities , -46 , -46 IMPOSSIBLE ROOTS . 53.
... values of y and that satisfy the equations A = 0 , B = 0 ; let these be a1 , α , & c . B1 , B. , & c . then a , + B1√ - 1 , a2 + B2 - 1 , & c . are the required roots . - - The series of quantities , -46 , -46 IMPOSSIBLE ROOTS . 53.
Σελίδα 69
... b , may be any system of values that will satisfy the given equations ( 4 ) . " S „ * am . ” b = 3a , { : } . ( C ) Sm'am " b1 = 0 , { } , ( † ) ; { # [ 1 ] If we have a single equation а INDETERMINATE EQUATIONS OF THE FIRST DEGREE . 69.
... b , may be any system of values that will satisfy the given equations ( 4 ) . " S „ * am . ” b = 3a , { : } . ( C ) Sm'am " b1 = 0 , { } , ( † ) ; { # [ 1 ] If we have a single equation а INDETERMINATE EQUATIONS OF THE FIRST DEGREE . 69.
Σελίδα 75
... satisfy the conditions c1 2 - ab , e - ba ; 2 2 c2 — a b1 , e2 — b1 ÷ a ; the equation is always possible . The equation ax2 + by2 = cx2 , in which a , b , and c are prime to each other , is possible , if the conditions ae2 + b2 ÷ c ...
... satisfy the conditions c1 2 - ab , e - ba ; 2 2 c2 — a b1 , e2 — b1 ÷ a ; the equation is always possible . The equation ax2 + by2 = cx2 , in which a , b , and c are prime to each other , is possible , if the conditions ae2 + b2 ÷ c ...
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Άλλες εκδόσεις - Προβολή όλων
A Synopsis of the Principal Formulae and Results of Pure Mathematics ... Charles Brooke Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
A Synopsis of the Principal Formulae and Results of Pure Mathematics Charles Brooke Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2019 |
Συχνά εμφανιζόμενοι όροι και φράσεις
a-log a.sin a₁ a² a² angle arcs Assume ax² axis ay² B.cos B.sin b₁ Biot Bour c₁ centre circle co-ordinates conjugate diameters const continued fraction converging fraction cosec cosine curve cx² determined differential coefficients e₁ ellipse formula functions G. G. A. Ch given equation hyperbola integral intersection Let the equation log Cot log Sin log Sin Blog logarithmic m₁ method modulus negative obtained parabola perpendicular plane possible root prime number primitive equation quadratic divisor quadratic equation quotients R₁ radius reduced remainders sin x sine solution square straight line substituting subtangent Suppose surface tana tangent ternary divisor ternary form theorem triangle u₁ unknown quantities values vers x₁ y-y₁ y₁ απ
Δημοφιλή αποσπάσματα
Σελίδα 112 - THEOREM. Every section of a sphere, made by a plane, is a circle.
Σελίδα 4 - Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.
Σελίδα 4 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.
Σελίδα 347 - Si, the formula assigned by Thomson to the mineral from Ireland, named " Anhydrous silicate of iron." Now, this slag had evidently been in a position favourable to the absorption of oxygen, namely, the...
Σελίδα 4 - To reduce a fraction to its lowest terms, divide both the numerator and denominator by their greatest common divisor.
Σελίδα 4 - The same quantity may be added to, or subtracted from, both sides of an equation. To...
Σελίδα 343 - The immutability, no less than the symmetry of its notation, (which should ever be guarded with a jealousy commensurate to its vital importance,) facilitates the translation of an expression into common language at any stage of an operation, - disburdens the memory of all the load of the previous steps, - and at the same time, affords it a considerable assistance in retaining the results.
Σελίδα 46 - These criteria were derived by a new transformation, namely the one which yields an equation whose roots are the squares of the differences of the roots of the given...
Σελίδα 161 - Straight line and circle. A straight line cannot cut a circle in more than two points. In fact, an unlimited straight line may (i) cut a circle in two points, eg AB or CD in fig.
Σελίδα 2 - Tiie square root of a quantity cannot be partly rational and partly a quadratic surd. If possible, let...