A Synopsis of the Principal Formulae and Results of Pure MathematicsJ. & J.J. Deighton, 1829 - 358 σελίδες |
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Σελίδα 73
... modulus 2a , or 2a + 1 , or 4a , as one of the 0 ° , 12 , 2o , 3o , & c . a2 . squares Table of the possible Forms of square Numbers for every Modulus from 3 to 20 . 3n 3n + 1 14n 4n 4n + 1 14n + 1 +2 +4 +7 +8 +9 +11 5n 5n + 1 15n 15n + ...
... modulus 2a , or 2a + 1 , or 4a , as one of the 0 ° , 12 , 2o , 3o , & c . a2 . squares Table of the possible Forms of square Numbers for every Modulus from 3 to 20 . 3n 3n + 1 14n 4n 4n + 1 14n + 1 +2 +4 +7 +8 +9 +11 5n 5n + 1 15n 15n + ...
Σελίδα 74
Charles Brooke. Table of the Remainders of Squares to every Modulus , not containing a square Factor , from 2 to 51 . ( B. p . 104. ) Mod . ( a ) 22 3 3 CO 2 1 1 5 14 6 134 7 124 10 145 6 9 11 134 59 13 1 3 4 9 10 12 14 124 7 8 9 11 15 ...
Charles Brooke. Table of the Remainders of Squares to every Modulus , not containing a square Factor , from 2 to 51 . ( B. p . 104. ) Mod . ( a ) 22 3 3 CO 2 1 1 5 14 6 134 7 124 10 145 6 9 11 134 59 13 1 3 4 9 10 12 14 124 7 8 9 11 15 ...
Σελίδα 75
... modulus is always impossible . ( B. 42-52 . ) Conditions of the possibility of the equation x2 — a y2 = b x2 , in which a and b are positive integers , and a < b . Let a number c be found such that c > b , and c2— a ÷ b ; C and let the ...
... modulus is always impossible . ( B. 42-52 . ) Conditions of the possibility of the equation x2 — a y2 = b x2 , in which a and b are positive integers , and a < b . Let a number c be found such that c > b , and c2— a ÷ b ; C and let the ...
Σελίδα 76
Charles Brooke. amongst the remainders of squares to the modulus a , the equation may be possible . If this condition is fulfilled , and the same relation exists between the remainders of a , and c , when divided by b , and those of a ...
Charles Brooke. amongst the remainders of squares to the modulus a , the equation may be possible . If this condition is fulfilled , and the same relation exists between the remainders of a , and c , when divided by b , and those of a ...
Σελίδα 86
... modulus a , as the cubes 03 , 13 , 23 , & c . ( a − 1 ) 3 . a3a to modulus 6 . The equations xx3 ± y3 = x3 , x3 y3 == and generally x3 ± y3 = 2x3 , mx3 ± nay3 = x3 , in which m is a number of an impossible form to modulus a , and n ...
... modulus a , as the cubes 03 , 13 , 23 , & c . ( a − 1 ) 3 . a3a to modulus 6 . The equations xx3 ± y3 = x3 , x3 y3 == and generally x3 ± y3 = 2x3 , mx3 ± nay3 = x3 , in which m is a number of an impossible form to modulus a , and n ...
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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...