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 22.
Σελίδα 158
... centre , r the radius ; then the equation to the circle is ( x a ) 2 + ( y − ẞ ) 2 + 2 ( x − a ) ( y − ẞ ) . cos x , y = r2 . - - - The equation between rectangular co - ordinates is ( x − a ) 2 + ( y — ß ) 2 = r2 . ( 1 ) If the ...
... centre , r the radius ; then the equation to the circle is ( x a ) 2 + ( y − ẞ ) 2 + 2 ( x − a ) ( y − ẞ ) . cos x , y = r2 . - - - The equation between rectangular co - ordinates is ( x − a ) 2 + ( y — ß ) 2 = r2 . ( 1 ) If the ...
Σελίδα 163
... centre and axes is b2 y2 = = a2 ( a2 — x2 ) ; or x2 y2 a2 + -- 1 . b2 AS . Sa BC2 = AC . SL . - The intersection of an ellipse with the straight line , y = ax + ß , may be determined from the equation y2- 2623 a2 a2 + bey + b2 ( ẞ2 — a2 ...
... centre and axes is b2 y2 = = a2 ( a2 — x2 ) ; or x2 y2 a2 + -- 1 . b2 AS . Sa BC2 = AC . SL . - The intersection of an ellipse with the straight line , y = ax + ß , may be determined from the equation y2- 2623 a2 a2 + bey + b2 ( ẞ2 — a2 ...
Σελίδα 165
... centre is the pole , the equation is 15 1 e u = a . 1- ( e cos 0 ) 2 The angle SPT = HPt . If SY , HZ be drawn perpendicular to the tangent , the points Y , Z are always in the circumference of a circle described on A a . PI = AC . SY ...
... centre is the pole , the equation is 15 1 e u = a . 1- ( e cos 0 ) 2 The angle SPT = HPt . If SY , HZ be drawn perpendicular to the tangent , the points Y , Z are always in the circumference of a circle described on A a . PI = AC . SY ...
Σελίδα 167
... centre , the equation is b2 y2 = a2 ( x2 — a2 ) ; a2 ) ; or x2 y2 - 1 . a2 b2 The lines in the above figure are analogous to those in the ellipse , on which the same letters are placed . The equation to the equilateral hyperbola is x2 ...
... centre , the equation is b2 y2 = a2 ( x2 — a2 ) ; a2 ) ; or x2 y2 - 1 . a2 b2 The lines in the above figure are analogous to those in the ellipse , on which the same letters are placed . The equation to the equilateral hyperbola is x2 ...
Σελίδα 169
... centre is the pole , the equation is - u = a . e2 . 1 1- ( e cos 0 ) 2 LHPT 4 SPT . = If SY and HZ be drawn perpendicular to PT , the locus of the points Y and Z is a circle described on Aa . PI = Pi = AC . SY.HZ BC2 . = ( H. C. S. 195 ...
... centre is the pole , the equation is - u = a . e2 . 1 1- ( e cos 0 ) 2 LHPT 4 SPT . = If SY and HZ be drawn perpendicular to PT , the locus of the points Y and Z is a circle described on Aa . PI = Pi = AC . SY.HZ BC2 . = ( H. C. S. 195 ...
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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...