Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 6-10 із 32
Сторінка 132
... called the Witch . Putting AC = a , AN x , PN = y , equation to the curve = x y2 = 4a2 ( 2 a − x ) . we find as the This curve is given by Donna Maria Agnesi in her In- stituzioni Analitiche , Art . 238 , and is called by her the ...
... called the Witch . Putting AC = a , AN x , PN = y , equation to the curve = x y2 = 4a2 ( 2 a − x ) . we find as the This curve is given by Donna Maria Agnesi in her In- stituzioni Analitiche , Art . 238 , and is called by her the ...
Сторінка 138
... called Geometria promota in VII de Cycloide libris . ( 9 ) The Companion to the Cycloid . If the ordinate QN ( fig . 20 ) of a semicircle be produced till it be equal to the arc CQ , its extremity will lie in a curve which is called the ...
... called Geometria promota in VII de Cycloide libris . ( 9 ) The Companion to the Cycloid . If the ordinate QN ( fig . 20 ) of a semicircle be produced till it be equal to the arc CQ , its extremity will lie in a curve which is called the ...
Сторінка 139
... called an Epitrochoid or a Hypotrochoid , according as the curve rolls on the exterior or interior of the fixed circle . Let O ( fig . 22 ) be the centre of the fixed circle , C that of the generating circle , a , b their radii . Let A ...
... called an Epitrochoid or a Hypotrochoid , according as the curve rolls on the exterior or interior of the fixed circle . Let O ( fig . 22 ) be the centre of the fixed circle , C that of the generating circle , a , b their radii . Let A ...
Сторінка 140
... called the Cardioid in common with the circle it possesses the property that all lines drawn through its pole and bounded both ways by the curve are of equal length . In the equations to the hypotrochoid , if we make h = b and b = a we ...
... called the Cardioid in common with the circle it possesses the property that all lines drawn through its pole and bounded both ways by the curve are of equal length . In the equations to the hypotrochoid , if we make h = b and b = a we ...
Сторінка 143
... called it spira mirabilis , and he was pleased to see in it a type of constancy amid changes and in adversity , and a symbol of the resurrection . As a specimen of the fanciful light in which he viewed the properties of this curve , I ...
... called it spira mirabilis , and he was pleased to see in it a type of constancy amid changes and in adversity , and a symbol of the resurrection . As a specimen of the fanciful light in which he viewed the properties of this curve , I ...
Інші видання - Показати все
Загальні терміни та фрази
a² b2 a²x² angle arbitrary constant assume asymptote becomes branches C₁ Cambridge circle co-ordinates condition Crelle's Journal curvature curve cycloid determine differential coefficients differential equation dx dx dx dy dx dx² dy dx dy dy dy dy dz dz dz eliminate ellipse equal Euler factor formula fraction function Geometry gives Hence hypocycloid infinite intersection John Bernoulli Let the equation lines of curvature locus logarithmic logarithmic spiral Multiply negative origin parabola perpendicular radius SECT singular points singular solution spiral Substituting subtangent surface tangent plane theorem triangle University of Cambridge vanish whence x²)³