The Doctrine of Limits with Its Applications: Namely, Conic Sections, the First Three Sections of Newton, the Differential Calculus. A Portion of a Course of University EducationJ. and J.J. Deighton, 1838 - Всего страниц: 172 |
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Стр. xvi
... ratio of two rays R , S is the same as the ratio of two other rays r , s , a number of intermediate rays were interposed in each case , as R ' , R " , R " " & c . , and r ' , r " , " " & c . It was then shown that the ratios of R to R ...
... ratio of two rays R , S is the same as the ratio of two other rays r , s , a number of intermediate rays were interposed in each case , as R ' , R " , R " " & c . , and r ' , r " , " " & c . It was then shown that the ratios of R to R ...
Стр. xvii
... ratios of equality , when the number of inter- mediate magnitudes R ' , R " , R " " & c . becomes indefinitely great : and therefore , compounding these ratios , the ratio of R to S is a ratio of equality , whatever be R and S ; which ...
... ratios of equality , when the number of inter- mediate magnitudes R ' , R " , R " " & c . becomes indefinitely great : and therefore , compounding these ratios , the ratio of R to S is a ratio of equality , whatever be R and S ; which ...
Стр. xix
... ratio of an evanescent space to an evanescent time ; but upon the axiom , that if a body move for a finite time , the velocity increasing by steps instead of increasing continuously , the first kind of motion has the second kind for its ...
... ratio of an evanescent space to an evanescent time ; but upon the axiom , that if a body move for a finite time , the velocity increasing by steps instead of increasing continuously , the first kind of motion has the second kind for its ...
Стр. xx
... and force , according to which they are the limiting ratios of the increments of space and time , and of velocity and time , are not given as defi- nitions , it became necessary to prove them as properties XX PREFACE .
... and force , according to which they are the limiting ratios of the increments of space and time , and of velocity and time , are not given as defi- nitions , it became necessary to prove them as properties XX PREFACE .
Стр. 6
... ratio to the ordinate of the semi - circle described on the axis major . This semi - circle is called the circular projection of the semi - ellipse : the point p is the circular projection of the point b , and the line Cp of the line CP ...
... ratio to the ordinate of the semi - circle described on the axis major . This semi - circle is called the circular projection of the semi - ellipse : the point p is the circular projection of the point b , and the line Cp of the line CP ...
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Часто встречающиеся слова и выражения
abscissa angular velocity Axiom axis body moves Book Cambridge centre of force chord of curvature circle circular projection conic section conjugate conjugate hyperbola cos² cotan CP² curve curvilinear cylinder d³y diameter differential coefficient ditto Doctrine of Limits dy dx ellipse equation equiangular spiral Euclid finite force tending function Hence HISTORY hyperbola increment indefinitely infinitely King's College latus rectum Lemma magnitude motion MP² ordinate parabola parallel parallelograms PARKER perpendicular polygon portions Prop propositions PUBLISHED BY JOHN quantity QV² radius ratio rectangle similar triangles sin² SP² space described straight line subtense tan² tangent Tate's Psalms U₁ ultimately equal University of Cambridge whence WILLIAM WHEWELL Y₁
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