Notes

Excerpts

• Notes

  In reading these equations it must be noted that a bracket is used in mathematical symbolism to mean that the operations within it are to be performed first. Thus $(1 + 3) + 2$ directs us first to add $3$ to $1$, and then to add $2$ to the result; and $1 + (3 + 2)$ directs us first to add $2$ to $3$, and then to add the result to $1$.

• Notes

  We perform first the operations in brackets and obtain 2 × 7 = 6 + 8 which is obviously true.

• Notes

  This fundamental ratio $\dfrac{SP}{PN}$ is called the eccentricity of the curve.

• Notes

  An ellipse with small eccentricity is very nearly a circle, and an ellipse of eccentricity only slightly less than unity is a long flat oval.

• Notes

  But it is possible for a series with terms partly positive and partly negative to be convergent, although the corresponding series with all its terms positive is divergent.

• Notes

  Such convergent series, which are not absolutely convergent, are much more difficult to deal with than absolutely convergent series.

Equations

• This equation is in Conic Sections (Conic Sections)

Problems

No exercises in this chapter.