Why must field lines from charge q connect in the Larmor formula derivation?

[albega]

Homework Statement

I need to derive this formula, and I'm basing it upon the following method (this has the diagram which I will be talking about below)
http://isites.harvard.edu/fs/docs/icb.topic1214926.files/Purcell-appendix-B.pdf

The Attempt at a Solution

I'm fine with everything apart from the reasoning that the parallel field lines (from where q is, and where it would be) have to join up in the middle region. The reasoning for this is given as

'A field line such as AB lies on a cone around the x-axis which includes a certain amount of flux from the charge q. If CD makes the same angle θ with the axis, the cone on which it lies includes the same amount of flux. Hence AB and CD must be parts of the same field line, connected by a segment BC.'

I don't see how the cones having equal flux implies the two field lines must be the same and so joined. Could anybody explain this? Thanks!

 

[albega]

Anyone please? It won't take too long to read the derivation!

 

[haruspex]

I've tried a couple of times to view the PDF, but it comes up blank on my system. Maybe others have the same problem.