Parans
Parans at your latitude
A paran is two planets angular at the same moment: one rising as another culminates, and so on. Unlike a line it belongs to a latitude rather than a place, so it holds right around the world at that latitude. It is also the part of the technique that has something to say when no line runs anywhere near you.
Why this works where a map does not
Most of the Earth is nowhere near any of your forty lines, which makes the commonest honest answer an astrocartography map can give about a specific place nothing in particular. Parans are the exception: they apply to a whole band of latitude, so somewhere with no line through it can still have several.
Questions about parans
Asked often enough to answer here.
Two planets angular at the same moment, for example one rising as another crosses the Midheaven. Because the pairing depends on latitude rather than longitude, a paran holds right around the world at that latitude: at 43 degrees north it applies in Boston, Rome and Sapporo alike.
A line is a curve on the map and you are either near it or not. A paran is a band of latitude, so it applies to everywhere at that latitude regardless of longitude. That is why parans can say something about a place where no line runs.
Yes, for the same reason astrocartography does. Parans are built from the angles, which move roughly one degree every four minutes. Without a birth time this page uses the middle of the day and says so, and the latitudes should be treated as approximate.