Qián gua: mirrored, like a mountain mirrored in a lake. The same mountain, but upside down, underwater. It might be in the realm of the gods, or like a shadow, or complementary. What was high is now deep, what was down at the foot is now undeep, close to the surface.
Qián yao, the mirrored line.
What was high on the flanks is now deep in the lake, what was at the bottom is now at the surface of the lake.
潛 [qián] to hide, to conceal, to dive, hidden, secret, latent. From 水 ‘water’ and 朁 zǎn (旡旡 over 日)
Zhi gua, related hexagram (one or more lines changed): “the sea in which the primary hexagram swims” (Karcher).
In old texts, there is no mention of first and last, or first going to second. Both can "be" at the same moment, although they have a different meaning. Zhi is only used for one line at a time, so like here, the related hex of more changing lines, is not really right.
Fan yao or paired line: same line but in related hexagram (eg 44.1 and 1.1): like the other end of a washing line across a street.
They carry the same load of laundry, but seen from the window on the opposite side of the street.The laundry has now an opposed sequence. What was up front is now in the distance.
There are no texts before the 11th century where the concept of changing lines is mentioned. Their first appearance is in the writings of Ouyang Xiu (1007-72).
In the 4th century BC, in the Zuo Zhuan, a line of a hexagram is indicated by the hexagram it changes to. Qian zhi dayou is hex.1, line 5, or "Hex.1 its Hex.14". Zhi can mean 'moving to', but probably it means simply 'its', a genitive particle, like qí. In one Zuo Zhuan-story zhi and qi are used alternatively. In the explanation of the oracle they did use the changes in the trigrams though. Water changing to lake etc. (information from Rutt "Zhouyi").
Pang tong gua or bian gua: complemenatry or opposite: all yang lines yin, all yin lines yang: like a negative of a photo. Like hex.1 and 2, or 3 and 50, or 27 and 28.
Same image, but the light is totally different, what was in the dark is now in the light, what was light is now dark.
Ban xiang, half-images, zhen and hui: zhen is ‘given’ or enduring. Hui means regret, has to do with actions and what happens.
Other names or descriptions: inner and outer, lower or upper, coming and going, earlier and later, beginning and ending, growing and dissipating.
Jiao gua, exchanged or interchanged trigrams: trigrams zhen and hui switched.
What was inside goes to outside, what was above is now below. What was a given is now uncertain, what was going out is now coming in.