下来/下去
xià lái / xià qù
下来 keeps it in your hand; 下去 lets it run on
The picture Water running downhill. Catch it in your hands and that is 下来; let it pass you and keep flowing and that is 下去.
Where the picture shows up in 下来/下去
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down toward me
你从楼上下来一下。
nǐ cóng lóushàng xià lái yí xià
Come down from upstairs for a second.
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down away from me
我先下去等你。
wǒ xiān xià qù děng nǐ
I'll go down first and wait for you.
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caught and kept
请把地址记下来。
qǐng bǎ dìzhǐ jì xià lái
Please take down the address.
The 下来 in 记下来 is not about downward. It is about holding something so it cannot flow away.
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settling to a stop
车突然停下来了。
chē tūrán tíng xià lái le
The car suddenly came to a stop.
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flowing on
别停，继续说下去。
bié tíng, jìxù shuō xià qù
Don't stop, keep talking.