This is my first thought:
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Draw a ‘cutting’ line and place it at one end of the line you want divided.
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Select your cutting line first then select the line you want divided using either shift-click or ctrl-click so that you have both lines selected (the selection order is important!).
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Use the ‘Copy Along Path’ tool to copy your cutting line as many times as you need.
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Then use the ‘node edit’ tool to place nodes at the intersections of you main line and your cutting lines.
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Lastly, delete your cutting lines.
Hope this helps.