Illustrated Commentary on Nine Chapters, Vol. 1

...if the tube is empty, then determine the length of the tube to be the altitude-ratio, and use the tube's diameter as the base-ratio. The number for the sun's distance from the person is the large altitude. The base of the large altitude is the sun's diameter. Although the shape of the heavens is like an arch, the sun can still be measured, so how much more so for the height of Mount Tai or the width of the rivers and seas? I, Hui, believe that the historical records of the present day merely list the objects of heaven and earth. To examine and discuss their numbers and record them in the annals is to manifest the beauty of the world's techniques. I have thus created the Double Difference and added a commentary to probe the intentions of the ancients. It is appended below the chapter on Base and Altitude gougu. For measuring heights, use double gnomons; for measuring depths, use successive squares A geometric tool for surveying.. For isolated objects, use three-fold observations; for distant objects, use four-fold observations. Touch the categories and extend them, and then even that which is hidden, distant, bizarre, or obscured will have nothing it cannot enter. May the learned gentlemen of wide learning examine this in detail.