<image> Logarithm$$($$born around 250 AD$$)$$ is a great mathematician in the history of Chinese numerals and holds an important place in the history of world mathematics as well. His masterpieces $$《$$The Nine Chapters on the Mathematical Art$$》$$ and $$《$$The Sea Island Mathematical Manual$$》$$ are valuable mathematical heritages of China.
$$(1)$$ One of these books focuses entirely on the measurement of heights and distances, using tools connected by vertical relationships, such as measuring rods and horizontal bars. All problems utilize data obtained from two or more measurements to calculate the height, depth, width, and distance of otherwise unreachable targets. This book was included in the Yongle Encyclopedia, compiled during the reign of Emperor Yongle, and is currently preserved in the library of the University of Cambridge, UK. The title of this book is ______.
$$(2)$$ The first question recorded in the masterpiece mentioned in $$(1)$$ by Liu Hui is: In the diagram shown, to measure the height $$AH$$ of a mountain peak on a sea island, two measuring poles $$BC$$ and $$DE$$, each 3 zhang high, are erected. The distance between the two poles $$BD$$ is 1000 steps, with points $$D$$, $$B$$, and $$H$$ aligned. Retreating 123 steps from point $$B$$ to point $$F$$, with the observer’s eye at ground level observing point $$A$$, points $$A$$, $$C$$, and $$F$$ also align. Retreating 127 steps from point $$D$$ to point $$G$$, with the observer’s eye at ground level observing point $$A$$, points $$A$$, $$E$$, and $$G$$ also align. Calculate the height $$AH$$ in zhang and the distance $$HB$$ in steps $$($$where 1 step$$=6$$ feet, and 1 zhang$$=10$$ feet$$)$$.