The first complete diagramming system was developed by S. W. Clark in A Practical Grammar: in which Words, Phrases, and Sentences are Classified According to their Offices, and their Relation to Each Other. Illustrated by a Complete System of Diagrams (1847). His system
I have scanned the first part of Clark's book (pp. 18-36), which includes an overview of the system, illustrative examples for various sentence types, and practice exercises (remarkable only for their abundant citation of bad poetry). I've made some effort to preserve the format of the original, although the original pagination and a few other features are ignored, and pictures appear larger than in the original for the sake of clarity. I've silently corrected a few obvious printer's errors, but the punctuation is original, and not always in keeping with modern practice. The scans here come from the 6th edition (1853). Some pages in my copy are foxed, hence the spotting in the images.
Note: Clark's terminology is antiquated and may confuse a reader familiar with the terms' modern meanings. In particular, note that an auxiliary sentence is a subordinate clause, and etymology does not just mean the origin of words but also includes morphology, that is, their inflections, etc.