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But whatever the number of the straight ray from the term may be, let it be eight, as has been said, when the Root is reversed; nevertheless, the differences of the numbers appear as if they germinated from their own places in the semicircles and types of the semi-diameters. And if in the following figure you should see that the first Root was marked with the number 1, then the Root would begin the comparison from number 1. Then I would elicit the difference from them, but you shall not inscribe it in the channel marked with the same letter 1. Instead, place it in the first one, even if it is marked with the letter A. For if we changed the two orders of the cells—namely, of the cells and of the channels—it would be the same as if a straight Root had existed. This is to be understood in the upper semi-diameters of the semicircles as well.
The lower semi-diameters of the semicircles (as indicated above) are to be established with the interior numbers of the same Rhomboid. However, you will not compare these with the first Root constrained above, but with the following one—namely, with the second. Here likewise the lengthening will produce the same form in which you operated in the upper semi-diameter: namely, by passing from 'a' to 'b'. Then to 'c' and 'd', as the alphabetical order teaches you. And here in like form it must be noted whether the Root is straight or reversed, namely the figure L; for if it were noted with a 1, then, as was said above concerning the making of the upper semi-diameters, one must operate here also: namely, by taking the beginning from the term of the Straight Root.
Finally, I have noted three things here. First, that if you should find cells here that are lacking to complete all the circles of the lower semi-diameter, then, as was said above concerning the upper semi-diameter, it is to be understood here also: namely, that in such a case you should recur to the first cell, unless one cell had not remained over in making the upper semi-diameter. (For then those would first have to be taken in the same form as was said above concerning the other semi-diameters). Then, if it is necessary, you should recur to the first interior cell. And this is the cause why I said above that both the upper and lower circles of the semi-diameters are coherent with each other, and of the same affinity; and according to their own plenty or abundance, they mutually grant and receive numbers.
Second, that these two Roots, which serve for comparing the primary numbers of the Rhomboids, are always named with more dignity than all the rest that run together into the orbit—as if the orbit were flowing down in the left part, whether straight or reversed. Because its power original: "valitas" surpasses all other numbers in worth, they therefore always occupy the first place in comparison.
Third, it must be noted that the differences of the interior numbers of the Rhomboid elicited according to the given teachings are to be placed in the lower semi-diameters of the semicircles.
...of the semicircles by this rule: You shall insert the first in the first channel of the same semi-diameter, starting from the lower part. Put the second in the second one near it. Place the third in the third, the fourth in the fourth, and so on in the others, as the alphabetical letters show in the attached example.
At the top left is a diamond-shaped grid titled "Rhomboides sinistra" (Left Rhomboid). It is labeled with "Angulus superior" (Upper Angle) and "Angulus inferior" (Lower Angle). The grid cells contain capital letters A through H, with lowercase letters (ah, bi, c, d, e, f) nested within certain cells. Additional labels around the diamond include "Cellulae exteriores" (Exterior cells), "Angulus interior" (Interior angle), and "Angulus exterior" (Exterior angle). A curved arc below the diamond is labeled "Brancia sinistra" (Left Branch) and contains the letters D, C, B, A.
At the top right is a mirrored diamond-shaped grid titled "Rhomboides dextra" (Right Rhomboid), featuring similar labels for the Angles and Cells. The arc below it is titled "Brancia dextra" (Right Branch) and contains the letters A, B, C, D. Two letters "R" are positioned between the rhomboids.
The lower half of the page contains two large semicircular diagrams labeled vertically as "Semicirculus sinister" (Left Semicircle) and "Semicirculus dexter" (Right Semicircle). Each consists of concentric arcs labeled A through I. Radial lines divide the semicircles into nine numbered segments (1 through 9) at the base. Marginal annotations "mn" and "lu" appear on the outer edges of the semicircles.