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Once the operation of the semi-diameters of the spherical order is completed, one must now apply labor to the remaining columns of the same order, so that the entire remainder may be finished. This will be done by the following method.

First, it was already said above that there must be as many quantities of columns in each order as there are numbers included in the Brachia Arms. I do not grow weary of repeating this here, so that it may be observed attentively. Then, to write the columns of the right semicircle first, take that first Root of your operation sitting before the middle channel, here marked with the letter P. Compare it with the first number of the right Branch marked A, and write every difference found in the first channel under the first column likewise marked with the letter A. Second, take the following number of the same Branch marked with the letter B with the same first Root. Whatever is elicited from this comparison, depict it in the same first channel, under the column inscribed with the same letter B. Then, to acquire the number for the first channel of the third column C, distribute that same first Root with the third number of that Branch. Again, you will line their difference in its proper place, as I said. Finally, seek the difference for the fourth Root and the fourth number of the Branch marked D. When the comparison is finished, put it in that first channel under the same letter D. In such a manner, the first order of each column is completed.

Second, you will then complete the order or small channel of the same right semicircle just as you did in the first: namely, you will compare your Root with the numbers of the same right Branch. They ought to be placed in their own proper columns as demonstrated alphabetically. In this alone, however, it differs: where above you used the first Root marked with the letter P to elicit the differences of the numbers, then for this second order, you should take the second Root inscribed with the letter Q.

In the same way, consider that the third order, as well as the fourth, fifth, and all the remaining orders or small channels of the right semicircle, are to be perfected with no dissimilar study. For you will take all the Roots that follow, one after another, to elicit the comparison: namely, the third for the third, the fourth for the fourth, and so on for the rest. The channels demonstrate them correctly made and inscribed with the Roots and applied to the orders. All of these are always to be compared with the numbers of that same Branch.

However, we call all the Roots that are reversed and marked with a +, which you find in the first work, "conversas" reversed, noting them now. For where in the combination of straight Roots with the numbers of the Branches, the operation is said to begin for all signs from number A, then to B, thirdly to C, and finally to D: to elicit the differences of these reversed ones, then in the Roots marked with a +, you will first compare your root at D. Then you should confer with the right side at C. Afterward, you will compare the number marked B, and fourthly you will finish the work at A. This is to be understood in the comparison of both the right and the left Branch.

It must be noted, however, that although in the reversed Roots, as was said, the numbers of the Branches are compared with the Roots in reverse, you should not...

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...take care to attach the reversed differences in that semicircle. Although this whole difference is thus taken from that number marked with the letter D, it is nevertheless to be placed not under column D, but under column A. Otherwise, you would be making not a reversed Root, but a straight one.

So that you may more easily establish the ordinary columns to be inscribed, friend, you will take the last Root of the middle channel, which is already stored as the first of the work, as we said. Having compared it with the numbers of the left Branch, you will draw the differences in the columns of the same semicircle in the same form as was said above concerning the right semicircle and Branch. Namely, you should put the comparison of the number marked A under column A, the difference of number B under column B, and so on for the rest. Similarly, here, after one Root has been used, transfer yourself to the following one, so that you may operate with it. Where in the right semicircle you proceed from the first Root of the operation to the second, then to the third and fourth, etc., through your whole work, here it is necessary to reorder the Roots of the middle channel. Namely, after the first one already repeated, which is the last of the same channel, you should come to the second Root of the operation, repeated a little. Then turn yourself to the drawn Root of the work, which in this progression again occupies the place afterward. You will approach the following ones likewise without any defect of looking backward with them, as we taught above. When similarly here in the reversed Roots marked with a +, believe that the beginning must be taken from the number of the Branch inscribed with the letter D, as I previously ordered to be done, as noted in the attached example behind.