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Left Rhomboid

Right Rhomboid

Two symmetrical diagrams composed of numbered grids in a rhombic or semi-circular arrangement. The left diagram is labeled "Rhomboides sinistra" and the right "Rhomboides dextera". Centered between them is the symbol "Rx" followed by the number "16" and a small cross. Various letters (A, B, C, D) and numbers (1, 3, 4, 6, 7, 10, 12, 16, 18, 27, 44) are placed along the curved outer perimeters of the shapes.

After the composition of the Branches, it is necessary to turn your attention to the spherical orbit. Before it is decorated with numbers, it must first be divided into various parts, as the logic of your inquiry requires. Follow the numbers and quantity of numbers we have drawn in the Branches, as was already said before. But let us come to the numbers to be placed in the semicircles of the Spherical Orbit, making a beginning from the semi-diameters of the same figure, which are the first to be drawn.

First, however, it must be known that the upper semi-diameters, as well as the lower ones of the semicircles, are coherent with each other, and belong to the same "Affinity of Fate" (so to speak). Thus, they mutually grant and receive from themselves their own numbers, whether in poverty or abundance, described for their construction. The numbers necessary for their making are, for the upper semi-diameter, all the interior cells of that Rhomboid: except only for the numbers already used for the making of the Branches. For the lower semi-diameter, however, all the interior ones, with none excepted, are joined in the interior area of that Rhomboid.

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You shall therefore write the upper semi-diameter, both the right and the left of the semicircle, thus: Take the number of the first cell of that Rhomboid marked with the letter A, and you will compare it with the first Root of your gnomon pointer or indicator placed at the beginning of the middle channel. Store the difference arising from them in the first channel of the same part, or semicircle, binding the same with the letter A. Then, by comparing the same Root with the number of the second cell marked B, carefully note it in the following channel of the same semicircle marked with the same letter B. Likewise, you will compare the third number in the third cell of the Rhomboid depicted with the letter C with that same first Root, and you will store the difference in the third channel of the Semicircle that follows. Operate thus in the remaining cells, always seeking the difference from their numbers with the same Root until you come to the last cell of the same Rhomboid which constitutes the lower Angle. Then, if it is necessary, add the exterior numbers of the Angle to the ends. If after their difference you recognize that other differences are necessary for the channels of your spherical figure, return to the first cell of the same Rhomboid already drawn above the first time; then to the following ones, which having gone out, you will take care to survey.

Nevertheless, before you return to the first cell, if various small channels should require it, it must be carefully sought: whether any cell from the interior cells of the Rhomboid ought not additionally to be used in the lower semi-diameter. You will easily recognize this if you observe whether these numbers exceed all the quantity of the small channels of the spherical orbit. Then, before you return to the first cell, after the exterior numbers of the angle are completed, you should turn yourself to these interior numbers not yet mentioned. Then, if it is necessary, return to the first cell.

But so that you can safely recognize which interior numbers are to be taken by you since many exist there, I have directed these interior cells of the writing in the following diagram with lowercase letters of the alphabet. From the first of them marked 'a', you should begin to count the small channels of your spherical orbit, proceeding according to the alphabetical order up to this quantity of small channels. Then you will recognize which ones are to be taken by you, so that they may be compared with your first Root. You will take them in the mentioned order according to the alphabet thereafter. For if, for example, two cells were left over from these interior numbers, whose order of departure was given for the making of the upper semi-diameters, and it happened that these two were, for example, 'l' and 'm', then you will take 'l' first, then go to 'm'.

And here likewise it should be correctly noted that if that Root were marked with a cross $\dagger$, then you will elicit all the differences alone, namely, where you will find the term by operating with the same Root if it were straight, where from the same cell, it takes its beginning in the exterior when reversed, thus proceeding in that same inversion until the end.