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Nevertheless, when the last cell of the entire Rhomboid, which is diametrically opposed to cell A, lacks a number and brings no difference, do not lack ingenuity at all, for it acts as the same number if you deny enough Mathematics. Again, to obtain the number even for this last cell, you will elicit the difference from the two numbers contained in the upper cells, which you see marked with the letters B and D, and thus all the cells of the table are completed in both Rhomboids as they ought to be.

In any other Language original: "Idiomate" (except for Hebrew), use these same Rules, because they vary nothing in the construction of these Rhomboids. However, in the Hebrew language, since the Rules are the same for both Rhomboids in capturing the numbers in the left Rhomboid, you place the first number in the first cell, the second in the fourth, the third in the second, the fourth in the fourth likely an error for another cell number, the fifth in the seventh, the sixth in the fifth, and so on for the rest. A transverse path must be run, where in the Latin language used above, specifically the movement is to be taken from left to right, there it was necessary to cross from right to left.

Furthermore, in the Hebrew language, for the cells of the first half of the right Rhomboid which remain empty there, likewise in taking the differences from the angles of the left Rhomboid, a reversed order must be observed. Specifically, after the superior Angle of which you inquire, you should take yourself to the demonstration we placed above, the cross † and the letter X. Then compare the lower Angle, and finally rest in the second Angle.

In the same way, in completing the left half of the Rhomboid according to the handed-down Rules, a reversed proportion must be taken. For where, for example, to elicit the difference in the superior first example for the last cell of the said left Rhomboid, the difference of 7 with 1 was taken; in such a case here in the reversed Hebrew order, you will compare 1 with 7, which you should diligently note similarly in extracting the difference for the last cell of the right Rhomboid.

But it should be Noted, however, that the reversed order of proportion is not to be observed, for even in this language the number of the first cell of the right Rhomboid is to be considered for the number of unity, with which others are to be compared, both in the Left and in the Right Rhomboid. Let this suffice for the operation in this chapter concerning other languages.

On the Fourth Operation

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Cap. V.

Now that the cells of the Rhomboids are filled, it remains for us to approach the general Doubt?, and let us give effort to constructing the Branches Brancas the curved, arm-like channels in the diagram, but first it is necessary to obtain their true Mathematical delineation: for which matter, act thus.

Let a channel be made, whose width is one finger; from whose mouth first two lines should be designated, which, having been led to the interior Angles of both Rhomboids, place their seat there. Then, after a very brief beginning of the same channel, you will delineate curved lines in the likeness of a semicircle, turning one from the left and the other from the right: which are terminated in the lower Angle of both Rhomboids.

Now, that which is delineated on the Right part, and formed from the right Rhomboid, you shall name the Right Branch Brancam Dexteram; that which indeed rests with an equal delineation on the left is called the Left Branch Branca Sinistra. Then underneath, with a similar very brief quantity, the channels placed spherically will take their beginning, which from each part of the middle channel will make as many as your query holds words; yet these channels themselves do not cross this middle channel, rather they will make themselves there as if in their own semi-diameter. The part whose orbit is delineated on the right shall be called the Right Semicircle Dexter Semicirculus, the other on the left shall be called the Left Semicircle Sinister Semicirculus. Just as each Diameter divides these two semicircles below the lines into four semi-diameters, the first of which, placed after the right Branch, shall be named the Superior Semi-diameter of the right Semicircle; the other indeed shall be called the Inferior Semi-diameter of the right Semicircle. Those which indeed are opposed to these in the left semicircle hold the same denomination. However, where it is called the Right Semicircle there, here the left Diameter shall be inscribed. You will establish the channels of these Semi-diameters partly closed and others open under the order. Make the first channel of each semicircle explicit open, paint the following one closed, let the third be open, the fourth indeed not, and so proceed. This will be in the other channels up to the end of the semicircles, alternately closing one and opening the next. Finally, you will cut each semicircle through columns, and divide it as many times as there were cells established in the exterior side of your Rhomboids besides the Angles, and with the same letters, which