Conclusion

...the same original: eandem [diameter] of the aforementioned circle exceeds [the side of the square] precisely by three half-parts. Or, it is a square whose side is exceeded—that is, surpassed—by the diameter of the same circle by precisely three half-parts. For the diameter of the circle was previously divided into precisely seven small parts, while the side of the square consists of five parts and a half of that same diameter; and so, to reach that number of seven, there remains exactly one part and a half, or three half-parts three half-parts tres dimidie particule, by which any side of such a square is surpassed by the diameter of the same circle.

And although this may perhaps be true in another sense, nevertheless in continuous quantity continuous quantity quantitate continua In medieval mathematics, this refers to geometry and the measurement of physical space which can be infinitely divided. it might seem to some to be contrary to the senses and outward appearance. This is because if a circle were divided into four equal portions, then any of those four parts (a quarter of the circle) seems to occupy only five small portions of the diameter, rather than five and a half, as the quarter of the circle should. Thus, it does not appear that they would be equal to one another.

But in the truth of the matter they are made equal, as we shall explain in detail original: enucleabimus; literally "to take out the kernel," meaning to clarify or explain thoroughly. below. This deceptive appearance is due to the circular or curved line of the circle, which, by its very definition, does not extend as far as a straight line does The author is noting that a curved line "covers" less linear distance than a straight line of the same length when measured against a rigid scale like a diameter.. And thus it is clear that any fourth part of the circle and any fourth part of the square itself are equal to each other.

However, this appears more clearly in discrete quantity discrete quantity quantitate discreta This refers to arithmetic and the study of whole numbers and counting.; for if you take the number five and a half four times, the number 22 will result immediately. From this number, a straight line and a circular line running around it The circumference. can be formed. For instance, if there were a circle of 22 degrees degrees graduum and it were divided into four equal parts, for each fourth part there would be 5 degrees and 30 minutes minutes minuta, as is evident; and thus five and a half are the fourth part of the circle from which one side of the square ought to be made. Since, therefore, any side or any fourth of this square is [surpassed] by the already di- The text breaks here at the catchword "di," likely for "dicta" (mentioned) or "diametro" (diameter) on the following page.