Part 12

The Greek letter η (eta) was consistently printed as if it were the ou-ligature ȣ. The Latin “-que” was written as an abbreviation resembling “-q´;”. It is shown here as .

Mathematical symbols seen in the section accompanying the diagrams could not be reproduced. The following substitutions were made: --The curly “P” used for “Pounds” is shown as {P}. --The “potestas” symbol, used to represent “x” (the unknown), is shown as {x}. --All roots were expressed as the “root” sign √ combined with symbols for the power of 2 (doubled for power of 4, or fourth root) and 3. They are shown as ²√ ³√ ⁴√.

Euclid:

The following Propositions were identified by number.

6.12: (How) to find a fourth (line) proportional to three given straight lines.

11.34: In equal parallelepipedal solids the bases are reciprocally proportional to the heights; and those parallelepipedal solids in which the bases are reciprocally proportional to the heights are equal.

11.36: If three straight lines are proportional, then the parallelepipedal solid formed out of the three equals the parallelepipedal solid on the mean which is equilateral, but equiangular with the aforesaid solid.

12.1: Similar polygons inscribed in circles are to one another as the squares on their diameters.

12.2: Circles are to one another as the squares on their diameters.

12.18 (“last”): Spheres are to one another in triplicate ratio of their respective diameters.