VITRUVIUS.
When therefore the magnitude of the hole is determined, the scutula, which in Greek is
called peritretas, is described, of which the length is holes II. F. Z.; the breadth two and a
sixth part. The described line is divided in half, and when divided the forms of the extre-
mities are contracted, so that the oblique formation may have a sixth part of the length and
of the breadth, at the return (versura) a fourth part. In that part also is the curvature in
which the points of the angles project, and the holes are turned, and the contractures of the
breadth return inwardly a sixth part: the hole is so much oblong as the epizygis is thick,
When it is described, it is divided around so that the extremity may have a gentle curvature::
the thicknefs of it is S. T. of a hole. The modiols are made II. :— holes, the breadth I.S.9.:::
the thickness, exclusive of what is inserted in the hole, is S. I. of a hole; at the extremity
also the breadth is I.T. of a hole. The length of the parastatae V. S.T.holes; the curvature a
half part of a hole; the thickness, U of a hole, and LX. part. At the middle the breadth
is enlarged as much as it is near the hole made in the description, in breadth and thick-
ness V. of a hole, the height IV. parts. The regula which is on the mensa, is in length
VI. holes, in breadth and thickness half of a hole; the cardo II. Z :::. The thickness of
the curvature of the regula T. 5. K. The breadth and thickness of the exterior regula are
the same; the length so much as is given by the same return (versura) of the formation, and
the breadth of the parastæe and its curvature K. The superior regulae are equal to the in¬
ferior K. The transverse pieces of the mensa U. U. K. of a hole. The length of the shaft of
the climaciclus is XIII. holes ::: the thickness III. K.
The breadth of the middle interval is a fourth part of a hole :: the thickness an eighth
part K. The superior part of the climaciclos, which is next to the arms, and which is joined
to the mensa, is in the whole length divided into five parts, of which two parts are given to
the hole in digits: thus astone weighing ten minae, required
the hole to be eleven digits in diameter; for 10 multi-
plied by 100 produces 1000, the cube root of which is
10; to which adding a tenth part, viz. 1, the amount is
11 digits for the diameter of the hole.
But we are not informed for what mina this rule is
calculated. The Attic mina contained 100 drachmas,
of which the Alexandrian contained 160, and the Ro-
man pendus 96; so that much depends on the weight
of the mina here to be understood, and which in following
this rule it is highly necessary to know. Heron himself
was of Alexandria; and this rule of his makes the holes
much larger for the minae he means, than Vitruvius allows
for an equal number of Roman pounds: these reasons
therefore, together wich Vitruviuss afsertioh—e that he
" has transcribed his acount from the Grek auhors,
t but in such a manner as to make it conform to the
* Roman weights and measures," render it probable that
it is the Alexandrian mina on which Heron's rule is
founded; and upon this supposition, allowing also for
the difference between the Roman and Greek foot, the
lizes of the holes found by this rule will nearly agree with
those given by Vitruvius, as well as those of Philo, who
seems to agree with Heron in using the Alexandrian
Another method was also used by the antients for find-
ing the sizes of the holes for stones of different weights,
which was this : Having the size of the hole for a stone
of any weight given, the size of the hole for a stone of any
other weight was found by the method used for doubling
the cube, i. e. by finding two mean proportionals. It is
by this method Buteo has made his calculation.