12

22

every geometrical point, that is every
individual of the set concerning which
the predication is made. This at the same
time and ipso facto describes any diagram
of any state of things to which the proposition
is applicable.
This part ends by stating in terms of those selectives exactly
what his assertion makes him responsible for.
This part is called the ἔκθεσις, or exposition.
Next comes his κατασκευή,
or contrivance; which is an ingenious
experiment that he performs upon the
diagram, by adding lines to it drawn
according to an exact precept, or his
supposing one part to be moved and
superposed in a particular way upon
another part. He now shows that it is
implied in what is already known that
this experiment must give a certain