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lid, having the common base, ABC ; then, if the folld EABC is not equal to the folid FABC, let it be equal to some solid as GA BC, either greater or less than EABC, which cannot be; for the one would contain the other, and if the solid angle is conG
tained by more than three plane angles, equal and similar to one
another, then it can EL
be divided into angles which are contained by three equal and fi. milar plane angles,
by Prop. 20. Book Vi. D
and parts have the
fame proportion B
C their like multiples,
by Prop. 15. Book V. wherefore universally, figures bounded by
an equal number of equal and similar planes are equal and fimilar.
N. B. In the references, when the proposition referred to is in the fame book with the proposition to be proved, the book is Bot named, but only the number of the proposition, but, if in any
other book, both are named.
the same plain, which touch each other, but do not lie in the
angles on each side thereof equal to one another, each of these
upon ther is called a perpendicular to that whereon it stands.
An obtuse angle is that which is greater than a right one.
ference, to which all right lines drawn from a certain point
ter, and terminated on both ends by the circumference, and
XVIII. A semicircle is a figure contained under any diameter, and the circumference cut off by that diameter.
A X I OM S.
V. Book I.
If from unequal things equal parts are taken, the remainders will be unequal.
VI. Things which are double one and the same thing are equal between themselves.
angles on the same side less than two right angles, these right
that at the vertex is named betwixt the other two..