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If the outward angle of
by producing one of its
into two equal angles
which also cuts the base
segments between the
and the extremeties of the
same ratio which the other
ngle have to one another. &
which the other sides of the tri
straight line drawn from
the point of sectional divide
angle of the triangle into
gles —
Theor — Prob —
straight line similarly to
line, that is into parts
the same ratio to one
the parts of the divided
line have —
ight lines be proportionals
contained by the extremes
square of the mean;
tangle contained by the
equal to the Square of the
aight lines are proportional.
XIV Theor —<p>ams about the diameter
elogram, are similar
and to one another.
led triangles the rectili
described upon the side
the right angle is
similar and similarly
ures upon the sides
the right angle.
The sides about the equal angles of
equiangular triangles are proportionals;
and those which are opposite to the
equal angles are homologous sides
that is, are the antecedents or
consequents of the ratios —
Prob XI Prob —
To find a third proportional to two
given straight lines
Prop XVIII Theor Prob —
Upon a given straight line to describe
a rectilineal figure similar and
similarly situated to a given rectilineal
figure
To describe a rectilineal figure
which shall be similar to one
and equal to another given rectilineal
figure —
If two triangles which have two Sides
of the one proportional to two sides of
the other, be joined at one the angle, so as
to have their homologous sides
parallel to one another, the remaining
sides shall be in a straight
line —
If the sides of two triangles, about each
of their angles be proportionals, the
triangles shall be equiangular and
shall have their equal angles those angles equal which
opposite to the homologous sides
To find a fourth proportional to
three given straight lines
Similar triangles are to one
another in the duplicate ratio of
their homologous Sides —
If two similar parallelograms
have a common angle and be
similarly situated: they are
about the same diameter —
In equal Circles, Angles, whether at
the Centers or Circumferences, have
the same ratio which the Circumferences
on which they stand have
to one another. So also have the Sectors —
If two triangles have one angle of the one
equal to one angle of the other and the
sides about the equal angles proportionals,
the triangles shall be equiangular,
and shall have those angles equal
which are opposite to the homologous
sides —
To find a mean proportional between
two given straight lines —
Similar polygons may be divided into
the same number of similar figures
triangles having the ratio to one
another that the polygons have:
and the polygons have to one another the
duplicate ratio of that which their
homologous sides have —
Of all parallelograms applied to the Same
straight line, and deficient by
parallelograms similar and similarly
situated to that which is described upon
the half of the line: that which is applied
to the half, and is similar to its defect
is greatest. —
If an angle of a triangle be bisectio by
a straight line, which likewise cuts
the base: the rectangle contained
by the sides of the triangle is equal
to the rectangle contained by the
segments of the base, together with the
square of the straight line bisecting the angle.
Identifier:  JB/135/072/006 "JB/" can not be assigned to a declared number type with value 135.



135 

072 
the propositions of the fifth and sixth books of euclid as expressed by simson those written with red ink are added by himself 

006 

private material 
3 

recto 

sir samuel bentham 
[[watermarks::[tall thin motif with prince of wales feathers] icv]] 

46190 
