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# JB/135/060/001

Completed

GEOMETRY

Book VI 1. Definition

Is it a sufficient definition of Similar Triangle say
they are such which have their angles equal each in one
to its correspondent in the others. That the boundaries of
such triangles are Proportionals may be demonstrated.
or vice versa either could serve as a definition with out the other

The term to be defined by this definition is very inadequate of
2. Definition itself to the Idea intended to be fixed to it. The idea itself
is expressed very obscurely and it does not seem to occur
enough to demand a particular term.

New definition Two lines are said to be divided proportionally when

Euclid says: that if the sides of a triangle be cut proportionally
Prop: 2. false
by expression
a line drawn from one point of Section to the other will be
parallel to the base. This Prop: will not be true unless
the relative situation of the 2 parts into which each side
is cut to be the same. For suppose each side be cut in
the proportion of 2 to 4 but that the sect parted represented
by 2 of in one side of the triangle be next the vertex
in the other next the base it is plain in this case
that the sides of the triangle would be cut proportionally and the
yet that the line joining the points of section can not
be parallel to the base.

In Book the 2d and other parts of the Elements what is asserted
Rectangle
not General
enough
of the sq rectangles of two given lines I believe might
have been of the Parallelogram of these lines since
or this expression is not proper some one might be
faed compr including all the species of Parallelogram
having one of the given lines as the base and the
other the altitude

nor Square

I would be better if the same term could be substituted instead
of Square the analogy would be easier perceived and the
difference would be marked by this. whenever in one case

Identifier: | JB/135/060/001
"JB/" can not be assigned to a declared number type with value 135.

not numbered

135

060

geometry

001

copy/fair copy sheet

2

recto

sir samuel bentham

[[watermarks::gr [with crown] [lion motif]]]

46178