EACH to EACH
et alibi prossim.
1. EACH TO EACH. An impression used by Euclid toThe meaning intended to be conveyed
by this expression is convey an Idea directly opposite to the litteral meaning one.
For example in the 4 Prop of 1. Book there is a Triangle the
A Triansuppose 2 Triangles to be given when angles are said
three angles which are said to be to be equal to the 3 angles
to be equal each to each assuming one of the angles
of another Triangle each to each. Take another of the
of one triangle, and it must be equal to each of
those in the Triangle assume take another and that
must be equal to each those of the other Triangle
again assume take the a third and this must be
equal to each of the other Triangle this one
assumed then is equal to any assumed one of the
other triangle. Again assume some other in the
same one triangle and by in the same manner
it may be found equal to any assumed one
in the other. Lastly assume the third angle
and in the former same manner prove this
equal to any assumed one in the other.
now then we have proved that every
one angle of one triangle is equal
any one of the other wherefore they are all
equal. But Euclid put this expression
to prevent the 3 angles of one Triangle
to be thought equal to the other in the
other any one to any one. Wherefore
his expression is false. vid EACH to ONE.
Each to Each
Euclid Defines. Oblong Rhombus & Rhomboides
neither of which he makes use of
He makes great use of Parall: which he does
Euclid makes no distinction between a Circle
as a line the circumference of that figure, and
the figure itself considered as a superficies
Examples 13th Prop. Book 3d.
He sometimes puts 2 propositions together so
as to be called one and sometimes he splits
a Proposition into two this is most frequent
when one is the Converse of the other.
Exteriour & interiour
Qu. Suppose 2 lines cross each other, of
the angles they make which are
exteriour which interiour? if at right angles.
and Large letters
The long Paragraphs in some of the Editors of
Euclid Particularly Simpson without any break
any dist distinguished by a different Type, or
any thing for the eye to catch, is enough to frighten
beginners, besides those the number of letters of
Reference which are so much larger than the common
letter press, which ar distinguish themselves from
the rest and as they cannot be understood without
reference to the Page Figure they tend to
make it more intelligible besides when
the reader has referred to a Page the Figure and
wishes to procede in the letter press he has not
no marks by which he can find again the place he
left off at and sometimes in the letters of reference
making use of the letter of reference as landmarks he is led into an error by mistaking some like those he left off at for the
real one. and by this mistake he either reads the same over again or skips what is worse skips some which he had not read.
Identifier: | JB/135/026/002
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copy/fair copy sheet
sir samuel bentham
[[watermarks::[gr with crown] [pro patria motif]]]