Last Updated：2025/12/20
Sentence
{{RQ:Barrow
Mathematical
Learning|chapter=Lecture
XVII.
Of
the
Names
and
Diversities
of
the
Twofold
Kind
of
Reason
or
Proportion,
viz.
Arithmetical
and
Geometrical|pages=323–324|pageref=324|passage=[I]f
two
Quantities
repreſented
by
the
Numbers
20
and
4
be
compared,
by
dividing
the
Antecedent
20
by
the
Conſequent
4,
the
Quotient
is
5;
but
inverting
the
Terms,
by
dividing
4
by
20
the
Quotient
is
tfrac
4
20=
tfrac
1
5.
By
which
Quotients
are
declared
the
Geometrical
Reaſons
of
the
propoſed
Quantities,
becauſe
if
the
Quotient
found
be
multiplied
by
the
Conſequent,
the
Product
is
equal
to
the
Antecedent;
for
in
the
former
Compariſon
5⨯4=20,
in
the
latter
tfrac
1
5⨯20=4;
as
Things
again
are
referred
to
Equality.}}
Quizzes for review
{{RQ:Barrow Mathematical Learning|chapter=Lecture XVII. Of the Names and Diversities of the Twofold Kind of Reason or Proportion, viz. Arithmetical and Geometrical|pages=323–324|pageref=324|passage=[I]f two Quantities repreſented by the Numbers 20 and 4 be compared, by dividing the Antecedent 20 by the Conſequent 4, the Quotient is 5; but inverting the Terms, by dividing 4 by 20 the Quotient is tfrac 4 20= tfrac 1 5. By which Quotients are declared the Geometrical Reaſons of the propoſed Quantities, becauſe if the Quotient found be multiplied by the Conſequent, the Product is equal to the Antecedent; for in the former Compariſon 5⨯4=20, in the latter tfrac 1 5⨯20=4; as Things again are referred to Equality.}}
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