289145
[Commentary:
Harriot refers to Euclid, .
If, as a whole is to a whole, so is a part subtracted to a part subtracted, the remainder will also be to the remainder as whole to whole. ]
If, as a whole is to a whole, so is a part subtracted to a part subtracted, the remainder will also be to the remainder as whole to whole. ]
Of 3 magnitudes in continuall proportion: there differences being
given; to find the
given; to find the
ffirst let us seeke out the theoreme delivering the proper
effection whereby it should be performed, by
effection whereby it should be performed, by
The planes of the proportionalles
being noted, let the difference
betwixt the first & second be
called : & betwixt the second &
third
being noted, let the difference
betwixt the first & second be
called : & betwixt the second &
third
Then suppose the first proportionall to be . then the second
wilbe . & the third
wilbe . & the third
Now seing the square of the second is æquall to the oblong
of the extremes. let the multiplications be performed
as here
of the extremes. let the multiplications be performed
as here
Then according to the art
let the æquation be [???]
& it wilbe
let the æquation be [???]
& it wilbe
The square of the first difference, is æquall to the obling, made of
the difference of the differences, & the first
or: The first difference is a meane proportionall betwixt the difference
of the differences &a; the first
Wherefour the rule is:
Square the first difference; & divide by the difference of the
differences, & the quotient wilbe the first proportionall
The second & third proportionalls are threfour known by their
the difference of the differences, & the first
or: The first difference is a meane proportionall betwixt the difference
of the differences &a; the first
Wherefour the rule is:
Square the first difference; & divide by the difference of the
differences, & the quotient wilbe the first proportionall
The second & third proportionalls are threfour known by their
What proportion therefore in Euclide wilbe the element whereby to demonstrate
the problem by composition is easily manifest. that is to say, the 19th of the 5th.
From it will issue these two
If these be 3 magnitudes in continuall proportion; as the first hath
to the second; so hath the first difference, to the second
And: The first difference is a meane proportionall
betwixt the first proportionall & the difference of
the problem by composition is easily manifest. that is to say, the 19th of the 5th.
From it will issue these two
If these be 3 magnitudes in continuall proportion; as the first hath
to the second; so hath the first difference, to the second
And: The first difference is a meane proportionall
betwixt the first proportionall & the difference of
zoom in
zoom out
zoom area
full page
page width
set mark
remove mark
get reference
digilib