291146
[Commentary:
Harriot refers to Euclid, .
If in a right-angle triangle a perpendicular be drawn from the right angle to the base, the triangles adjoining the perpendicular are similar both to the whole and to one another. ]
If in a right-angle triangle a perpendicular be drawn from the right angle to the base, the triangles adjoining the perpendicular are similar both to the whole and to one another. ]
Of 3 magnitudes in continuall proportion:
There differences being known: to find lineate the
There differences being known: to find lineate the
For sake of understanding, suppose it first don. the first proportionall, the
second & the third. The difference betwixt the first & second ; betwixt
the second & third . The difference of differences that is betwixt & ,
The construction of the problem
let the first difference be : the second , the difference of those differences
from the poynt rayse a perpendicular . In it let be æquall to . make
æquall to . from to draw a right line. Make , a rectangle.
& produce till it meet with . by the 8th of the 6th it is a meane
proportionall betwixt & . Therefour is the first proportionall sought
must therefour be the second or . & the third. as is manifest
by the corollaries in the paper
second & the third. The difference betwixt the first & second ; betwixt
the second & third . The difference of differences that is betwixt & ,
The construction of the problem
let the first difference be : the second , the difference of those differences
from the poynt rayse a perpendicular . In it let be æquall to . make
æquall to . from to draw a right line. Make , a rectangle.
& produce till it meet with . by the 8th of the 6th it is a meane
proportionall betwixt & . Therefour is the first proportionall sought
must therefour be the second or . & the third. as is manifest
by the corollaries in the paper
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