3719
[Translation: ]
[Translation: ]
[Commentary:
The problem pursued in this and many other folios in Add MS 6784 is 'the cutting-off of an area',
as set out in Pappus, Mathematicae collectiones, Book 7. In Commandino's edition of 1588, the problem is stated on page 158v
(Pappus .
Per datum punctum rectam lineam ducere secantem a duabus rectis lineis positione datis ad data in ipsis puncta lineas, quæ spacium contineant dato spacio æquale.
Through a given point, draw a line cutting off line segments from two lines given in position, to points given on them, which contain an area equal to a given area.
Using Harriot's lettering, the problem may be stated as follows. Given the lines , , the point , and an area of size , construct the line so that . There are many variations of the problem according to the relative positions of , , and , which Harriot explored in this and other folios.
This example, in Add MS f. f. , demonstrates the use of Viète's concepts of zetetic, exegetic, and poristic. There is also a direct reference on Add MS 6784 f. to Viète, Effectionum geometricarum, (Viète 1593b, Props 11, .
The three pages Add MS f. to f. appear to have been written out for Thomas Aylesbury in December 1608 (see Add MS 6784 f. ), perhaps as a 'worked example' of Viète's methods. ]
Per datum punctum rectam lineam ducere secantem a duabus rectis lineis positione datis ad data in ipsis puncta lineas, quæ spacium contineant dato spacio æquale.
Through a given point, draw a line cutting off line segments from two lines given in position, to points given on them, which contain an area equal to a given area.
Using Harriot's lettering, the problem may be stated as follows. Given the lines , , the point , and an area of size , construct the line so that . There are many variations of the problem according to the relative positions of , , and , which Harriot explored in this and other folios.
This example, in Add MS f. f. , demonstrates the use of Viète's concepts of zetetic, exegetic, and poristic. There is also a direct reference on Add MS 6784 f. to Viète, Effectionum geometricarum, (Viète 1593b, Props 11, .
The three pages Add MS f. to f. appear to have been written out for Thomas Aylesbury in December 1608 (see Add MS 6784 f. ), perhaps as a 'worked example' of Viète's methods. ]
a) De resectione spatij,
[Translation: On the cutting off of an area, ]
[Translation: On the cutting off of an area, ]
Data:
, , lineæ infinitæ
, , termini.
. punctum
,
[Translation: Given infinite lines , , endpoints , , a point and an area .
, , lineæ infinitæ
, , termini.
. punctum
,
[Translation: Given infinite lines , , endpoints , , a point and an area .
Quæsitum:
Ducere lineam :
ut
[Translation: Sought:
To draw a line so that:
Ducere lineam :
ut
[Translation: Sought:
To draw a line so that:
Zetetike
Sit iam factum:
ut fiat: parall. .
. parall.
[Translation: Zetetic.
Let it be already done, so that is parallel to and parallel to .
Sit iam factum:
ut fiat: parall. .
. parall.
[Translation: Zetetic.
Let it be already done, so that is parallel to and parallel to .
[Translation: ]
[Translation: ]
ergo si
fiat
æqualis
vel ,
problema
absoluitur.
dupliciter
enim
[Translation: Therefore if becomes equal to or , the problem is solved, for it is twofold.
fiat
æqualis
vel ,
problema
absoluitur.
dupliciter
enim
[Translation: Therefore if becomes equal to or , the problem is solved, for it is twofold.
Vieta de effect
prop. 11. &
[Translation: Viète, De effectionum, propositions 11 and ]
prop. 11. &
[Translation: Viète, De effectionum, propositions 11 and ]