757379
[Commentary:
The reference on this page is to the Lemma of Monachos, as found in Proposition 59 of Commandino's edition
of Pappus Mathematicae collectiones
(Pappus .
Theorema LVI. Propositio LIX.
Semicirculo existente AEB, & diametro AB, existentibusque perpendicularibus CE & ducta recta linea EFG, & ad ipsam perpendiculari BG, tria porro contingunt, videlicet rectangulum quidem CBD aequale esse quadrato ex BG; rectangulum vero contentum AC BD quadrato ex FG, & contentum AD CB quadrato ex
Given a semicircle AEB with diameter AB, and perpendiculars CE, DF, and having drawn the line EFG, and the perpendicular to it, BG, then three things come about, namely, the rectangle CB.BD is equal to the square of BG; and the rectangle AC.BD to the square of FG, and teh rectangle AD.CB to the square of EG.
Harriot's note about the diagram is difficult to read. In the diagram given by and are symmetrically placed about the centre so that is parallel to . Harriot's diagram is therefore more general. ]
Theorema LVI. Propositio LIX.
Semicirculo existente AEB, & diametro AB, existentibusque perpendicularibus CE & ducta recta linea EFG, & ad ipsam perpendiculari BG, tria porro contingunt, videlicet rectangulum quidem CBD aequale esse quadrato ex BG; rectangulum vero contentum AC BD quadrato ex FG, & contentum AD CB quadrato ex
Given a semicircle AEB with diameter AB, and perpendiculars CE, DF, and having drawn the line EFG, and the perpendicular to it, BG, then three things come about, namely, the rectangle CB.BD is equal to the square of BG; and the rectangle AC.BD to the square of FG, and teh rectangle AD.CB to the square of EG.
Harriot's note about the diagram is difficult to read. In the diagram given by and are symmetrically placed about the centre so that is parallel to . Harriot's diagram is therefore more general. ]
In Monachos lemma.
prop. 59. lib. 7. pappi. pag.
[Translation: On the lemma of Monachos, Proposition 59, Book 7 of Pappus, page ]
prop. 59. lib. 7. pappi. pag.
[Translation: On the lemma of Monachos, Proposition 59, Book 7 of Pappus, page ]
Data seu posita
semicirculo
. Diameter.
cui , , perpendiculares.
producta
cui perpendic-
[Translation: Given or supposed, a semicircle with diameter , to which and are perpendiculars, and extended, to which is a perpendicular.
semicirculo
. Diameter.
cui , , perpendiculares.
producta
cui perpendic-
[Translation: Given or supposed, a semicircle with diameter , to which and are perpendiculars, and extended, to which is a perpendicular.
Diagrapha [???]
in Græco [???]
et apud
[Translation: Diagram [???]
in the Greek [???]
and in ]
in Græco [???]
et apud
[Translation: Diagram [???]
in the Greek [???]
and in ]
Tria
Consequentia
[Translation: Three consequences to be ]
Consequentia
[Translation: Three consequences to be ]
Constructiones seu linearum ductiones
[…]
Consequentia ex ductis et constructis.
[…]
quia puncta , , , , sunt in circulo.
quia super eadem peripheriam.
quia , , , , sunt in circulo. [???]
diameter.
[…]
Tum: Traing. et sunt æquiangula. quia communis utrisque.
[…]
Prima
[Translation: Construction ordrawing of the lines
Consequence from the drawing and ex ductis construction.
becasue the opoints , , , are on a circle.
because on the same circumference.
because , , , are on a circle. [???] diameter.
Then triangles et are equiangular because is common to both.
First ]
[…]
Consequentia ex ductis et constructis.
[…]
quia puncta , , , , sunt in circulo.
quia super eadem peripheriam.
quia , , , , sunt in circulo. [???]
diameter.
[…]
Tum: Traing. et sunt æquiangula. quia communis utrisque.
[…]
Prima
[Translation: Construction ordrawing of the lines
Consequence from the drawing and ex ductis construction.
becasue the opoints , , , are on a circle.
because on the same circumference.
because , , , are on a circle. [???] diameter.
Then triangles et are equiangular because is common to both.
First ]
per primam consequens.
2
[Translation: by the first consequence
Consequence ]
2
[Translation: by the first consequence
Consequence ]
per primam consequens.
3.
[Translation: by the first consequence
Consequence ]
3.
[Translation: by the first consequence
Consequence ]
, , , non necessario
et omissa. apud
Commandinum.
etiam superflua.
Malo etiam in
[Translation: , , are not necessary and is omitted by Commandino.
is also superfluous.
Also badly done in the ]
et omissa. apud
Commandinum.
etiam superflua.
Malo etiam in
[Translation: , , are not necessary and is omitted by Commandino.
is also superfluous.
Also badly done in the ]