405203
[Commentary:
The reference to Pappus is to Commandino's edition of Books III to Mathematicae collectiones
(Pappus . The proposition on page 47 is Proposition IV.14. Harriot's diagram is the same as the one given by Commandino except for his use of lower case letters. A second diagram for the same proposition appears on Add MS 6784
f. .
Theorema XIIII. Propositio XIIII.
Sint duo semicirculi BGC BED: & ipsos contingat circulus EFGH: a cuius centro A ad BC basim semicirculorum perpendicularis ducatur AM. Dico ut BM as eam, quæ ex centro circuli EFGH, ita esse in prima figura vtramque simul CB BD ad earum excessum CD; in secunda vero, & tertia figura, ita esse excessum CB BD ad vtramque ipsarum CB
Let there be two semicircles BGC and BED, and their touching circle EFGH, from whose centre A to BC, the base of the semicircle, there is drawn the perpendicular AM. I say that as BM is to that line from the centre of the circle EFGH, inthe first figure will be CB and BD togher to their excess, CD; but in the second and third figure, it will be as the excess of CB over BD to both of CB and BD ]
Theorema XIIII. Propositio XIIII.
Sint duo semicirculi BGC BED: & ipsos contingat circulus EFGH: a cuius centro A ad BC basim semicirculorum perpendicularis ducatur AM. Dico ut BM as eam, quæ ex centro circuli EFGH, ita esse in prima figura vtramque simul CB BD ad earum excessum CD; in secunda vero, & tertia figura, ita esse excessum CB BD ad vtramque ipsarum CB
Let there be two semicircles BGC and BED, and their touching circle EFGH, from whose centre A to BC, the base of the semicircle, there is drawn the perpendicular AM. I say that as BM is to that line from the centre of the circle EFGH, inthe first figure will be CB and BD togher to their excess, CD; but in the second and third figure, it will be as the excess of CB over BD to both of CB and BD ]
pappus. pag.
[Translation: Pappus, page ]
[Translation: Pappus, page ]