401201
[Commentary:
The reference to Pappus is to Commandino's edition of Books III to Mathematicae collectiones
(Pappus . The proposition on page 48v–49 is Proposition IV.15 (not 13, as Harriot appears to have written). A diagram for this proposition appears on Add MS 6784
f. ; this page shows only calculations of ratios.
Theorema XV. Propositio XV.
Iisdem positis describatur circulus HRT, qui & semicirculos iam dictos, & circulum LGH contingat in punctis HRT, atque a centris A P ad BC basim perpendiculares ducantur AM PN. Dico vt AM vna cum diametro circuli EGH ad diametrum ipsius, ita esse PN ad circuli HRT
The same being supposed [as in Proposition 14], there is drawn the circle HRT, which touches both the semicircles already given and the circle LGH, in the points H, R, T. And from the centres A and P to the base there are drawn perpendiculars AM and PN. I say that as AM together with the diameter of the circle EGH is to that that diameter itself, so is PN to the diamter of the circle ]
Theorema XV. Propositio XV.
Iisdem positis describatur circulus HRT, qui & semicirculos iam dictos, & circulum LGH contingat in punctis HRT, atque a centris A P ad BC basim perpendiculares ducantur AM PN. Dico vt AM vna cum diametro circuli EGH ad diametrum ipsius, ita esse PN ad circuli HRT
The same being supposed [as in Proposition 14], there is drawn the circle HRT, which touches both the semicircles already given and the circle LGH, in the points H, R, T. And from the centres A and P to the base there are drawn perpendiculars AM and PN. I say that as AM together with the diameter of the circle EGH is to that that diameter itself, so is PN to the diamter of the circle ]
5.) pappus. prop. 13. pag.