10754
[Commentary:
Some working for Lemma II, preceding Problem IX of Apollonius Gallus
(Viete 1600a, Prob 9, Lemma . Harriot notes some cases missed by Viète.
Lemma II.
Sint duo circuli, unius ABCD, alter EFGH; jungens autem eorum centra KL secet circulum primum in A, D; secundum vero in E, H; & in ea sumatur M punctum, a quo acta MGFCB recta secet circulm primum in B, C, secundum in F, G, & sint similia segmenta, & puncta quidem sectionum A, B sint remotior a ipsis C, & puncta F, E ipsis C, H. Ajo id quod fit sub MG, MB aequari id quod fit sub MH,
Lemma II. Let there be two circles ABCD and EFGH; moreover the line KL joining their centres cuts the first circle in A and D, and the second in E and H; and in that line there is taken the point M, from which the straight line MGFCB cuts the first circle in B and C, and the second in F and G, and the segments are similar, and the points A, B are further away than C, D, and the points F, E than C, H. I say that the rectangle formed by MG, MB is equal to that formed by MH, ]
Lemma II.
Sint duo circuli, unius ABCD, alter EFGH; jungens autem eorum centra KL secet circulum primum in A, D; secundum vero in E, H; & in ea sumatur M punctum, a quo acta MGFCB recta secet circulm primum in B, C, secundum in F, G, & sint similia segmenta, & puncta quidem sectionum A, B sint remotior a ipsis C, & puncta F, E ipsis C, H. Ajo id quod fit sub MG, MB aequari id quod fit sub MH,
Lemma II. Let there be two circles ABCD and EFGH; moreover the line KL joining their centres cuts the first circle in A and D, and the second in E and H; and in that line there is taken the point M, from which the straight line MGFCB cuts the first circle in B and C, and the second in F and G, and the segments are similar, and the points A, B are further away than C, D, and the points F, E than C, H. I say that the rectangle formed by MG, MB is equal to that formed by MH, ]
Apol: Gallus. Lemma 2. pag.
[Translation: Apollonius Gallus, Lemma II, page ]
[Translation: Apollonius Gallus, Lemma II, page ]