Apollonius <Pergaeus>; Lawson, John, The two books of Apollonius Pergaeus, concerning tangencies, as they have been restored by Franciscus Vieta and Marinus Ghetaldus : with a supplement to which is now added, a second supplement, being Mons. Fermat's Treatise on spherical tangencies

Table of contents

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[21.] LEMMA II.
Page: 20 ((8))
[22.] LEMMA III.
Page: 20 ((8))
[23.] PROBLEM X.
Page: 20 ((8))
[24.] PROBLEM XI.
Page: 21 ((9))
[25.] PROBLEM XII .
Page: 22 ((10))
[26.] LEMMA IV.
Page: 23 ((11))
[27.] LEMMA V.
Page: 23 ((11))
[28.] PROBLEM XIII.
Page: 23 ((11))
[29.] PROBLEM XIV.
Page: 24 ((12))
[30.] SUPPLEMENT. PROBLEM I.
Page: 26 ((14))
[31.] PROBLEM II.
Page: 26 ((14))
[32.] PROBLEM III.
Page: 26 ((14))
[33.] PROBLEM IV.
Page: 28 ((16))
[34.] PROBLEM V.
Page: 28 ((16))
[35.] PROBLEM VI.
Page: 29 ((17))
[36.] General Solution.
Page: 29 ((17))
[37.] A SECOND SUPPLEMENT, BEING Monſ. DE FERMAT’S Treatiſe on Spherical Tangencies. PROBLEM I.
Page: 31 ((19))
[38.] PROBLEM II.
Page: 32 ((20))
[39.] PROBLEM III.
Page: 33 ((21))
[40.] PROBLEM IV.
Page: 33 ((21))
[41.] PROBLEM V.
Page: 34 ((22))
[42.] PROBLEM VI.
Page: 34 ((22))
[43.] PROBLEM VII.
Page: 35 ((23))
[44.] LEMMA I.
Page: 36 ((24))
[45.] LEMMA II.
Page: 36 ((24))
[46.] LEMMA III.
Page: 36 ((24))
[47.] LEMMA IV.
Page: 37 ((25))
[48.] LEMMA V.
Page: 37 ((25))
[49.] PROBLEM VIII.
Page: 38 ((26))
[50.] PROBLEM IX.
Page: 39 ((27))
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page |< < ((11)) of 161 > >|
23(11)
The point M being found as in the preceding Lemma, I ſay that it is a pro-
perty of the ſaid point, that MG x MB = MH x MA: as alſo that MF x
MC = ME x MI.
For joining CI and GH, it is evident that theſe lines will alſo be parallel.
Hence MI: MC: : MH: MG, but MI: MC: : MB: MA, therefore
MH: MG: : MB: MA, and MG x MB = MH x MA. Again MH: MG
: : MF: ME, but MH: MG: : MI: MC, therefore MF: ME: : MI: MC
and MF x MC = ME x MI.

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