The elements of Euclid for the use of schools and colleges; comprising the first six books and portions of the eleventh and twelfth books; (1903)
Euclid, Todhunter, I. (Isaac), 1820-1884, ed. edt, Simson, Robert, 1687-1768, ed. edt · London; New York, Macmillan · leaf 409
to DN.Similarly CK is parallel to DM.Now TD : TN :: TM : TD; [IIL 37, YL 16, :: TK : TC ; [VL 4. .*. rect. TC, TD^rect. TK, TN.Similarly rect. TL, TM^rect.TC, TD.If each of the given circles is without the other we may suppose thestraight line which touches both circles to meet AB at T^ hetween A… … Since AK, BM are parallel, .. TK is to TM as AK to BM ;and similarly TL is to TN as AK to BN,i.e. in the ratio of the radii; .*. all straight lines drawn through T, or T, are cut b}^ tlie circles inthe same constant ratio. Hence either of the points, T or T, is called a Centre of Similitude,one…
Euclid's Elements · Geometry · Mathematics, Greek
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