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 417
/. AN is the harmonic mean between AH and AC Corollary. Since AP^:^ AN . AG, AV is the geometric mean IjetweenAN and AO, that is, The geometric mean between tivo given straight lines AB, AC is alsothe geometric mean between the arithmetic and harmonic ineans betweenthe same two straight lines. 94.… … For BD : DC :: BA : AC, [VI. 3. and BE : EC :: BA : AC ; [VI. 4. /. BD : DC :: BE : EC. .-. BE : BD :: EC : DC ; [V. 16. that is, as BE - BC to BC-BD.BD, BC, BE are in harmonical progression. 95. Def. When a straight line BC is divided internally and exter-nally in the same ratio at D and E, the…
Euclid's Elements · Geometry · Mathematics, Greek
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