Exercises on Euclid and in modern geometry for the use of schools, private students, and junior university students (1881)
McDowell, James L · Cambridge, Deighton, Bell, and Co. · leaf 169
de-pendently. 175. The reciprocals of lines in harmonical progressionare in arithmetical progression, and conversely, the reciprocalsof lines in arithmetical progression are in harmonical progres-sion. (See 150, Def.) It will be sufficient to consider three consecutive terms of theprogression,… … Draw OD, OB, OC, OAf respectively perpendicular to OD,OB, OG, OA. Therefore OA is parallel to AD, and the anglesDOD, BOB are right angles; therefore, taking away the commonangle BOD, the angles DOB and DOB are equal. Similarly, theangles BOO and BOG, GO A and CO A! are equal. Therefore thepencils 0…
Geometry
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