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 170
art of the above theorem may be expressed thus:— .1 1-1 2 1 1 AB AC + AD °r AB~AO + AD which is to be read, twice the reciprocal of the harmonic meanbetween two lines is equal to the sum of the reciprocals of tlieextremes. 176.] AND IN MODERN GEOMETRY. 141 176. Given two unequal straight lines;… … semicircle with centre Ot Draw the tangent AP and PB perpen-dicular to AD. Join PO. , AO is evidently the arithmetic mean, for the difference betweenAC and AO is equal to the difference between AO and AD. AP is the geometric mean, for AP2 =AC.AD (III. 36). Also AB is the harmonic mean, for PB is…
Geometry
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![An illustration from Nicolai Copernici Torinensis De reuolutionibus orbium coelestium, libri VI : Habes in hoc opere iam recens nato, & aedito, studiose lector, motus stellarum, tam fixarum, quàm erraticarum, cum ex ueteribus, tum etiam ex recentibus obseruationibus restitutos: & nouis insuper ac admirabilibus hypothesibus ornatos. Habes etiam tabulas expeditissimas, ex quibus eosdem ad quoduis tempus quàm facillime caculare poteris. Igitur eme, lege, fruere. [Line in Greek] (1543)](https://img.insideoutlibrary.com/img/200/ia-nicolaicopernici00cope-168-96.webp)
