Euclid i. 32 Corr

Details Euclid i. 32 Corr Euclid i. 32 Corr

Nov 1900

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1900natur..63...58t&link_type=abstract

Nature, Volume 63, Issue 1620, pp. 58 (1900).

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HAMBLIN SMITH writes, these ``corollaries were first given in Simson's edition of `Euclid''' (edition 1872, &c.). J. Walmstey, ``Introduction to Geometry'' (1880, &c), styles them Simson's corollaries. Hall and Stevens say these ``theorems were added as corollaries to Prop. 32 by Robert Simson'' (1888, &c), and finally, Loney, in his edition of Todhunter's ``Euclid,'' writes, ``the corollaries were added by Simson.'' Many years ago it was pointed out to me that these corollaries, with many interesting applications, were given by Clavius in his edition of the Elements (1607), see pp. 105-108. On p. 107, he cites ``ex Campano, si pentagoni singula latera producantur in partem utramque, ita ut quælibet duo extra pentagonum coeant, efficientur quinque anguli ex lateribus coeuntibus æquales duobus solum rectis.'' Clavius probably is not the first publisher of these results.

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