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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Impossible lunar example
From: George Huxtable
Date: 2010 Sep 2, 09:19 +0100
From: George Huxtable
Date: 2010 Sep 2, 09:19 +0100
Douglas Denny wrote- "Which might be causing the confusion in the text with Janet Taylor because spherical angles are not solid angles." Yes they are. A spherical triangle on the Earth's surface subtends a solid angle at its centre. That is presumably the solid angle that the Euclid statement applies to. George. contact George Huxtable, at george@hux.me.uk or at +44 1865 820222 (from UK, 01865 820222) or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. ----- Original Message ----- From: "Douglas Denny"To: Sent: Thursday, September 02, 2010 9:10 AM Subject: [NavList] Re: Impossible lunar example Dear Robin, I have looked at:www.fer3.com/arc/m2.aspx?i=113627 (second jpg) and now understand what is your query. It seems to me that Janet Taylor has it wrong completely. There is no proposition 20 book XII in the modern set of Euclids Elements which I looked up; but there is a prop 20 in book XI which deals with _solid geometry_ and solid angles... prop 20 book XI: "If a solid angle is contained by three plane angles, then the sum of any two is greater than the remaining one". Which might be causing the confusion in the text with Janet Taylor because spherical angles are not solid angles. ------ In a spherical triangle, you can have, in a limit, two sides of 90 and one of 180 -which is a hemisphere. ------- I have put the values for the spherical triangle in my calculator with HP as quoted, (now having amused myself recently by programming it for clearing lunar distances) and find the result to be: 103deg-0'-35".2 ... not the 103deg-0'-16" as suggested by Janet Taylor in the text. Perhaps my calculator comes up with slightly different value because it includes 'modern' refraction correction which might be different with what they used then. Douglas Denny. Chichester. England. ---------------------------------------------------------------- NavList message boards and member settings: www.fer3.com/NavList Members may optionally receive posts by email. To cancel email delivery, send a message to NoMail[at]fer3.com ----------------------------------------------------------------