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Dear all,
I report the table by Luis with the addition of the third column from the 
toleta de Martolio by Andra Bianco (1436) multiplied by 1.75, being 10 its base 
against 17.5 in the others.
The figures from the marteloio fit quite well the modern numbers and are very 
close to the ones by Pedro de Medina.


                        Modern calc.            P. de Medina    Rodr. Zamorano  
old by Zamorano Figure on MapHist       Ret. marteloio (x 17.5) 
Norte                   17.50                   17.50                   17.50   
                        17.5                            17.5                    
                17.5
                                17.84                                           
                                                                                
        18                                              17.85
NNE                     18.94                   19.33                   19.38   
                        19.5                            19                      
                        19.25
                                21.05                                           
                                                                                
        21                                              21
NE                              24.75                   24.50                   
24.75                           25.0                            25              
                                24.5
                                31.50                                           
                                                                                
        31.5                                    31.5
ENE                     45.73                   45.00                   45.75   
                        46.5                            46                      
                        45.5
"E cuarta ENE"  89.70                   89.00                   89.75           
                88.0                            88                              
                89.25

The origin of the XVI numbers may be rooted in the figures from the Marteloio, 
which are the oldest numbers applied to courses.

vladimiro


Il giorno 31/dic/2011, alle ore 13.29, Luis Robles Macías ha scritto:
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> 
> 
> Dear all,
> 
> I have compared the series of numbers of the wind rose sent by Bill Thoen 
> (18, 19, 21,... 88) with similar series found in two Spanish 16th-century 
> navigation manuals, by Pedro de Medina (Regimiento de navegación, 1563) and 
> Rodrigo Zamorano (Compendio de la Arte de Navegar, 1581) and with a modern 
> calculation. You will find a table with all the numbers at the end of this 
> message.
> 
> The three sets of numbers are are all very close to each other but subtle 
> differences nevertheless exist.The figures reported by Mr Thoen are equal to 
> those by Zamorano, rounded to the closest integer, except for the last one, 
> 88. This value, rather inaccurate, is far away from Zamorano's 89 3/4 (very 
> close to the real 89.70) and also from Medina's 89.
> 
> Interestingly, Zamorano also reports the contents of a similar older table 
> (no date mentioned) that gives a value of 88 for this angle. This  hints that 
> Mr Thoen's figure might date to earlier than 1581, maybe the first half of 
> the 16th century. I am curious to compare these numbers with other 
> 16th-century sources already mentioned in the discussion. 
> 
> Best,
> Luis A. Robles Macías
> 
> Blog: http://historiaymapas.wordpress.com/
> 
> 
> 
> Modern calculation    Pedro de Medina Rodrigo Zamorano        Old table cited 
> by Zamorano     Figure shown on MapHist
> Norte 17.50   17.50   17.50   17.5    17.5
> 
> 17.84 
> 
> 
> 18
> NNE   18.94   19.33   19.38   19.5    19
> 
> 21.05 
> 
> 
> 21
> NE    24.75   24.50   24.75   25.0    25
> 
> 31.50 
> 
> 
> 31.5
> ENE   45.73   45.00   45.75   46.5    46
> "E cuarta ENE"        89.70   89.00   89.75   88.0    88
> 
> 
> 2011/12/28 Ed Dahl <ed.d...@sympatico.ca>
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> News: If you don't get messages anymore, go to http://www.maphist.nl for news 
> about the new MapHist Forum
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> 
> 
> 
> I sent some of the messages relating to this topic to Corradino Astengo in 
> Savona, Italy, and he sent this first reply. I asked his permission to post 
> it 
> on MapHist, and he added the 2nd reply and said posting it was fine.  
>       Ed Dahl
> 
> *****
> Begin forwarded message:
> 
> From: 2...@unige.it
> Date: December 28, 2011 3:07 AM
> To: Ed Dahl <ed.d...@sympatico.ca>
> Subject: RE: Odd Numbers on an Old Wind Rose
> 
> Dear Ed,
> I agree with Joaquim Alves Gaspar and Wolfgang Köberer. It is an application 
> of
> the "Regimiento", but the figures have been rounded so it is impossible to say
> if it is the original (Evora and Munich) or the one corrected by Pedro Nunes.
> Everything is clearly explained in the book by Joaquim Bensaude, L'astronomie
> nautique  au Portugal a l'époque des grandes decouvertes, Berne 1912/17,
> reprinted by N. Israel in 1967.
> Dino
> 
> 
> On Dec 28, 2011, at 10:50 AM, Corradino Astengo wrote:
> 
> I agree also with Vladimiro Valerio: the system of the "Regimento" is the same
> as the "toleta", but it is in a way more refined, because you don't need to
> calculate the miles (or leagues) sailed, which is always very difficult, in
> order to know your position. It is sufficient to follow a rhumb and to
> calculate your latitude. You might also keep track of the miles sailed in 
> order
> to compare the two different observations, but it is suggested, in case they 
> are
> different, to use the one calculated with the latitude. The "Regimento" is 
> also a
> system to calculate the longitude.
> Fernando Colombo at the Junta de Badajoz gave in 1424 a "parecer" in which he
> stated that to resolve the problem of Moluccas it was necessary to calculate
> their longitude and he suggested five different methods to do it, the first of
> them is this one, even if he admits that it is unsafe "por la imposibilidad 
> que
> hay de caminar el navio por reta linea".
> Cheers
> Dino
> 
> 
> 
> 
> 
> 
> 
> 
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