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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

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.

Luis A. Robles Macías


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

18  NNE 18.94 19.33 19.38 19.5 19

21  NE 24.75 24.50 24.75 25.0 25

31.5  ENE 45.73 45.00 45.75 46.5 46  "E cuarta ENE" 89.70 89.00 89.75 88.0

2011/12/28 Ed Dahl <>

> This is a MapHist list message.
> News: If you don't get messages anymore, go to for
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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: *
> *Date: *December 28, 2011 3:07 AM
> *To: *Ed Dahl <>
> *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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