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Dear Daniel (Joel, Terry and all), I fear that trying to find the right date of the "Carte Generale des Royaumes Etats & Domaines, que les Rois & La Couronne de la Grande-Bretagne ont Possédez ou Possédent en Europe en Afrique & en Amerique", is of no help for the question posed by you, Daniel. Your question was: how is it possible we face a map "drafted on a Lambert conformal conic with standard parallel of 75°" before its mathematization by Lambert in 1772? (Daniel post of yesterday) The problem is that its projection is not at all a "Lambert conformal conic with standard parallel of 75°" but simply and, I dare say, obviously, a polar stereographic projection, known and used since long time. Why you, Daniel, did not think about more obvious and simple solutions? And why you did not check it, before trying a more sophisticated and antihistorical solution? I wondered why the cartographer of the "Carte Generale . . ." had to choose a "conformal conic with standard parallel of 75°" and not one of the many known and used in his time!? In fact, he used a stereographic projection. The problem is solved whatever may be the date of compilation of that map. Ciao. vladimiro Il giorno 30/set/2011, alle ore 02.55, Daniel Strebe ha scritto: > This is a MapHist list message (when you hit 'reply' you're replying to the > whole list) > o + o + o + o + o + o + o + o + o + o + o + o + o + o + o + o + o + o + o + > > > Vladimiro: > > Thanks for the comments. Normally I would not be (too) surprised to find a > map projection used earlier than it was known to have been developed. Most > map projections of the era were geometrical in conception; they were > developed in order for their manual construction to be tractable. It would > not be surprising for two people to come up with the same idea independently. > Such ideas do not represent new mathematics; they represent new assemblages > of known methods. > > This map is a another matter entirely. The mathematical principles upon which > it was founded had not been even been described yet. For this map to exist > from the era it appears to exist from, would mean that the history of > mathematics needs to be revised. > > Only two conformal projections preceded this one. Neither was developed for > its conformality. The fact that they were conformal was incidental and > unrecognized in any modern sense. One of those is Mercator’s famed 1569 > projection, developed for the virtue of straight rhumbs. The Mercator could > not be constructed by purely geometric means; it required laborious > calculations to set up the parallel spacing. The other early conformal > projection is the stereographic, which is a perspective projection. It was > widely used in that era because it could be constructed geometrically, and > gave double hemispheric views with the meridians and parallels being > orthogonal. > > By the known history of map projections (and mathematics), the conic > projection of this map “Carte Generale des Royaumes Etats & Domaines…” ought > to be a perspective conic or an equidistant conic or a conic with ad hoc > parallel spacing. It is trivially not an equidistant conic because the > parallel spacing varies blatantly. With more investigation, I have ruled out > any perspective conic. There simply are no other candidates. This is either a > Lambert conformal conic or an ad hoc contrivance that magically mimics a > Lambert to within the margins of error inherent in the paper medium. The > probability of that last happening is remote. > > The question then becomes, what motivated this projection? Unlike the > Mercator or the stereographic, there is no rationale that could lead to the > projection except the wish for a conformal projection. It has no other useful > properties: Rhumbs are not portrayed favorably; distances are not correct > across useful portions of the map; overall distortion is not minimized; > directions in the large receive no favorable treatment. > > In other words, someone made it specifically to be a conformal conic. Yet the > rigorous notion of conformality “should” not have existed. The mathematics > needed to calculate the projection’s coordinates (the generating formulæ) are > advanced for the time but not intractable. What was intractable was the > mathematics needed to characterize the conformal condition and to thence > construct those generating formulæ in order to fulfill the conformal > conditions. > > I am more inclined to think that the map’s dating is wrong than to think > someone developed (and then calculated!) such a projection in 1736. Hence my > appeal to those with copies of the map in their collections. > > Best, > — daan Strebe > > > On Sep 29, 2011, at 2:21 AM, Vladimiro Valerio wrote: > >> This is a MapHist list message (when you hit 'reply' you're replying to the >> whole list) >> o + o + o + o + o + o + o + o + o + o + o + o + o + o + o + o + o + o + o + >> >> Daniel and all, >> just one short, brief, remark. >> >> Before Gaspard Monge published his fundamental treatise Géometrie >> Descriptive in 1799 (an VII of Republican Calendar) the method of orthogonal >> projections were used almost all over the world since the first millennium >> Before our Era. Monge put together and gave a geometrical structure, founded >> on principles, to all the disseminated pieces of orthographic >> representations. >> It means that well before Monge we may found "perfect" orthogonal >> projections (see Durer in 1525, also Piero della Francesca in 1475 c. and . >> . . so on back) even if they are not so defined or claimed! >> >> The way in which the human mind may reach goals and scientific conquests are >> quite different. Philosophically speaking, we may reach the truth in several >> ways. >> >> with sympathy >> vladimiro >> >> >> Il giorno 29/set/2011, alle ore 08.40, Daniel Strebe ha scritto: >>> This is a MapHist list message (when you hit 'reply' you're replying to the >>> whole list) >>> o + o + o + o + o + o + o + o + o + o + o + o + o + o + o + o + o + o + o + >>> Colleagues: >>> >>> I would appreciate help from those with this publication in their >>> collection: >>> “L’Histoire d’Angleterre”, Paul de Rapin-Thoyras, 1724 and later >>> >>> with Volume XI, p. 121, containing the map titled, >>> “Carte Generale des Royaumes Etats & Domaines, que les Rois & La >>> Couronne de la Grande-Bretagne ont Possédez ou Possédent en Europe en >>> Afrique & en Amerique” >>> >>> I am studying this map, stated by the sell to have been published circa >>> 1736. >>> >>> The problem is that the map is impossible. I bought the map as a curiosity >>> because it is drafted on a conic projection, which were rarely used at the >>> time. When I received the map I wanted to ascertain which specific conic it >>> is. I am bemused to report that, with a high degree of confidence, the map >>> is drafted on a Lambert conformal conic with standard parallel of 75°. >>> >>> The problem with this assessment is that the projection and the >>> mathematical principles that motivate it were supposedly unknown in 1736. >>> The projection, the mathematics for it, and the entire mindset that >>> motivates it, were published by Johannes Heinrich Lambert in 1772. >>> Lambert’s treatise is considered the seminal work in mathematical >>> cartography. The projection wasn’t supposed to be possible before that >>> publication. >>> >>> My questions: >>> >>> • Does this map exist in editions of “L’Histoire d’Angleterre” prior to >>> 1772? >>> • Does the map look substantially like this? >>> http://mapthematics.com/Downloads/CarteGenerale.png >>> >>> Thanks & regards, >>> — daan Strebe >>> >>> _______________________________________________ >>> MapHist: E-mail discussion group on the history of cartography >>> hosted by the Faculty of Geosciences, University of Utrecht. >>> The statements and opinions expressed in this message are those of >>> the author and do not necessarily reflect those of the University of >>> Utrecht. The University of Utrecht does not take any responsibility for >>> the views of the author. >>> List Information: http://www.maphist.nl >>> >>> Maphist mailing list >>> [email protected] >>> http://mailman.geo.uu.nl/mailman/listinfo/maphist >> >> _______________________________________________ >> MapHist: E-mail discussion group on the history of cartography >> hosted by the Faculty of Geosciences, University of Utrecht. >> The statements and opinions expressed in this message are those of >> the author and do not necessarily reflect those of the University of >> Utrecht. The University of Utrecht does not take any responsibility for >> the views of the author. >> List Information: http://www.maphist.nl >> >> Maphist mailing list >> [email protected] >> http://mailman.geo.uu.nl/mailman/listinfo/maphist > > _______________________________________________ > MapHist: E-mail discussion group on the history of cartography > hosted by the Faculty of Geosciences, University of Utrecht. > The statements and opinions expressed in this message are those of > the author and do not necessarily reflect those of the University of > Utrecht. The University of Utrecht does not take any responsibility for > the views of the author. > List Information: http://www.maphist.nl > > Maphist mailing list > [email protected] > http://mailman.geo.uu.nl/mailman/listinfo/maphist
_______________________________________________ MapHist: E-mail discussion group on the history of cartography hosted by the Faculty of Geosciences, University of Utrecht. The statements and opinions expressed in this message are those of the author and do not necessarily reflect those of the University of Utrecht. The University of Utrecht does not take any responsibility for the views of the author. List Information: http://www.maphist.nl Maphist mailing list [email protected] http://mailman.geo.uu.nl/mailman/listinfo/maphist
