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Navigation: The Method of the Marteloio (p. 47a)


Navigation: The Method of the Marteloio (p. 47a)


Venetian mariners often kept close to the coasts when navigating, but they still needed a method of course plotting—a technique called the marteloio. Michael says here that the marteloio was a method of navigating "mentally." The technique did not depend on the use of a sea chart, but on established rules applied to a table of trigonometric values that was pre-calculated for eight "quarter" winds. Michael writes out the table here. He then explains how to use the table to plot a course to a destination 100 miles to the east (levante) when sailing directly in that direction would be impossible. These kinds of calculations were crucial to navigation, but Michael placed his account of the marteloio in his section on mathematics.

See enlargement:

+ Ihesus + Questa raxion chiamada martoloyo per navichar a mente, chomo di sutto pono per singolo. Prima sie alargar, segonda sie avanzar, terza sie ritorno, quarta sie avanzo di ritorno, e chadauna de queste à fiolle 8. E prima: Alargar 8, zoè 20, 38, 55, 71, 83, 92, 98, 100. Avanzar 8, zoè 98, 92, 83, 71, 55, 38, 20, 0. Ritorno 8, zoè 51, 26, 18, 14, 12, 11, 10 1/5, 10. Avanzo di ritorno, zoè 50, 24, 15, 10, 6 1/2, 4, 2 1/5, 0. E per exenpio dela ditta riegolla ponamo che una tera te stia per levante mia 100, quanto voio andar in- tro levante e sirocho, che son quarte 2, che la tera me stia quarta de tramontana al griego, che son quar- te 7, e che seroyo alargo dal ditto luogo? E questo sie lo muodo sutto scritto per raxion sovra ditta. Prendi l'alargar de quel che tu domandi che tu vuol che romagna, che son quarte 7, che son 98/10. Poi zon- zeremo 2/4 che tu va e 7 che tu domandi, serano 9. Adoncha chì è lo ritorno de quarte 9, sono 10 1/5. Moltipichemo e dixemo in questo muodo 98/10 51/5, e molti- pichado insirà, moltipichado e partido, mia 99 48/50. E tanto seramo alargi dal ditto luogo //

+ Jesus + This method is called the 'marteloio' for navigating mentally, as I set forth systematically below. First is the distance off course; second is the advance; third is the return; fourth the advance on the return, and each of these has 8 daughters. And first: The distance off course 8, that is 20, 38, 55, 71, 83, 92, 98, 100. The advance 8, that is 98, 92, 83, 71, 55, 38, 20, 0. The return 8, that is 51, 26, 18, 14, 12, 11, 10 1/5, 10. The advance on the return 8, that is 50, 24, 15, 10, 6 1/2, 4, 2 1/5, 0. And for an example of this rule, let's say that a land is 100 miles to the east, how much do I want to go east southeast, which is 2 quarters, so that the land will be north by east, which is 7 quar- ters, and how far would I be from that place? And this is the method below written according to this method above said. Take the distance off course that you want that you want to remain, which is 7 quarters, which is 98/10, then we will add the 2 quarters that you go and the 7 that you seek, which will be 9. So here is the return of 9 quarters, which is 10 1/5. We multiply and we say in this way 98/10 51/5, and multi- plied together, multiplied and divided, is 98 44/50 miles. And we will be that far wide of the place.