JF Ptak Science Books Post #81 (Expanded)
These lovely images weren’t intended to show people living in the Renaissance and Baroque eras how to actually record data on their hands—they were intended rather as templates to show how they could use their fingers and hands for calculating and as memory devices. Much like Frances Yates has shown us so beautifully in The Art of Memory and how info and data was stored in imagined and compartmental palaces in the mind (relying upon images), the hands were also used as a theatre of memory in addition to extended calculation.
These mnemonic devices were necessary—especially during the Renaissance—because of the general lack of and access to affordable vellums or paper and writing instruments. Having notebooks filled with memoir or history of calculation was generally not something that was happening for even the not-wealthy but not struggling class. These mental images were used widely in the areas of religion, palmistry, astrology mathematics, astronomy, astrology, alchemy, music, and other such fields. 
The first image (from a German manuscript) of the hand-theatre was found and deciphered by Claire Richter Sherman (Folger Shakespeare Theatre) and is religious in nature, an intentional piece of memory for the devoted and for devotions. The needs of religion were splayed out as the hand was opened and fingers flexed, and working from thumb to pinkie, from finger tip and joint—“do God’s will, examine your conscience, repent, confess”, and so on, and above all be content with your lowly penitente stature. If there were 28 of these admonitions or reminders at different points of the hand and you memorized them all, it would be a much simpler time to recall and keep them in order if you merely had to touch a part of your hand where that memory should be to invoke what it was you were supposed to do. Therefore you could theoretically cast about with your creator with your hands in your pockets—if you had pockets.
The next two images (including the enlargement of the hand section) are from a work from 1587 entitled Musique and are attributed to John Cousin the Younger (1522-1597).
The basic premise for this device—it seems to me—was to be able to order the different chords of 20 different instruments. 
Another musical hand mnemonic was the Guidonian hand, a survivor of Medieval times, and possibly named after Guido of Arezzo (a musical theorist), and was an aid to singers learning to sight sing.
The entry for the Guidonian hand in Wiki explains it use rather well: “The idea of the Guidonian hand is that each portion of the hand represents a specific note within the hexachord system, which spans nearly three octaves from "Γ ut" (that is, "Gamma ut") (the contraction of which is "gamut", which can refer to the entire span) to "E la" (in other words, from the G at the bottom of the modern bass clef to the E at the top of the treble clef). In teaching, an instructor would indicate a series of notes by pointing to them on their hand, and the students would sing them. This is similar to the system of hand signals sometimes used in conjunction with solfege…”
The final two examples come from Jakob Leupold’s (1674-1727) Theatrum Machinarum (1724)—this was a complex work involving nine sections and addressed the theoretical aspirations of engineering (load, flexure, that sort) and its applications to its daily practitioners. In one section of the book he sought to explain the connections (and correlations) of hand motion and symbolism to the origins of the number systems, carrying it out further still into body language, so that two people conversant in these symbols could talk and bargain between themselves in economic/body terms. Barbara Maria Stafford, in her Artful Science, Enlightenment,
Entertainment and the Eclipse of Visual Education (1994) points out the long history of this tradition, and that it reached far back into misty time: Leupold knew that Appian, the Venerable Bede, and Aventinus had been fascinated by manuloquio, or natural language with the hands. He thus linked counting to a global….medium of prearranged gestures…”
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