Danti's numbers

[Gianni Ferrari]

Danti’s numbers. On the facade of the church of Saint Maria Novella in Florence, Egnazio Danti in 1572 designed and put an elaborate astronomical instrument from him called “Il quadrante Astronomico di Claudio Tolomeo” (The Astronomical quadrant of Claude Ptolemy), an armillary sphere and 4  sundials.    The quadrant was so called by Danti because it was described by Ptolemy in the Almagest.  It is made by a plate of marble, with sides of 154 cm and 146.5 cm and with a thickness of around 8 cm, fixed perpendicular to the facade of the church,  that is turned toward South: the two sides are therefore faced East and West.    The quadrant was set at around 7 m. of height, was supported on  a marble bracket and brought two horizontal gnomons set in proximity of the higher South vertexes of the faces.  The instrument had been built for measuring the height of the Sun in its passage across the meridian (the Sun’s rays are in this condition tangent to the faces) : from this measure, made on the Equinoxes, it is possible to calculate the value of the Ecliptic  inclination.   It also contains 3 solar clocks with Babilonic hours (counted from dawn), Italic hours (counted from sunset) and Astronomical hours (counted from noon).    Today the quadrant has been moved and it is no more in its original position: I don't know for what reason (perhaps for a restoration), when it was removed and where it is.    The bracket that sustained the quadrant is formed by two parts,  one on the other. The superior part contains on the West side a writing in which Danti devotes the tool to the Tuscany grad duke Cosimo I.                   It says :  COSM. MED. MAGN. ETR. DUX NOBILIUM ARTIUM STU DIOSUS ASTRONOMIAE STUDIOSIS DEDIT ANNO D. MDLXXII     On the East side there is the writing where we may read the numbers that are of interest to Divine Kumahs.   DILIGETI OBSERVATIONE PERSPEC TA TROPICOR DISTANZIA G. XLVI. LVII. XXXIX. L. ET ANGULO SECTIONIS G. XXIII. XXVIII. XXXXVIIII. LV.   That means : with industrious observations (I find) the distance between the Tropics (that is)  46° 57’ 39” 50’”  and the angle of the section, (that is)   23° 28’ 49” 55”’ These numbers give, in the pure sexagesimal notation used by Ptolemy and also by Danti, the value of the ecliptic obliquity and his double.  The angles are given writing the number of the degrees, of the arc minutes (primi), of the arc seconds (secundi)  and of arc thirds (terti).  Then 23° 28’ 49” 55”’ = 23° + 28/60 +49/(60x60) + 55/(60x60x60) = 23.480532°  with the precision (supposed, but not true) of  1 "tertius" = 1/60 of arc second , about 5 millionth of degree.  Modern calculations give for the value of the ecliptic inclination in 1572 the value 23.4948 = 23° 29’41.3”  : the error of Danti is about 51”. In the lowest part of the bracket, under the writings, we find two sundials facing East and West with  French hours (or as Danti writes “ore Franzesi”), that is with the hours counted from midnight ( as in our local solar time). On the facade of the church, that faces South, there are another two sundials on the sides of the Quadrant: one with  seasonal hours (Danti writes unequal or Planetary hours), the other with  Canonical hours (system used by the monks of the monasteries in the Middle Ages).    All the  information that I have reported come from two books  written by the well known Italian dialist Giovanni Paltrinieri:  the beautiful book “Meridiane e orologi solari d’Italia” (Sundials and solar clocks of Italy) and a small but precious  booklet with only 34 pages, in which Paltrinieri describes completely the sundials and the quadrant of Danti, departing from the volume “Trattato dell’uso e della fabbrica dell’astrolabio” (Treatise on the use and on the making of the astrolabe ) written by Egnazio Danti in 1569.    If someone has interested I can send 4 photos of the sundials , taken on June 8th 2004 : the images are enough heavy (about 500-700 kb each)     Gianni Ferrari