Teaching Astronomy & Mathematics in the Early Modern Period

Johannes de Sacro Bosco (c.1195-c.1256)

Libellus de Sphaera. Accessit… Computus Ecclesiasticus [with] Libellus de Anni Ratione, Cisius Ianus in carmine redactus.

Wittenberg: Johann Krafft, 1550


Bound with:

Gemma Frisius (1508-1555)

Arithmeticae practicae methodus facilis, per Gemmam Frisium medicum ac mathematicum.

Wittenberg: (Heirs of Peter Seitz), 1551 (1550)

Octavo: Two volumes in one: 16 x 10 cm. I. 136 lvs. Collation: A-R8 (with final two blanks present). II. 86 lvs. Collation: A-L8

Woodcut astronomical diagrams and mathematical equations throughout. First work with an armillary sphere on the title page and volvelles on four diagrams (two of them hand-colored) Second work with a woodcut vignette of a teacher and pupil on the title. Bound in contemporary blind-stamped pigskin over wooden boards, stamped "IRH 1515" [or 1518?] on upper board and with a roll-tool dated 1544. With two catch-plates and one clasp, binding rubbed and slightly chipped. With inscriptions on the fffep dated 1551 and 1553 (names scored through); Bernhardus Matthaeus, inscription dated 1670, written over an earlier inscription, and his black wax seal on title with the initials BM.

A fine sammelband comprising Sacrobosco's "Sphere", the most important astronomical work of the Middle Ages, the influence of which continue to be felt into the 17thc., with the "Mathematical method", the most popular mathematics textbook of the 16thc. , written by the great astronomer-cartographer-mathematician Gemma Frisius. The Sacrobosco volume also includes "Themata qvae continent, ethodicam tractationem de horizonte rationali" of Erasmus Reinhold (1511-1553).

Sacrobosco’s “Sphere”:

“Sacrobosco’s fame rests firmly on his ‘De Sphaera’, a work based on Ptolemy and his Arabic commentators, published about 1220 and antedating the ‘Sphaera’ of Grosseteste. It was quite generally adopted as the fundamental astronomy text, for often it was so clear that it needed little or no explanation. It was first used at the University of Paris. There are four chapters to the work. Chapter one defines a sphere, explains its divisions, including the four elements, and also comments on the heavens and their movements. The revolutions of the heavens are from east to west and their shape is spherical. The earth is a sphere, acting as the middle (or center) of the firmament; it is a mere point in relation to the total firmament and is immobile. Its measurements are also included. Chapter two treats the various circles and their names- the celestial circle, the equinoctial, the movement of the ‘primum mobile’ with its two parts, the north and south poles, the zodiac, the ecliptic, the colures, the meridian and the horizon, and the Arctic and Antarctic circles. It closes with an explanation of the five zones. Chapter three explains the cosmic, chronic, and heliacal risings and settings of the signs and also their right and oblique ascensions. Explanations are furnished for the variations in the length of days in different global zones namely the equator, and in zones extending from the equator to the two poles. A discussion of the seven climes ends the chapter. The movement of the sun and other planets and the causes of lunar and solar eclipses form the brief fourth chapter.” (Dictionary of Scientific Biography)

Gemma Frisius' "Arithmeticae Methodus":

"Gemma Frisius applied his mathematical abilities in the areas of geography, astronomy and map making. His work on applying trigonometric methods to astronomical problems led to his correctly determining that comets displayed a proper motion against the background stars. He described the theory of trigonometric surveying and was the first to use triangulation as a means of locating places. He also proposed a method for finding the longitude of a place using a clock. Gemma produced a world map with lines and longitude and sophisticated variations on the astrolabe such as the “astronomical ring.” The instrument is suspended by a piece attached to a split ring, allowing the outer meridian ring to slide and be set for a given latitude using two engraved quadrants, one for northern, one for southern latitudes. The self-orientating device avoids the use of a magnetic compass. His "Arithmeticae Methodus" was first published in 1540, became one of the most successful mathematics book of the 16thc."(Nolan)

Sacro Bosco: Tomash & Williams S5, S4; USTC 667489; VD16 J728; Gemma: Tomash & Williams G33; Hoogendoorn p.358 GemF04 (no copy examined); VD16 G1115 (same setting of the title-page and same colophon, but with date 1550 on title-page); Rara Arithmetica p. 203