Rome: Sumptibus N[icoli]. A[ngeli]. Tinassij, 1679.
Two volumes: Octave: 12.8 x 9 cm. Vol. I: , 316,  p. Collation: A12 (-blank A1), A-T8, V6, chi1. With 24 added woodcut “plates”. Vol. II: ,  p. Collation: π1, A-Z8, Aa-Bb8, C1 (-blank C2)
Complete in 2 volumes. A fine set in matching contemporary vellum, complete with all 24 inserted leaves with woodcuts (as called for). The text is in fine, crisp condition with only minor cosmetic faults: Vol. I: Light dampstain to head of first few leaves only. Cut a little close, with some headlines slightly shaved. 24 inserted woodcuts. Vol. II: light dampstain to sigs. L and M. only. In addition to the added woodcut “plates”, the first volume is illustrated with numerous diagrams. The Greek encomium “Eis aideisimazaton patera Athanasion Kircherion enkōmion" is signed by Johann Theodor Fritzer.
“The ‘Tariffa’ is perhaps the rarest of all Kircher’s works. It is organized in the traditional format for mathematical works, with problems, propositions and proofs. The term ‘tariffa’ was used in Kircher’s days for compilations of tables used by navigators ‘from which valuable knowledge might be had without labor,’ but, as is explained in the preliminary pages, Kircher titled his book ‘Tariffa’ ‘not only because valuable knowledge might be had, but because one may understand [from it] the universal art of mathematical computation.’”(Merrill)
“The ‘Tariffa’, together with Kircher’s multi-purpose calculator and measuring device, the Pantometrum Kircherianum, which for years had already provided the instrumental equivalent, is the ultimate expression of Kircherian mathematics… Its aim is practical, even if the author, in accordance with the Lullian ideal, never accepts the separation of the practical from the theoretical, and firmly believes that the ‘combinatorial art’ -the supreme speculative tool- will provide him the means ‘to distill all the scientific arts, both practical as well as speculative, down to one universal principle’…
“The introduction in the first volume is strictly Kircherian in its ideology: Kircher wrote the book at the request of nobles and illustrious persons who, occupied with weighty matters and obligations, do not have time to study mathematics and make calculations. The dedication to Livio Odescalchi, Duke of Ceri and nephew of Pope Innocent XI, was written by the editor of the book, the Bolognese Benedetto Benedetti, professor of mathematics at Rome, who worked “iussu, et precibus huius Authoris”(at the direction and request of the author). [Merrill asserts that Benedetti is a pseudonym and that Kircher himself wrote the dedication and preface, and revised and amplified the work, adding “This is the only work published by Kircher pseudonymously”.] In the preface we are told that Kircher had other obligations that made it impossible for him to finish editing the “Tariffa”, a work that, given its great value, could not be delayed any longer.
“The book is divided into five Syntagmata, listed at the beginning to highlight the thematic breadth of the work. Syntagma I teaches how to calculate flat areas. Syntagma II extends the calculation to the cubature of solid bodies, and gives suggestions for other numerical operations…. Syntagma III concerns plane trigonometry. In this chapter (p. 182 ff.) the Pantometrum Kircherianum is presented: an instrument that summarizes the functions of the trigonometric quadrant and tables, and is used to make planimetric surveys and other measurements… Syntagma IV, pompously called ‘Metamorphoticum’, teaches how to transform flat geometric figures into equivalent squares, or to multiply the surfaces while keeping them similar to themselves. The value of 22/7, suggested by Archimedes, is assumed for the approximate squaring of the circle. The equivalence of the spatial figures is made with respect to the sphere.
Syntagma V (p. 259 ff.) is dedicated to the Pantometrum, its construction, and its use. The device, as its name suggests, was universal, capable of measuring all “latitudes, longitudes, altitudes, depths and surfaces, terrestrial and celestial bodies, and whatever indeed we are accustomed to doing with other instruments.” It consisted of a square frame, a sighting tube (dioptra), a disc with a built-in compass, and a space for putting a sheet of paper. The disc could turn freely within the square, or be locked in a fixed position. Mounted on this apparatus was a movable ruler parallel to the edge of the square on which the dioptra was attached. The device could be used to measure the distance of objects by triangulating from two different points on a baseline.
“The ‘Tariffa’, together with the Pantometrum, which for years had already provided the instrumental equivalent, is the last expression of Kircherian mathematics… It provides us with the precise measure of Kircher's mathematical aptitudes: therefore it allows to understand its strengths and its limits…. It is quite obvious that he knows how to use all these arithmetical, geometrical and mechanical tools for the questions that his experience proposes to him; and they are always for him (as already for Ramus) practical questions… He grasps well the degree of mathematical precision required by the problem at hand, and he stops there, he goes no further. That which requires greater mathematical rigor he leaves to Clavius and other true mathematicians.”(Saverio Corradino, “Athanasius Kircher matematico” in Studi Secenteschi , 37 (1996), pp. 159-180)
“The ‘Kircherian Tables’ [offered] a detailed description of the miraculous Kircherian combinatorial art that would quickly allow all the princes and nobles of Europe— and presumably anyone else ‘occupied by more important business’ who could read Latin—to master all of geometry and arithmetic. In fact, Kircher himself seems to have become exactly that sort of person by 1679—at least this was how his associates wished to describe him rather than acknowledging that he was no longer capable of completing his own books. Kircher consigned the final preparation of the ‘Tariffa’ to Benedetto Benedetti, professor of mathematics at La Sapienza, who described how ‘new occupations of great moment’ had obliged Kircher to offer him the privilege of becoming its editor.”(Findlen, “Athanasius Kircher, The Last Man who Knew Everything”, p. 4).
De Backer-Sommervogel IV, col. 1070, no. 37; Merrill 28; Clendening 12.24; De Backer I, 431-31; Brunet III, 669. Literature: Saverio Corradino, “Athanasius Kircher matematico” in Studi Secenteschi , 37 (1996), pp. 159-180. The plates in Vol. I are found at pages: 28, 44, 138, 158, 166, 184, 186, 198, 199, 208, 222, 224, 246, 248, 250, 252, 254, 264, 266, 268, 274, 282, 284, 292. North American copies: BYU, Hopkins, Mich, Wisc, Clendening, Berkeley, Minn, Harv, Columbia, Stanford, Huntington, Boston College, NY Public, LC.