In the preface to the appendix containing the local arithmetic he states that, while devoting all his leisure to the invention of these abbreviations of calculation, and to examining by what methods the toil of calculation might be removed, in addition to the logarithms, rabdologia and promptuary, he had hit upon a certain tabular arithmetic, whereby the more troublesome operations of common arithmetic are performed on an abacus or chess-board, and which may be regarded as an amusement A facsimile of this document is given by Mark Napier in his Memoirs of John Napier (1834), p. 248.
In his large study, the walls of which were hung to the ceiling with Persian rugs, bearskins, and weapons, sat Dolokhov in a traveling cloak and high boots, at an open desk on which lay an abacus and some bundles of paper money.
He wrote also treatises on the astrolabe (a copy of this is in the British Museum), on the abacus (three copies exist in the Vatican library, the library of Leiden University and the Bibliotheque Nationale in Paris), translations of the Kharismian Tables and an Arabic Introduction to Astronomy.
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The same historian tells us that Gerbert borrowed from the Arabs (Saraceni) the abacus with ciphers (see Numerals).
To assist his lectures on astronomy he constructed elaborate globes of the terrestrial and celestial spheres, on which the course of the planets was marked; for facilitating arithmetical and perhaps geometrical processes he constructed an abacus with twenty-seven divisions and a thousand counters of horn.
Although the pointed arches used are sometimes equilateral and sometimes drop-arches, the lancet-arch is the most characteristic. The period is best recognized in England by the great depth given to the hollows of the mouldings, alternating with fillets and rolls, by the decoration of the hollows with the dog-tooth ornament, by the circular abacus of the capitals, and the employment of slender detached shafts of Purbeck marble which are attached to piers by circular moulded shaftrings (Fr.