This richly illustrated book is a brilliant example of historical scholarship as applied to the study of scientific instruments. Its purpose seems deceptively simple, namely, an attempt to determine the provenance of two brass plates, one of them with an inclined sundial attachment, both representing cartographic projections of the world as it was known in medieval Islamic times. In addition, the cartographic projection on the plates is centered on the holy city of Mecca, towards which every Muslim must turn five times a day during ritual prayers, and as such it preserves the directions to Mecca as well as the distances to it from any city in the then known world. \par When we remember that the direction to Mecca is defined by the intersection of the plane of the local horizon of any city on the terrestrial globe with the plane of the great circle that passes through the zenith of that city and the zenith of Mecca, it becomes immediately obvious that the determination of such a direction necessarily results in a non-trivial spherical astronomical problem. Similarly, the distance between the two cities, also defined by the arc of the same great circle that separates the zenith of the chosen locality from that of Mecca, is also part of the same spherical problem. And since there is no projection of any kind that can render, without some distortion, all positions on the surface of a globe onto positions on a plane, the problem becomes a problem of choosing which features one wishes to preserve in a projection and which features can be slightly distorted. In this instance direction to Mecca and the distances to it are essentially preserved as accurately as possible. \par King's problem surfaced first when one of these brass plates, here called instrument A, bearing such a projection was brought to his attention sometime in 1989. By the looks of it, and by comparison to other scientific instruments such as astrolabes and the like, he justifiably felt that it could have been made in Iran during Safavid times (1501--1722) and maybe towards the end of that period when that kind of metalwork tradition had reached its maturity. The instrument itself carried neither a date nor a maker's name. The immediate problem though was that the projection it carried was not known from anywhere else except from a European literary source in the early part of the twentieth century. On that basis alone, people who had examined the instrument before King assumed that it was executed under European influence and thus had to have come from a much later period, closer to the nineteenth century if not even later. But the problem could not be so easily dismissed by King, who knew more than anyone else about the Islamic and European traditions of map projections, and, more importantly, also knew more about Islamic metal work and about scientific instruments. His very educated hunch was to persist in seeking the origins of that plate in Safavid Iran. \par As he began working on refining his first impressions of this instrument, some six years later another instrument, here called instrument B, surfaced in the antiquarian market, carrying the same projection, almost identical geographic coordinates with very few variations, and carrying two additional parts: an inclined sundial, with definite European influence in its number markings, and a compass house still intact with glass cover and all. In almost every other respect both instruments looked very much like copies of one another. In fact, instrument A also had at one point a compass house as well, now left empty after the loss of the glass cover and the compass needle itself. It also had provisions for an inclined sundial to be attached to it, now also missing. In addition, instrument B carried the name of a maker, someone called Muhammad Husayn. \par Without paying too much attention to the European influence on the markings on the attached sundial of instrument B, King persisted in focusing on the cartographic projection on the base plate itself, where he thought that at least his original hunch that such instruments came from the Shi'ite domain of Safavid Iran was partially vindicated with the second instrument carrying such a particular name combination as that of Muhammad Husayn. The name combination itself fits well in a Shi'ite milieu, especially during the Safavid period, since the first part of it, Muhammad, was usually carried as an honorific name, and the second part, Husayn, was the name of the most famous martyr of Shi'ite Islam ever. With that in mind, King felt he was closer to the solution of the original problem of the provenance of such instruments. \par But as things began to look simpler, the problem began to look more intricate as well. First, instrument B had all the features of being a later copy of A, or at least inspired by A. That conclusion was based on the names of a few geographical localities that had changed name over time, and in A had carried the older names. Second, the attachments and the compass were still intact in B, and missing in A. One could then reason that if B were later than A then, if the dates of Muhammad Husayn could be determined, that fact alone would give King a terminus ante quem for instrument A. The only unfortunate part is that both names, Muhammad and Husayn, as well as their juxtaposition, are as common in Shi'ite circles as John and Smith in the English-speaking world. \par But the importance of King's scholarship, and his mastery of the subject, begin to be felt as one follows his stubborn, detective-like attempts to locate the technical aspects of those instruments within the general historical context, both materially in the sense of metalwork craftsmanship, and theoretically in the sense of the mathematics necessary to perform such specialized projections with such accuracy. The similarity of the workmanship on those instruments to that abundantly exhibited on Safavid astrolabes, the closest ``relatives'' to such instruments as A and B, and profusely exhibited in museums and private collections all around the world, is obvious even to naked-eye observation. On the theoretical mathematical level, no European would have had the interest in devising a cartographic projection centered on Mecca, a purely Islamic context, let alone the mathematical know-how to do so before the nineteenth century. Moreover, no such actual instrument is known to exist anywhere in Europe. On the technical level as well, King is absolutely justified in seeking the origins of such projections in ninth-century Baghdad, where a famous astronomer and mathematician by the name of Ḥabash al-Ḥāsib (fl.\ 850) had already devised an astrolabe plate with a projection that had the same property of preserving azimuthal directions, due to which the rete of the astrolabe was rendered in what became a famous melon-shaped astrolabe recently studied by E. S. Kennedy et al. This Ḥabash was followed by other astronomers, most famous among them being the polymath Bīrūnī\ (d.c.\ 1049), who produced a magisterial text on mathematical geography all centered around the intricate problem of finding the local direction to Mecca from the city of Ghazna in modern-day Afghanistan, but in the meantime covering almost all that needs to be asked about the theoretical questions connected with map projections. Other astronomers and mathematicians were fascinated by the problem and also tried their own hand at all sorts of projections, both for astrolabes as well as for laying down further foundations for cartographic productions. \par Knowing all that, King reasoned correctly that the instruments at hand represented the apex of that long Islamic tradition in mathematical geography, and the mathematical knowledge needed to produce the projections now represented on those plates was already conceived as early as ninth-century Baghdad and thus there was no need to seek the inspiration from Europe. What King was confronting with this line of reasoning was another sacred cow, namely, the Orientalist assessment of Islamic science, one in which sophisticated mathematical and astronomical work was assumed to have been produced during the so-called golden age of Islamic science, which was assumed to stretch between the ninth and the eleventh centuries only, and with some license maybe up to the fourteenth century, but certainly did not stretch enough to include Safavid Iran in the sixteenth century and thereafter. The existence of such a sophisticated mapping assumed by King to be the product of late seventeenth-century Iran flies directly in the face of such commonly held opinions about the periodization of Islamic science. This reviewer, who has spent much time working on the sophisticated mathematics of sixteenth-century astronomers of Safavid Iran, could not agree more with King about the ability of astronomers working in that milieu to produce cartographic projections of the highest sophistication. \par Add to that the geographic coordinates that are mapped on both of those two plates which are also of Islamic provenance, that is, they are mainly of Islamic cities, and use the same zero meridian for longitude measurements and the same latitudes that are used in the majority of geographical tables still extant in various manuscript forms and other instrument plates such as astrolabe maters. No European would have had the interest in documenting those same cities, even if their coordinates were known to him. Furthermore, with assiduous and painstaking research King has managed to isolate the source from which such coordinates were ultimately derived and managed to locate it in a geographical table originating also from Iran or nearby Central Asia sometime during the Timurid times of the fourteenth or fifteenth centuries. All this led King to favor with strong conviction the hypothesis that those plates were most likely produced in Iran during Safavid times. But being careful as he always is, King goes on to say in the conclusion of the book, p.\ 366, that his conclusions are so tentative ``because there are so many unknowns, [and thus] the reader will not find my conclusions clearly stated anywhere in this book''. \par This does not mean that King is averse to admitting European influence on Islamic science in general or on Islamic scientific instruments in particular. In fact, he devotes the whole of Chapter Eight to that problem in particular. But what he does not find is the influence on the very idea that brought those instruments into being, namely, the cartographic projections that they carry and the contents of the geographical coordinates that they preserve, for that idea could be convincingly located well within the long Islamic tradition of mathematical geography and instrument making. And in order to illustrate this conviction, King pursues here his usual admirable methodology by always trying to locate textual evidence for every innovation one encounters on a scientific instrument. He did that when he first encountered universal plates of astrolabes, or when he examined sundials, and has done so now by locating the geographical table from which the cities' coordinates on both instruments were inscribed, all because he simply instinctively believes that with manuscript textual evidence one has a better grasp of how to construct and manipulate scientific instruments that are usually either left to speak for themselves or marked with lines whose function cannot always be explained with certainty. And lines on instruments may at times be very silent witnesses, as any historian of scientific instruments would readily admit, no matter how much one tries to force them to speak. \par Despite his inability to settle the problem of these instruments' provenance with any certainty, in his pursuit of that goal King managed to gather together a treasure trove of mathematical geographical material, fully tabulated in well-annotated appendices, pp.\ 455--638, and to contextualize those sources in the rest of the book. But no book of such volume and of such scope could be free from occasional errors, mainly typos, which this reviewer will communicate to Professor King directly. \par There remain a few issues that the reviewer wishes to take up with Professor King and which could be of some general interest for the reader as well. I will take issue, for example, with the remark he makes in the introduction, p.\ xxiv, and elsewhere, where he cites the Arabic name of an instrument maker ʿAbd al-ʿAlī\ as a mistake for the Persian ʿAbd-iʿAlī, on the basis of the maker being a Shi'ite, and thus must have intended his name to be rendered in the Persian version to mean ``slave of ʿAlī''. I would simply assert that even Shi'ites, who spoke Persian at home, and who admittedly would not mind calling themselves ``slaves of ʿAlī'' or ``slaves of Husayn'' or slaves of any of the twelve imāms, were still sometimes conversant in Arabic and even wrote in that language, and thus one should also give them the benefit of the doubt if they also wished to call themselves ʿAbd al-ʿAlī, ``slaves of the most High'', where al-ʿAlī\ is one of the names of the Lord, and not ʿAlī\ the cousin of the prophet Muḥammad and the first imām of the Shi'ites. The frequent occurrence of the form ʿAbd al-ʿAlī\ on several medieval manuscripts as well as the equally ubiquitous modern and classical Persian names employing one of the ninety-nine names of the Lord or other, such as ʿAbd al-Karīm, ``slave of the Generous'', ʿAbd al-Hādī, ``slave of the Guiding One'', etc., simply makes it highly unlikely that all those ʿAbd al-ʿAlī's are mistakes for ʿAbd-ī\ ʿAlī. \par Another point raised in this book, pp.\ 301--302, and left without an adequate answer, is why most geographic maps that come from the Islamic domain have the south pole on top of the map rather than the usual north pole that we see on European maps. To this phenomenon this reviewer wishes to send the reader to Aristotle's book {\it On the heavens}, where he argues convincingly for that arrangement, and the practice that needs to be explained is the European one that has no theoretical or philosophical basis as far as this reviewer knows. \par Finally, the adjective appended to the city of Najaf, p.\ 149, n. 56, left undeciphered by King, may very well be al-Mashhad al-Gharbī, ``The western place of martyrdom'', where the great martyr al-Husayn was killed and buried, in contrast to the present-day city of Meshhed in Eastern Iran where the eighth imām was buried. \par To conclude, this book makes for a most enjoyable reading, not only because it is so richly illustrated with pictures of actual scientific instruments produced over almost a full millennium, but because it also places those instruments in their natural context, supplies the mathematical basis for each of them, and supports almost every claim made about them by textual evidence from the manuscript tradition. As a result it constitutes a veritable introduction to the whole field of mathematical astronomy in Islam, and more particularly to the field of mathematical geography, a field sorely in need of much more study before its full scope can be rightly appreciated. But most importantly, by demonstrating the mathematical sophistication behind the mappings preserved on those scientific instruments, and by demonstrating its continuity with the long mathematical astronomical and geographic tradition going as far back as the ninth century, and by insisting that those instruments were produced in the latter part of the seventeenth century rather than much later as others would want to believe, King has also demonstrated extremely well how little we know about those later centuries of Islamic civilization that have been conveniently dismissed so far as centuries of decline in Islamic science. If for no other reason except to make this radical shift in the commonly held periodization of Islamic intellectual history, this book ought to be read very closely by anyone with the slightest interest in that subject.