Railways have played an immense part in the history of New South Wales. The parallel lines extended as the population grew and themselves made possible new settlement and new industries. Railways crossed the mountain barriers that surround Sydney and opened up both the vast hinterland and the northern and southern coasts. Railways joined every part of New South Wales to Sydney in a distinctive, centralized pattern. They also joined New South Wales to the neighbouring colonies and states.

_________________ 'Compelling... Part Bill Bryson, part Nick Hornby, part memoir and part pastiche ... Light, lively and, above all, right: what every enthusiast should be expected to know' - The Times 'Michael Palin meets Nick Hornby meets What the Victorians Did for Us ... wacky and amiable' - Independent on Sunday 'A gloriously disingenuous front for the most acerbic and humorous criticism of public transport policy ... a more entertaining and incisive read will not be found this year' - Glasgow Herald _________________ A brilliantly witty story of one man's encounter with the British railways For 175 years the British have lived with the railway, and for a long while it was a love affair - the grandeur of the Victorian heyday, the glorious age of steam, the romance of Brief Encounter. Then the love affair turned sour - strikes, bad food, delays, disasters... Parallel Lines tells the story of these two railways: the real railway and the railway of our dreams. Travelling all over Britain, Ian Marchant examines the history of the British railway and meets those who still hold the railways close to their hearts - the model railway enthusiasts, the train-spotters and bashers (a hybrid of train-spotting where the individual - usually male - has to travel behind a certain locomotive in order to catalogue it), the steam enthusiasts. He swaps stories with commuters at the far reaches of London suburbia, he travels to deserted railway museums, and smokes cigarettes on remote, windswept stations in the furthest corners of Scotland, turning his characteristic eye for character, humour and surprise to one of the great shared experiences of the British nation. _________________ 'The trip keeps its pace and purpose, fuelled by the genial, flexible rhythms of the prose and enriched by two centuries of railway-culture hinterland' - Independent

This book offers a general introduction to the geometrical studies of Gottfried Wilhelm Leibniz (1646-1716) and his mathematical epistemology. In particular, it focuses on his theory of parallel lines and his attempts to prove the famous Parallel Postulate. Furthermore it explains the role that Leibniz’s work played in the development of non-Euclidean geometry. The first part is an overview of his epistemology of geometry and a few of his geometrical findings, which puts them in the context of the seventeenth-century studies on the foundations of geometry. It also provides a detailed mathematical and philosophical commentary on his writings on the theory of parallels, and discusses how they were received in the eighteenth century as well as their relevance for the non-Euclidean revolution in mathematics. The second part offers a collection of Leibniz’s essays on the theory of parallels and an English translation of them. While a few of these papers have already been published (in Latin) in the standard Leibniz editions, most of them are transcribed from Leibniz’s manuscripts written in Hannover, and published here for the first time. The book provides new material on the history of non-Euclidean geometry, stressing the previously neglected role of Leibniz in these developments. This volume will be of interest to historians in mathematics, philosophy or logic, as well as mathematicians interested in non-Euclidean geometry.

Through Euclid's Window Leonard Mlodinow brilliantly and delightfully leads us on a journey through five revolutions in geometry, from the Greek concept of parallel lines to the latest notions of hyperspace. Here is an altogether new, refreshing, alternative history of math revealing how simple questions anyone might ask about space -- in the living room or in some other galaxy -- have been the hidden engine of the highest achievements in science and technology. Based on Mlodinow's extensive historical research; his studies alongside colleagues such as Richard Feynman and Kip Thorne; and interviews with leading physicists and mathematicians such as Murray Gell-Mann, Edward Witten, and Brian Greene, Euclid's Window is an extraordinary blend of rigorous, authoritative investigation and accessible, good-humored storytelling that makes a stunningly original argument asserting the primacy of geometry. For those who have looked through Euclid's Window, no space, no thing, and no time will ever be quite the same.

By making believe there are no straight edges or rulers in the world, the reader learns the geometric principles of straight, parallel, and perpendicular lines.

Blondie's Parallel Lines mixed punk, disco and radio-friendly FM rock with nostalgic influences from 1960s pop and girl group hits. This 1978 album kept one foot planted firmly in the past while remaining quite forward-looking, an impulse that can be heard in its electronic dance music hit “Heart of Glass.” Bubblegum music maven Mike Chapman produced Parallel Lines, which was the first massive hit by a group from the CBGB punk underworld. By embracing the diversity of New York City's varied music scenes, Blondie embodied many of the tensions that played out at the time between fans of disco, punk, pop and mainstream rock. Debbie Harry's campy glamor and sassy snarl shook up the rock'n'roll boy's club during a growing backlash against the women's and gay liberation movements, which helped fuel the “disco sucks” battle cry in the late 1970s. Despite disco's roots in a queer, black and Latino underground scene that began in downtown New York, punk is usually celebrated by critics and scholars as the quintessential subculture. This book challenges the conventional wisdom that dismissed disco as fluffy prefab schlock while also recuperating punk's unhip pop influences, revealing how these two genres were more closely connected than most people assume. Even Blondie's album title, Parallel Lines, evokes the parallel development of punk and disco-along with their eventual crossover into the mainstream.

This is the story of a young boy's journey from a sleepy provincial town in Hungary during the Second World War to the concentration camp in Bergen-Belsen. Peter Lantos revisits his past from the perspective of the present and finally lays to rest the ghosts of his past.

LOBACHEVSKY was the first man ever to publish a non-Euclidean geometry. Of the immortal essay now first appearing in English Gauss said, "The author has treated the matter with a master-hand and in the true geometer's spirit. I think I ought to call your attention to this book, whose perusal cannot fail to give you the most vivid pleasure." Clifford says, "It is quite simple, merely Euclid without the vicious assumption, but the way things come out of one another is quite lovely." * * * "What Vesalius was to Galen, what Copernicus was to Ptolemy, that was Lobachevsky to Euclid." Says Sylvester, "In Quaternions the example has been given of Algebra released from the yoke of the commutative principle of multiplication - an emancipation somewhat akin to Lobachevsky's of Geometry from Euclid's noted empirical axiom." Cayley says, "It is well known that Euclid's twelfth axiom, even in Playfair's form of it, has been considered as needing demonstration; and that Lobachevsky constructed a perfectly consistent theory, where- in this axiom was assumed not to hold good, or say a system of non- Euclidean plane geometry. There is a like system of non-Euclidean solid geometry." GEORGE BRUCE HALSTED. 2407 San Marcos Street, Austin, Texas. * * * *From the TRANSLATOR'S INTRODUCTION. "Prove all things, hold fast that which is good," does not mean demonstrate everything. From nothing assumed, nothing can be proved. "Geometry without axioms," was a book which went through several editions, and still has historical value. But now a volume with such a title would, without opening it, be set down as simply the work of a paradoxer. The set of axioms far the most influential in the intellectual history of the world was put together in Egypt; but really it owed nothing to the Egyptian race, drew nothing from the boasted lore of Egypt's priests. The Papyrus of the Rhind, belonging to the British Museum, but given to the world by the erudition of a German Egyptologist, Eisenlohr, and a German historian of mathematics, Cantor, gives us more knowledge of the state of mathematics in ancient Egypt than all else previously accessible to the modern world. Its whole testimony con- firms with overwhelming force the position that Geometry as a science, strict and self-conscious deductive reasoning, was created by the subtle intellect of the same race whose bloom in art still overawes us in the Venus of Milo, the Apollo Belvidere, the Laocoon. In a geometry occur the most noted set of axioms, the geometry of Euclid, a pure Greek, professor at the University of Alexandria. Not only at its very birth did this typical product of the Greek genius assume sway as ruler in the pure sciences, not only does its first efflorescence carry us through the splendid days of Theon and Hypatia, but unlike the latter, fanatics cannot murder it; that dismal flood, the dark ages, cannot drown it. Like the phoenix of its native Egypt, it rises with the new birth of culture. An Anglo-Saxon, Adelard of Bath, finds it clothed in Arabic vestments in the land of the Alhambra. Then clothed in Latin, it and the new-born printing press confer honor on each other. Finally back again in its original Greek, it is published first in queenly Basel, then in stately Oxford. The latest edition in Greek is from Leipsic's learned presses.