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58-535: The scale was tested from 1972 to 1975 and was made public at a meeting of the Royal Meteorological Society in 1975. The scale sets T0 as the equivalent of 8 on the Beaufort scale and is related to the Beaufort scale (B), up to 12 on the Beaufort scale, by the formula: and conversely: The Beaufort scale was first introduced in 1805, and in 1921 quantified. It expresses the wind speed as faster than v in

116-451: A circle rolled along another curve of uniform curvature . The cycloid, epicycloids, and hypocycloids have the property that each is similar to its evolute . If q is the product of that curvature with the circle's radius, signed positive for epi- and negative for hypo-, then the similitude ratio of curve to evolute is 1 + 2 q . The classic Spirograph toy traces out hypotrochoid and epitrochoid curves. The cycloidal arch

174-468: A cusp (where y=0 ). The map from t to ( x , y ) is differentiable, in fact of class C , with derivative 0 at the cusps. The slope of the tangent to the cycloid at the point ( x , y ) {\displaystyle (x,y)} is given by d y d x = cot ⁡ ( t 2 ) {\textstyle {\frac {dy}{dx}}=\cot({\frac {t}{2}})} . A cycloid segment from one cusp to

232-669: A cycloid path. Such a pendulum is isochronous , with equal-time swings regardless of amplitude. Introducing a coordinate system centred in the position of the cusp, the equation of motion is given by: x = r [ 2 θ ( t ) + sin ⁡ 2 θ ( t ) ] y = r [ − 3 − cos ⁡ 2 θ ( t ) ] , {\displaystyle {\begin{aligned}x&=r[2\theta (t)+\sin 2\theta (t)]\\y&=r[-3-\cos 2\theta (t)],\end{aligned}}} where θ {\displaystyle \theta }

290-624: A given time, one proves the line is always tangent to the lower arc at P 2 {\displaystyle P_{2}} and orthogonal to the upper arc at P 1 {\displaystyle P_{1}} . Let Q {\displaystyle Q} be the point in common between the upper and lower circles at the given time. Then: Using the above parameterization x = r ( t − sin ⁡ t ) ,   y = r ( 1 − cos ⁡ t ) {\textstyle x=r(t-\sin t),\ y=r(1-\cos t)} ,

348-405: A quadrature. This result and others were published by Torricelli in 1644, which is also the first printed work on the cycloid. This led to Roberval charging Torricelli with plagiarism, with the controversy cut short by Torricelli's early death in 1647. In 1658, Blaise Pascal had given up mathematics for theology but, while suffering from a toothache, began considering several problems concerning

406-476: A site, photographs, videos, or descriptions of damage may be utilised. The 12 categories for the TORRO scale are listed below, in order of increasing intensity. Although the wind speeds and photographic damage examples are updated, which are more or less still accurate. However, for the actual TORRO scale in practice, damage indicators (the type of structure which has been damaged) are predominantly used in determining

464-538: A subscription is required for some. However certain "classic" papers are freely available on the Society's website. The society has several local centres across the UK. There are also a number of special interest groups which organise meetings and other activities to facilitate exchange of information and views within specific areas of meteorology. These are informal groups of professionals interested in specific technical areas of

522-1022: A total collapse of some weak/average greenhouse structures likely. Garage roofs torn away, some to significant damage to tiled roofs and chimney stacks with many tiles missing, particularly to weak wooden framed homes, though typically thatched roofs with small eaves/smooth surface suffer only minor damage, outbuildings lose entire roofs and suffer some degree of damage to actual structure. Guttering pulled from some houses with some siding damage possible, older single glazed windows blown in or out of frames or smashed. Significant damage to most tree types, some big branches twisted or snapped off, most small and shallow rooted trees whether in leaf or not are uprooted or snapped. Mobile homes overturned / badly damaged; light caravans severely damaged or destroyed; garages and weak outbuildings severely damaged or destroyed; house roof timbers considerably exposed with more strongly built brick masonry houses suffering major roof damage with chimneys at risk of collapse, though structure/walls of

580-518: A visible lean to one side; shallowly anchored high rises may be toppled; other steel-framed buildings buckled. Many steel-framed/concrete buildings badly damaged though some of structure may remain standing albeit shifted in position on foundation; skyscrapers toppled; locomotives or trains likely blown over and rolled a short distance from tracks with damage to its exterior, empty train cars however are likely to be flipped and rolled repeatedly some distance away from tracks with some levitation likely along

638-584: Is a real parameter corresponding to the angle through which the rolling circle has rotated. For given t , the circle's centre lies at ( x , y ) = ( rt , r ) . The Cartesian equation is obtained by solving the y -equation for t and substituting into the x - equation: x = r cos − 1 ⁡ ( 1 − y r ) − y ( 2 r − y ) , {\displaystyle x=r\cos ^{-1}\left(1-{\frac {y}{r}}\right)-{\sqrt {y(2r-y)}},} or, eliminating

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696-408: Is equal to the height difference multiplied by the full arch length 8 r . If a simple pendulum is suspended from the cusp of an inverted cycloid, such that the string is constrained to be tangent to one of its arches, and the pendulum's length L is equal to that of half the arc length of the cycloid (i.e., twice the diameter of the generating circle, L = 4r ), the bob of the pendulum also traces

754-764: Is one of the world's leading sources of original research in the atmospheric sciences. The chief executive officer is Liz Bentley . The Royal Meteorological Society traces its origins back to 3 April 1850 when the British Meteorological Society was formed as "a society the objects of which should be the advancement and extension of meteorological science by determining the laws of climate and of meteorological phenomena in general". Along with nine others, including James Glaisher , John Drew , Edward Joseph Lowe , The Revd Joseph Bancroft Reade , and Samuel Charles Whitbread , Dr John Lee , an astronomer, of Hartwell House , near Aylesbury , Buckinghamshire founded in

812-1011: Is primarily used in the United Kingdom whereas the Fujita scale has been the primary scale used in North America, continental Europe, and the rest of the world. At the 2004 European Conference on Severe Storms, Dr. Meaden proposed a unification of the TORRO and Fujita scales as the Tornado Force or TF Scale. In 2007 in the United States, the Enhanced Fujita Scale replaced the original Fujita Scale from 1971. It made substantial improvements in standardizing damage descriptors through expanding and refining damage indicators and associated degrees of damage, as well as calibrated tornado wind speeds to better match

870-444: Is the "amplitude", ω {\displaystyle \omega } is the radian frequency of the pendulum and g the gravitational acceleration. The 17th-century Dutch mathematician Christiaan Huygens discovered and proved these properties of the cycloid while searching for more accurate pendulum clock designs to be used in navigation . Several curves are related to the cycloid. All these curves are roulettes with

928-433: Is the angle that the straight part of the string makes with the vertical axis, and is given by sin ⁡ θ ( t ) = A cos ⁡ ( ω t ) , ω 2 = g L = g 4 r , {\displaystyle \sin \theta (t)=A\cos(\omega t),\qquad \omega ^{2}={\frac {g}{L}}={\frac {g}{4r}},} where A < 1

986-944: Is three times the area of the rolling circle. The arc length S of one arch is given by S = ∫ 0 2 π ( d x d t ) 2 + ( d y d t ) 2 d t = ∫ 0 2 π r 2 − 2 cos ⁡ t d t = 2 r ∫ 0 2 π sin ⁡ t 2 d t = 8 r . {\displaystyle {\begin{aligned}S&=\int _{0}^{2\pi }{\sqrt {\left({\frac {dx}{dt}}\right)^{2}+\left({\frac {dy}{dt}}\right)^{2}}}dt\\&=\int _{0}^{2\pi }r{\sqrt {2-2\cos t}}\,dt\\&=2r\int _{0}^{2\pi }\sin {\frac {t}{2}}\,dt\\&=8r.\end{aligned}}} Another geometric way to calculate

1044-465: Is used when available, and sometimes photogrammetry or videogrammetry estimates wind speed by measuring tracers in the vortex. In most cases, aerial and ground damage surveys of structures and vegetation are utilised, sometimes with engineering analysis. Also sometimes available are ground swirl patterns ( cycloidal marks) left in the wake of a tornado. If an on site analysis is not possible, either for retrospective ratings or when personnel cannot reach

1102-539: The brachistochrone problem , the solution of which is a cycloid. The cycloid through the origin, generated by a circle of radius r rolling over the x - axis on the positive side ( y ≥ 0 ), consists of the points ( x , y ) , with x = r ( t − sin ⁡ t ) y = r ( 1 − cos ⁡ t ) , {\displaystyle {\begin{aligned}x&=r(t-\sin t)\\y&=r(1-\cos t),\end{aligned}}} where t

1160-467: The cusps pointing upward, is the curve of fastest descent under uniform gravity (the brachistochrone curve ). It is also the form of a curve for which the period of an object in simple harmonic motion (rolling up and down repetitively) along the curve does not depend on the object's starting position (the tautochrone curve ). In physics, when a charged particle at rest is put under a uniform electric and magnetic field perpendicular to one another,

1218-420: The differential equation : If we define h = 2 r − y = r ( 1 + cos ⁡ t ) {\displaystyle h=2r-y=r(1+\cos t)} as the height difference from the cycloid's vertex (the point with a horizontal tangent and cos ⁡ t = − 1 {\displaystyle \cos t=-1} ), then we have: The involute of

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1276-1039: The Mason Gold Medal (established in 2006) are pre-eminent. The two medals are awarded alternately. Other awards include the Buchan Prize, the Hugh Robert Mill Award, the L F Richardson Prize, the Michael Hunt Award, the Fitzroy Prize, the Gordon Manley Weather Prize, the International Journal of Climatology Prize, the Society Outstanding Service Award and the Vaisala Award. The society has a number of regular publications: All publications are available online but

1334-565: The T-Scale formula may be expressed as: or TORRO claims it differs from the Fujita scale in that it is "purely" a wind speed scale, whereas the Fujita scale relies on damage for classification, but in practice, damage is utilised almost exclusively in both systems to infer intensity. That is because such a proxy for intensity is usually all that is available, although users of both scales would prefer direct, objective, quantitative measurements. The scale

1392-425: The arch traced by a rolling wheel as part of a larger circle with a radius 120% larger than the smaller wheel. Galileo originated the term cycloid and was the first to make a serious study of the curve. According to his student Evangelista Torricelli , in 1599 Galileo attempted the quadrature of the cycloid (determining the area under the cycloid) with an unusually empirical approach that involved tracing both

1450-573: The area under one arch, 0 ≤ t ≤ 2 π , {\displaystyle 0\leq t\leq 2\pi ,} is given by: A = ∫ x = 0 2 π r y d x = ∫ t = 0 2 π r 2 ( 1 − cos ⁡ t ) 2 d t = 3 π r 2 . {\displaystyle A=\int _{x=0}^{2\pi r}y\,dx=\int _{t=0}^{2\pi }r^{2}(1-\cos t)^{2}dt=3\pi r^{2}.} This

1508-463: The associated damage. However, the EF Scale, having been designed based on construction practices in the United States, is not necessarily applicable across all regions. The EF-scale and variants thereof are officially used by the United States, Canada, France, and Japan, as well as unofficially in other countries, such as China. Unlike with the F scale, no analyses have been undertaken at all to establish

1566-1101: The building below roof itself mostly intact except for windows breaking especially from any small flying objects. Most large healthy trees lose many big branches and many are snapped or uprooted, lighter cars flipped. Cars levitated. Mobile homes/lighter caravans airborne / destroyed; garden sheds obliterated and airborne for considerable distances; entire roofs removed from some houses; roof timbers of stronger brick or stone houses completely exposed; gable ends torn away. "Weak" framed wooden houses will receive some damage to structure though most of structure still standing. Numerous strong trees uprooted or snapped with all trees within damage path receiving some debranching. Heavy vehicles such as buses/lorries (trucks) overturned or overturned and displaced some distance in excess of 10 metres though with minimal levitation, lighter vehicles such as passenger cars thrown large distances. Wind turbines built from strong material suffer significant blade damage with blades ending up shredded or broken/ possibly suffering permanent deformation of tower/blades with winds on

1624-403: The cycloid has exactly the same shape as the cycloid it originates from. This can be visualized as the path traced by the tip of a wire initially lying on a half arch of the cycloid: as it unrolls while remaining tangent to the original cycloid, it describes a new cycloid (see also cycloidal pendulum and arc length ). This demonstration uses the rolling-wheel definition of cycloid, as well as

1682-426: The cycloid. His toothache disappeared, and he took this as a heavenly sign to proceed with his research. Eight days later he had completed his essay and, to publicize the results, proposed a contest. Pascal proposed three questions relating to the center of gravity , area and volume of the cycloid, with the winner or winners to receive prizes of 20 and 40 Spanish doubloons . Pascal, Roberval and Senator Carcavy were

1740-755: The evergreen variety. Moderate damage to trees, with a few medium sized branches in leaf snapping on the upper bound of T1, trees without leaves on them likely remaining mostly unscathed except for significant twig breakage, although for some a few small branches could break. Very weak/unhealthy trees, particularly those in leaf and of softwood variety such as conifers are likely to be nearly or completely uprooted. Heavy mobile homes displaced with some damage to exterior, light caravans lose majority of roof and/or are blown over, particularly from upper bound winds of T2, bonnets blown open on some vehicles, average strength sturdy garden sheds destroyed, greenhouses of weak/average construction lose entire plastic/glass roofing cover with

1798-546: The fact that the F scale is a damage scale, not a wind speed scale. Tornadoes are rated after they have passed and have been examined, not whilst in progress. In rating the intensity of a tornado, both direct measurements and inferences from empirical observations of the effects of a tornado are used. Few anemometers are struck by a tornado, and even fewer survive, so there are very few in-situ measurements. Therefore, almost all ratings are obtained from remote sensing techniques or as proxies from damage surveys. Weather radar

TORRO scale - Misplaced Pages Continue

1856-425: The first published proof. Fifteen years later, Christiaan Huygens had deployed the cycloidal pendulum to improve chronometers and had discovered that a particle would traverse a segment of an inverted cycloidal arch in the same amount of time, regardless of its starting point. In 1686, Gottfried Wilhelm Leibniz used analytic geometry to describe the curve with a single equation. In 1696, Johann Bernoulli posed

1914-481: The formula: Most UK tornadoes are T6 or below with the strongest known UK tornado estimated as a T8 (the London tornado of 1091 ). For comparison, the strongest detected winds in a United States tornado (during the 1999 Oklahoma tornado outbreak ) would be T11 using the following formulas: where v is wind speed and T is TORRO intensity number. Wind speed is defined as a 3-second gust at 10 m AGL . Alternatively,

1972-454: The generating circle and the resulting cycloid on sheet metal, cutting them out and weighing them. He discovered the ratio was roughly 3:1, which is the true value, but he incorrectly concluded the ratio was an irrational fraction, which would have made quadrature impossible. Around 1628, Gilles Persone de Roberval likely learned of the quadrature problem from Père Marin Mersenne and effected

2030-498: The instantaneous velocity vector of a moving point, tangent to its trajectory. In the adjacent picture, P 1 {\displaystyle P_{1}} and P 2 {\displaystyle P_{2}} are two points belonging to two rolling circles, with the base of the first just above the top of the second. Initially, P 1 {\displaystyle P_{1}} and P 2 {\displaystyle P_{2}} coincide at

2088-426: The intersection point of the two circles. When the circles roll horizontally with the same speed, P 1 {\displaystyle P_{1}} and P 2 {\displaystyle P_{2}} traverse two cycloid curves. Considering the red line connecting P 1 {\displaystyle P_{1}} and P 2 {\displaystyle P_{2}} at

2146-465: The judges, and neither of the two submissions (by John Wallis and Antoine de Lalouvère ) was judged to be adequate. While the contest was ongoing, Christopher Wren sent Pascal a proposal for a proof of the rectification of the cycloid; Roberval claimed promptly that he had known of the proof for years. Wallis published Wren's proof (crediting Wren) in Wallis's Tractatus Duo , giving Wren priority for

2204-461: The length of the cycloid is to notice that when a wire describing an involute has been completely unwrapped from half an arch, it extends itself along two diameters, a length of 4 r . This is thus equal to half the length of arch, and that of a complete arch is 8 r . From the cycloid's vertex (the point with a horizontal tangent and cos ⁡ t = − 1 {\displaystyle \cos t=-1} ) to any point within

2262-472: The library of his house the British Meteorological Society, which became the Royal Meteorological Society. It became The Meteorological Society in 1866, when it was incorporated by Royal Charter , and the Royal Meteorological Society in 1883, when Her Majesty Queen Victoria granted the privilege of adding 'Royal' to the title. Along with 74 others, the famous meteorologist Luke Howard joined

2320-656: The lower floors. Trains whether stationary or not are blown over. All large branches torn/stripped from trees down to the trunk, some small-medium sized trees are thrown. Noticeable debarking of any standing tree trunks from flying debris. Cars and other larger/heavier vehicles such as trucks hurled great distances. Strong wooden-framed houses and their contents dispersed over long distances; strong stone or brick masonry buildings severely damaged or largely destroyed with one or two sections of walls blown away; steel reinforced concrete homes/large buildings suffer significant to major structural damage. Skyscrapers badly twisted and may show

2378-566: The multiple-valued inverse cosine: r cos ( x + y ( 2 r − y ) r ) + y = r . {\displaystyle r\cos \!\left({\frac {x+{\sqrt {y(2r-y)}}}{r}}\right)+y=r.} When y is viewed as a function of x , the cycloid is differentiable everywhere except at the cusps on the x -axis, with the derivative tending toward ∞ {\displaystyle \infty } or − ∞ {\displaystyle -\infty } near

TORRO scale - Misplaced Pages Continue

2436-440: The next is called an arch of the cycloid, for example the points with 0 ≤ t ≤ 2 π {\displaystyle 0\leq t\leq 2\pi } and 0 ≤ x ≤ 2 π {\displaystyle 0\leq x\leq 2\pi } . Considering the cycloid as the graph of a function y = f ( x ) {\displaystyle y=f(x)} , it satisfies

2494-489: The original 15 members of the Society at its first ordinary meeting on 7 May 1850. As of 2008 it has more than 3,000 members worldwide. The chief executive of the Society is Professor Liz Bentley. Paul Hardaker previously served as chief executive from 2006 to 2012. There are four membership categories: The society regularly awards a number of medal and prizes, of which the Symons Gold Medal (established in 1901) and

2552-633: The particle’s trajectory draws out a cycloid. It was in the left hand try-pot of the Pequod, with the soapstone diligently circling round me, that I was first indirectly struck by the remarkable fact, that in geometry all bodies gliding along the cycloid, my soapstone for example, will descend from any point in precisely the same time. Moby Dick by Herman Melville , 1851 The cycloid has been called "The Helen of Geometers" as, like Helen of Troy , it caused frequent quarrels among 17th-century mathematicians, while Sarah Hart sees it named as such "because

2610-455: The precise design needed and possibility of it actually successfully providing adequate safety during such a tornado is very speculative for now. Royal Meteorological Society The Royal Meteorological Society is a long-established institution that promotes academic and public engagement in weather and climate science. Fellows of the Society must possess relevant qualifications, but Members can be lay enthusiasts. Its Quarterly Journal

2668-416: The profession of meteorology. The groups are primarily a way of communicating at a specialist level. Source: Cycloidal In geometry , a cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping. A cycloid is a specific form of trochoid and is an example of a roulette , a curve generated by a curve rolling on another curve. The cycloid, with

2726-489: The properties of this curve are so beautiful". Historians of mathematics have proposed several candidates for the discoverer of the cycloid. Mathematical historian Paul Tannery speculated that such a simple curve must have been known to the ancients , citing similar work by Carpus of Antioch described by Iamblichus . English mathematician John Wallis writing in 1679 attributed the discovery to Nicholas of Cusa , but subsequent scholarship indicates that either Wallis

2784-428: The quadrature in 1634 by using Cavalieri's Theorem . However, this work was not published until 1693 (in his Traité des Indivisibles ). Constructing the tangent of the cycloid dates to August 1638 when Mersenne received unique methods from Roberval, Pierre de Fermat and René Descartes . Mersenne passed these results along to Galileo, who gave them to his students Torricelli and Viviani, who were able to produce

2842-606: The roof mostly or entirely blown/torn off. The oldest, weakest buildings may collapse completely. Strong framed wooden buildings largely or completely destroyed, Strongly built brick masonry houses lose entire roofs just like T5 though exterior walls on second floor now likely blown down or collapsed with significant interior damage, windows broken on skyscrapers, more of the less-strong buildings collapse, national grid pylons severely damaged or blown down/bent and deformed, Strong trees that aren't uprooted /snapped will suffer major debranching with most leaves torn off, other trees excluding

2900-406: The same arch, the arc length squared is 8 r 2 ( 1 + cos ⁡ t ) {\displaystyle 8r^{2}(1+\cos t)} , which is proportional to the height difference r ( 1 + cos ⁡ t ) {\displaystyle r(1+\cos t)} ; this property is the basis for the cycloid's isochronism . In fact, the arc length squared

2958-712: The tornado intensity. Loose light litter such as paper, leaves and twigs raised from ground level in spirals. Secured tents and marquees seriously disturbed; a few exposed tiles/slates on roofs dislodged. Twigs and perhaps weak small branches that are in leaf snapped from some trees; minimal or no damage to trees with no leaves, trail visible through crops. Deckchairs, small plants/plants in small pots, heavy litter becomes airborne; minor damage to sheds. More serious/numerous dislodging of tiles, slates and chimney pots with some tiles/slates blown off typical/average strength roofs. Low quality wooden fences damaged or flattened. Slight damage possible to low lying shrubs/bushes, particularly of

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3016-557: The upper bounds of T5. Strong framed wooden buildings/weak brick masonry buildings receive more significant damage than T4 though walls on ground floor will probably remain, some wall damage on second/upper floor connected to roof is likely though with one or two walls blowing down/collapsing, some/significant damage likely inside of these buildings. Stronger brick masonry homes may lose a few rows of bricks on second floor, though overall structure below roof itself largely standing with bottom floor relatively intact except for doors and windows,

3074-659: The upper end of the scale was possible. The TORRO scale has more graduations than the F scale which makes it arguably more useful for tornadoes on the lower end of the scale; however, such accuracy and precision are not typically attainable in practice. Brooks and Doswell stated that "the problems associated with damage surveys and uncertainties associated with estimating wind speed from observed damage make highly precise assignments dubious". In survey reports, Fujita ratings sometimes also have extra qualifications added ("minimal F2" or "upper-end F3 damage"), made by investigators who have experience of many similar tornadoes and relating to

3132-408: The veracity and accuracy of the T scale damage descriptors. The scale was written in the early 1970s, and does not take into account changes such as the growth in weight of vehicles or the great reduction in numbers and change of type of railway locomotives, and was written in an environment where tornadoes of F2 or stronger are extremely rare, so little or no first-hand investigation of actual damage at

3190-403: The very heaviest ones for example locomotives/trains weighing hundreds of tons and the strongest of buildings made low to the ground with specific very aerodynamic designs and incredibly thick load bearing steel concrete walls with no windows/discernible roof will "survive" a tornado of this strength, survival would be reliant on these specialised structures or out of path of the tornado itself. But

3248-980: The way. Strong brick masonry buildings/houses almost or completely destroyed with large sections of houses/building blown away from foundation. Concrete pathways slightly above soil level could be shifted in position by several inches. Complete debarking of any standing tree-trunks. Entire very well built houses/buildings lifted bodily or completely from foundations and carried a large distance to disintegrate. Steel-reinforced concrete buildings severely damaged or almost obliterated. (e.g. 1930 Montello tornado) Exceptionally well built very thick walled (40-80cm) brick masonry buildings are completely destroyed and swept off foundations entirely with only flooring or foundations remaining with even these potentially damaged or with sections pulled off entirely; Well built steel-reinforced concrete structures/homes are completely destroyed. Tall buildings collapse. Cars, trucks and train cars thrown in excess of 1-3 miles. In terms of man made objects, only

3306-774: The widest and strongest ones are snapped/uprooted, very large heavy branches thrown large distances. Lighter vehicles thrown upto a mile in some cases, heavy vehicles such as buses lofted and tossed tens of metres away, trains derailed/blown over while in motion. Strongly built wooden-framed/weak brick masonry buildings/houses wholly demolished; some walls of more strongly built stone / brick masonry houses beaten down or collapse with significant damage to overall structure, with some shifting on foundations likely; skyscrapers twisted; steel-framed warehouse-type constructions may buckle slightly. Well built steel reinforced concrete buildings/houses suffer total roof loss with some damage to overall structure though most walls remain standing, particularly

3364-473: Was mistaken or the evidence he used is now lost. Galileo Galilei 's name was put forward at the end of the 19th century and at least one author reports credit being given to Marin Mersenne . Beginning with the work of Moritz Cantor and Siegmund Günther , scholars now assign priority to French mathematician Charles de Bovelles based on his description of the cycloid in his Introductio in geometriam , published in 1503. In this work, Bovelles mistakes

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