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| {{EngvarB|date=January 2014}}
| | Although the Weight Watchers flex plan is regarded as the better fat loss diets, the Weight Watchers system can become especially expensive if youve already done a session but havent reached a goal yet. If youre like various of us, we may have performed the Weight Watchers meetings in the previous and had several terrific success. If you nonetheless desire to lose weight, to do Weight Watchers successfully at home with a components from the meetings. Dont worry should you dont have the Weight Watchers contents, check the hyperlinks inside this particular article for strategies on where you are able to purchase them for less.<br><br>One should follow a healthy diet plus include foods like soy goods, egg whites, lean meat, dairy foods without fats, veggies plus fruits in their daily diet inside order to lose weight fast and safely. Avoid eating junk foods. Try to include salads, pastas and fibrous foods in the daily diet. You are able to replace white bread with brown bread. Use skimmed milk inside area of the usual one, because it has less amount of fats.<br><br>The right foods for weight reduction are fresh all-natural food, nutritionally thick, excellent in fiber, low inside fat plus calories, low in sodium plus processed sugars. They also consist of higher amounts of complex carbohydrates, fibers, good quality proteins and excellent water content. Some of the best foods to consume inside purchase to lose weight are vegetables, fruits, legumes, baked potato, complete grain foods (including wholemeal pasta, oatmeal, muesli, etc), boiled brown rice, baked potato and fresh fish.<br><br>Have breakfast. Skipping breakfast leads to low blood glucose mid morning that results in cravings for sugary foods to pump the blood sugar back up. A vicious cycle results plus continues throughout the day. The breakfast should consist of complete grains, a protein source and fruit. It doesn't need to be fancy. A cut of complete wheat toast spread with a tablespoon of low fat peanut butter and an apple can do just fine. Or you could blend 1/2 cup of nonfat cottage cheese with chopped fresh peaches along with a couple of entire wheat crackers. Another possibility is a scrambled egg served on an English muffin with a glass of orange juice.<br><br>And whenever I am seized with all the temptation of the wicked doughnut, I can resist-at least for a time [http://safedietplansforwomen.com/how-to-lose-weight-fast lose weight fast]. And then another moment, until I've put enough time between your impulse and the action, plus the craving has subsided.<br><br>As my fianc plus I were preparing the soup, I created the comment which, "Geez, no wonder you lose thus much weight found on the diet! I'm burning a zillion calories getting it ready!" We had to peel two bags of carrots plus chop up a lot of vegetables. As I place everything in the pots (I do not have a stew pot, so I used 2 big pots) I couldn't enable however think of how healthy it looked.<br><br>Losing fat is surprisingly difficult, nevertheless with this you should be capable to receive to your weight goal. If you have any query, comments or concerns please feel free to comment. For an expert opinion please contact the localized physician or dietician. |
| {{Use dmy dates|date=January 2014}}
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| {{refimprove|date=August 2013}}
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| {{For|other people with the same name|James Gregory (disambiguation)}}
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| {{Infobox scientist
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| |name = James Gregory
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| |image = James_Gregory.jpeg|300px
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| |image_size = 300px
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| |caption = James Gregory (1638–1675)
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| |birth_date = November 1638
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| |birth_place = [[Drumoak]], [[Aberdeenshire (historic)|Aberdeenshire]], Scotland
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| |death_date = October 1675 (aged 36)
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| |death_place = [[Edinburgh]], Scotland
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| |residence = Scotland, England, [[Republic of Venice|Venice]]
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| |citizenship = Scotland
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| |nationality = Scottish
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| |ethnicity =
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| |field = Mathematics <br> [[Astronomy]]
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| |work_institutions = [[University of St. Andrews]], [[University of Edinburgh]]
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| |alma_mater = [[Marischal College]] ([[University of Aberdeen]]), [[University of Padua]]
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| |doctoral_advisor =
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| |doctoral_students =
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| |known_for = [[Gregorian telescope]]<br>[[Diffraction grating]], [[Calculus]]
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| |author_abbrev_bot =
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| |author_abbrev_zoo =
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| |influences = [[Stefano degli Angeli]]
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| |influenced = [[David Gregory (mathematician)|David Gregory]]
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| |prizes =
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| |religion = [[Church of Scotland]]
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| |footnotes = Nephew of [[Alexander Anderson (mathematician)|Alexander Anderson]]. Uncle of [[David Gregory (mathematician)|David Gregory]].
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| |signature =
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| }}
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| '''James Gregory''' (also spelled ''James Gregorie'') [[Fellow of the Royal Society|FRS]] (November 1638 – October 1675) was a Scottish mathematician and [[astronomer]]. He described an early practical design for the [[reflecting telescope]] – the [[Gregorian telescope]] – and made advances in [[trigonometry]], discovering [[infinite series]] representations for several trigonometric functions.
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| In his book ''Geometriae Pars Universalis'' (1668), Gregory gave the first published proof of the [[fundamental theorem of the calculus]] (stated from a geometric point of view, and only for a special class of the curves considered by later versions of the theorem).<ref>[http://www-history.mcs.st-and.ac.uk/~edmund/GpsStAnd/Groups07a.html Edmund F. Robertson. James Gregory: Regius Professor of Mathematics.]</ref><ref>Michael Nauenberg. [http://arxiv.org/abs/1111.6145 Barrow and Leibniz on the fundamental theorem of the calculus].</ref><ref>Andrew Leahy. [http://www.maa.org/publications/periodicals/convergence/a-euclidean-approach-to-the-ftc-introduction A Euclidean Approach to the FTC – Gregory's Proof of the FTC].</ref><ref>Ethan D. Bloch. [http://books.google.com/books?id=r0qcU9U2_I4C&pg=PA316 The Real Numbers and Real Analysis], pg. 316.</ref>
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| == Biography ==
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| The youngest of the 3 children of John Gregory, an [[Episcopalianism in the Church of Scotland|Episcopalian]] [[Church of Scotland minister]], James was born in the [[manse]] at [[Drumoak]], [[Aberdeenshire (historic)|Aberdeenshire]], and was initially educated at home by his mother, Janet Anderson (~1600–1668). It was his mother who endowed Gregory with his appetite for [[geometry]], her uncle – [[Alexander Anderson (mathematician)|Alexander Anderson (1582–1619)]] – having been a pupil and editor of French mathematician [[Viète]]. After his father's death in 1651 his elder brother David took over responsibility for his education. He was sent to [[Aberdeen Grammar School]], and then to [[Marischal College]], graduating in 1657.
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| In 1663 he went to London, meeting [[John Collins (mathematician)|John Collins]] and fellow Scot [[Robert Moray]], one of the founders of the [[Royal Society]]. In 1664 he departed for the [[University of Padua]], in the [[Venetian Republic]], passing through [[Flanders]], Paris and Rome on his way. At Padua he lived in the house of his countryman [[James Caddenhead]], the professor of philosophy, and he was taught by [[Stefano Angeli]].
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| Upon his return to London in 1668 he was elected a [[Fellow of the Royal Society]], before travelling to [[St Andrews]] in late 1668 to take up his post as the first [[Regius Professor of Mathematics]], a position created for him by [[Charles II of England|Charles II]], probably upon the request of Robert Moray.
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| He was successively professor at the [[University of St Andrews]] and the [[University of Edinburgh]].
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| He had married Mary, daughter of [[George Jameson]], painter, and widow of Peter Burnet of Elrick, Aberdeen; their son James was Professor of Physics at King's College Aberdeen. He was the grandfather of [[John Gregory (moralist)|John Gregory]] (FRS 1756); uncle of [[David Gregory (mathematician)|David Gregorie]] (FRS 1692) and brother of [[David Gregory (physician)|David Gregory]] (1627–1720), a physician and inventor.<ref>[http://www2.royalsociety.org/DServe/dserve.exe?dsqIni=Dserve.ini&dsqApp=Archive&dsqCmd=Show.tcl&dsqDb=Persons&dsqPos=0&dsqSearch=%28Surname%3D%27gregory%27%29 DServe Archive Persons Show<!-- Bot generated title -->]</ref>
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| About a year after assuming the Chair of Mathematics at [[Edinburgh]], James Gregory suffered a stroke while viewing the moons of Jupiter with his students. He died a few days later at the age of 36.
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| ==Published works==
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| ===''Optica Promota''===
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| In the ''Optica Promota'', published in 1663, Gregory described his design for a [[reflecting telescope]], the "[[Gregorian telescope]]". He also described the method for using the [[transit of Venus]] to measure the distance of the Earth from the Sun, which was later advocated by [[Edmund Halley]] and adopted as the basis of the first effective measurement of the [[Astronomical Unit]].<ref>[http://www.st-andrews.ac.uk/~jglectures/james_gregory.php]</ref>
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| ===''Vera Circuli et Hyperbolae Quadratura''===
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| In 1667, Gregory issued his ''Vera Circuli et Hyperbolae Quadratura'', in which he showed how the areas of the [[circle]] and [[hyperbola]] could be obtained in the form of [[Infinite series|infinite convergent series]]. This work contains a remarkable geometrical proposition to the effect that the [[ratio]] of the area of any arbitrary sector of a circle to that of the inscribed or circumscribed [[regular polygon]]s is not expressible by a finite number of terms. Hence he inferred that the [[quadrature of the circle]] was impossible; this was accepted by [[Jean-Étienne Montucla|Montucla]], but it is not conclusive, for it is conceivable that some particular sector might be squared, and this particular sector might be the whole circle. Nevertheless Gregory was effectively among the first to speculate about the existence of what are now termed [[transcendental numbers]]. In addition the first proof of the [[fundamental theorem of calculus]] and the discovery of the [[Taylor series]] can both be attributed to him.
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| The book also contains series expansions of [[sine|sin]](''x''), [[cosine|cos]](''x''), arcsin(''x'') and arccos(''x''). (The earliest enunciations of these expansions were made by [[Madhava of Sangamagrama|Madhava]] in India in the 14th century). It was reprinted in 1668 with an appendix, ''Geometriae Pars'', in which Gregory explained how the volumes of [[solids of revolution]] could be determined. | |
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| ==Gregorian telescope==
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| [[Image:Gregory-Teleskop.svg|thumb|370px|Diagram of a Gregorian reflecting telescope.]]
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| {{main|Gregorian telescope}}
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| In his 1663 ''Optica Promota'', James Gregory described his reflecting telescope which has come to be known by his name, the Gregorian telescope. Gregory pointed out that a [[reflecting telescope]] with a [[parabolic reflector|parabolic mirror]] would correct [[spherical aberration]] as well as the [[chromatic aberration]] seen in [[refracting telescope]]s. In his design he also placed a concave [[secondary mirror]] with an elliptical surface past the focal point of the parabolic [[primary mirror]], reflecting the image back through a hole in the primary mirror where it could be conveniently viewed. According to his own confession, Gregory had no practical skill and he could find no optician capable of actually constructing one.<ref>[http://books.google.com/books?id=9EYBAAAAQAAJ&pg=PA175-IA1&dq=parabolic+James+Gregory A Biographical Dictionary of Eminent Scotsmen By Robert Chambers, Thomas — Page 175]</ref>
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| The telescope design attracted the attention of several people in the scientific establishment such as [[Robert Hooke]], the Oxford physicist who eventually built the telescope 10 years later, and Sir [[Robert Moray]], [[polymath]] and founding member of the [[Royal Society]].
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| The Gregorian telescope design is rarely used today, as other types of reflecting telescopes are known to be more efficient for standard applications. Gregorian optics are also used in [[radio telescopes]] such as [[Arecibo Observatory|Arecibo]], which features a "Gregorian dome".<ref>{{cite web |url=http://www.pbs.org/safarchive/3_ask/archive/qna/3291_cordes.html |title=Jim Cordes Big Dish |accessdate=22 November 2007}}</ref>
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| == Mathematics ==
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| The following excerpt is from the ''[[Pantologia]]. A new (cabinet) cyclopædi'' (1813)
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| <blockquote>
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| Mr. James Gregory was a man of a very acute and penetrating genius. ...The most brilliant part of his character was that of his mathematical genius as an inventor, which was of the first order; as will appear by... his inventions and discoveries [which include] quadrature of the circle and hyperbola, by an infinite converging series; his method for the transformation of curves; a geometrical demonstration of [[William Brouncker, 2nd Viscount Brouncker|Lord Brounker's]] series for squaring the hyperbola—his demonstration that the meridian line is analogous to a scale of logarithmic tangents of the half complements of the latitude; he also invented and demonstrated geometrically, by help of the hyperbola, a very simple converging series for making the logarithms; he sent to [[w:John Collins (mathematician)|Mr. Collins]] the solution of the famous [[Kepler problem|Keplerian problem]] by an infinite series; he discovered a method of drawing [[Tangent]]s to curves geometrically, without any previous calculations; a rule for the direct and inverse method of tangents, which stands upon the same principle (of [[Method of exhaustion|exhaustions]]) with that of [[Method of Fluxions|fluxions]], and differs not much from it in the manner of application; a series for the length of the arc of a circle from the tangent, and vice versa; as also for the secant and logarithmic tangent and secant, and vice versa. These, with others, for measuring the length of the elliptic and hyperbolic curves, were sent to Mr. Collins, in return for some received from him of [[Isaac Newton|Newton's]], in which he followed the elegant example of this author, in delivering his series in simple terms, independent of each other.<ref>[[John Mason Good]], [[Olinthus Gilbert Gregory]], Newton Bosworth, [http://books.google.com/books?id=kWgIAAAAQAAJ ''Pantologia A new (cabinet) cyclopædi''] (1813)</ref>
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| </blockquote>
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| ==Other work==
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| In 1671, or perhaps earlier, he established the theorem that
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| :<math>\theta = \tan \theta - (1/3) \tan^3 \theta + (1/5) \tan^5 \theta - \ldots</math>,
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| the result being true only if θ lies between −(1/4)π and (1/4)π.
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| This formula was later used to calculate digits of [[pi|π]], although more efficient formulas were later discovered.
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| James Gregory discovered the [[diffraction grating]] by passing [[sunlight]] through a bird [[feather]] and observing the diffraction pattern produced.<ref>Letter from James Gregory to John Collins, dated 13 May 1673. Reprinted in: ''Correspondence of Scientific Men of the Seventeenth Century....'', ed. Stephen Jordan Rigaud (Oxford, England: [[Oxford University Press]], 1841), vol. 2, pages 251–255; see especially page 254. Available on-line at: [http://books.google.com/books?id=0h45L_66bcYC&pg=PA254&dq=feather+ovals&ie=ISO-8859-1&output=html Books.Google.com].</ref> In particular he observed the splitting of sunlight into its component colours – this occurred a year after Newton had done the same with a [[prism (optics)|prism]] and the phenomenon was still highly controversial.
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| Gregory, an enthusiastic supporter of Newton, later had much friendly correspondence with him and incorporated his ideas into his own teaching, ideas which at that time were controversial and considered quite revolutionary.
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| The crater [[Gregory (lunar crater)|Gregory]] on the Moon is named after him. He was the uncle of mathematician [[David Gregory (mathematician)|David Gregory]].
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| == See also ==
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| *[[Kerala_school_of_astronomy_and_mathematics#Possibility_of_transmission_of_Kerala_School_results_to_Europe|Possible transmission of Kerala mathematics to Europe]]
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| *[[James Gregory Telescope|James Gregory Telescope, St Andrews]]
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| *[[Leibniz_Institute_for_Astrophysics_Potsdam#GREGOR|Gregor telescope]] at the [[Teide Observatory]].
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| *[[Gregorian telescope]] is a type of telescope.
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| ==References==
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| {{reflist}}
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| == Further reading ==
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| * {{cite journal | author = Turnbull, H. W. | title = Early Scottish Relations with the Royal Society: I. James Gregory, F.R.S. (1638–1675) | journal = Notes and Records of the Royal Society of London | year = 1940–1941 | volume = 3 | pages = 22–38 | jstor=531136 | doi = 10.1098/rsnr.1940.0003}}
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| *{{cite web| author= J J O'Connor and E F Robertson | title=Biography of James Gregory | publisher=University of St Andrews School of Mathematics and Statistics | url=http://www-history.mcs.st-andrews.ac.uk/Biographies/Gregory.html | accessdate=4 May 2009}}
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| *{{cite thesis |type=PhD |first=Antoni |last=Malet |title=Studies on James Gregorie (1638–1675) |publisher=Princeton University |year=1989}}
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| ==External links==
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| {{commons|James Gregory|James Gregory (astronomer and mathematician)}}
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| * {{cite web | author = Tunrbull, H. W. | year = 1938 | title = The Tercentenary of the birth of James Gregory | url = http://www-groups.dcs.st-and.ac.uk/~history/Extras/Turnbull_address.html | accessdate = 19 October 2008}}
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| * {{MacTutor Biography|id=Gregory|title=James Gregory}}
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| * [http://www.maths.tcd.ie/pub/HistMath/People/Gregory/RouseBall/RB_JGregory.html Trinity College Dublin History of Mathematics]
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| *[http://mathdl.maa.org/convergence/1/?pa=content&sa=viewDocument&nodeId=388&bodyId=343 James Gregory's Euclidean Proof of the Fundamental Theorem of Calculus] at [http://mathdl.maa.org/convergence/1/ Convergence]
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| *[http://www.jamesgregory.org.uk/ James Gregory Public Lectures on Religion and Science, University of St Andrews]
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| *[http://www.17centurymaths.com James Gregory "s "''Optica Promota''" (English translation)]
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| *[http://math.knox.edu/aleahy/gregory/WORKING/gpu.html James Gregory's "''The Universal Part of Geometry''" (Andrew Leahy's English translation of Gregory's "''Geometriae Pars Universalis''").]
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| {{Authority control|VIAF=39475242}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME = Gregory, James
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = Scottish mathematician and astronomer
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| | DATE OF BIRTH = 1638
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| | PLACE OF BIRTH = [[Drumoak]], [[Aberdeenshire (historic)|Aberdeenshire]], Scotland
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| | DATE OF DEATH = 1675
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| | PLACE OF DEATH = [[Edinburgh]]
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| }}
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| {{DEFAULTSORT:Gregory, James}}
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| [[Category:1638 births]]
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| [[Category:1675 deaths]]
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| [[Category:People from Kincardine and Mearns]]
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| [[Category:17th-century mathematicians]]
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| [[Category:Scottish astronomers]]
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| [[Category:Scottish inventors]]
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| [[Category:Scottish mathematicians]]
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| [[Category:Alumni of the University of St Andrews]]
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| [[Category:Academics of the University of St Andrews]]
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| [[Category:Academics of the University of Edinburgh]]
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| [[Category:Scientific instrument makers]]
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| [[Category:17th-century Scottish people]]
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| [[Category:Fellows of the Royal Society]]
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| [[Category:People educated at Aberdeen Grammar School]]
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| [[Category:University of Padua alumni]]
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| [[Category:Scottish Episcopalians]]
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| [[Category:17th-century astronomers]]
| |
Although the Weight Watchers flex plan is regarded as the better fat loss diets, the Weight Watchers system can become especially expensive if youve already done a session but havent reached a goal yet. If youre like various of us, we may have performed the Weight Watchers meetings in the previous and had several terrific success. If you nonetheless desire to lose weight, to do Weight Watchers successfully at home with a components from the meetings. Dont worry should you dont have the Weight Watchers contents, check the hyperlinks inside this particular article for strategies on where you are able to purchase them for less.
One should follow a healthy diet plus include foods like soy goods, egg whites, lean meat, dairy foods without fats, veggies plus fruits in their daily diet inside order to lose weight fast and safely. Avoid eating junk foods. Try to include salads, pastas and fibrous foods in the daily diet. You are able to replace white bread with brown bread. Use skimmed milk inside area of the usual one, because it has less amount of fats.
The right foods for weight reduction are fresh all-natural food, nutritionally thick, excellent in fiber, low inside fat plus calories, low in sodium plus processed sugars. They also consist of higher amounts of complex carbohydrates, fibers, good quality proteins and excellent water content. Some of the best foods to consume inside purchase to lose weight are vegetables, fruits, legumes, baked potato, complete grain foods (including wholemeal pasta, oatmeal, muesli, etc), boiled brown rice, baked potato and fresh fish.
Have breakfast. Skipping breakfast leads to low blood glucose mid morning that results in cravings for sugary foods to pump the blood sugar back up. A vicious cycle results plus continues throughout the day. The breakfast should consist of complete grains, a protein source and fruit. It doesn't need to be fancy. A cut of complete wheat toast spread with a tablespoon of low fat peanut butter and an apple can do just fine. Or you could blend 1/2 cup of nonfat cottage cheese with chopped fresh peaches along with a couple of entire wheat crackers. Another possibility is a scrambled egg served on an English muffin with a glass of orange juice.
And whenever I am seized with all the temptation of the wicked doughnut, I can resist-at least for a time lose weight fast. And then another moment, until I've put enough time between your impulse and the action, plus the craving has subsided.
As my fianc plus I were preparing the soup, I created the comment which, "Geez, no wonder you lose thus much weight found on the diet! I'm burning a zillion calories getting it ready!" We had to peel two bags of carrots plus chop up a lot of vegetables. As I place everything in the pots (I do not have a stew pot, so I used 2 big pots) I couldn't enable however think of how healthy it looked.
Losing fat is surprisingly difficult, nevertheless with this you should be capable to receive to your weight goal. If you have any query, comments or concerns please feel free to comment. For an expert opinion please contact the localized physician or dietician.