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How To Use Arity In A Sentence

  • These provisions, although expressed at a level of great generality, have often been invoked by those who posit the existence of a broad international duty to cooperate or a right to solidarity.
  • This absorbing profile muses on his universal popularity and compulsive desire to draw and paint. Times, Sunday Times
  • With no money and hand-me-down charity, they still manage to look 100 times more chic and svelte than the rest of us.
  • Although there are a couple of jarring transitions, the bulk of the movie unfolds with organic clarity.
  • Records, is among the thousands of devoted followers who have raised figure skating to new heights of popularity.
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  • The term "gentilhomme" is so liable to be confounded with "gentleman" that it needs explaining, for, despite the similarity of derivation, no two words can be more distinct. Lippincott's Magazine of Popular Literature and Science Volume 17, No. 097, January, 1876
  • But it is precisely the familiarity of the urban terrain to those who live there that enables them to use it to the advantages of ambushes, surprise attacks and rapid redeployment.
  • The line of stemware and tumblers feature a unique magnesium-based crystal that the company says eliminates the trade-off between clarity and durability in this product category.
  • There is very little to break the familiarity and deadening monotony of Aslam's routine.
  • Vulnerability is not weakness, and the uncertainty, risk, and emotional exposure we face every day are not optional. Our only choice is a question of engagement. Our willingness to own and engage with our vulnerability determines the depth of our courage and the clarity of our purpose; the level to which we protect ourselves from being vulnerable is a measure of our fear and disconnection. Brene Brown 
  • A man of good humour and a great sense of fun, he enjoyed popularity among his teaching colleagues and pupils, many of whom were present at the removal of remains and burial.
  • Opera is different from the mainstream entertainment industry, which uses packaging and promotion to increase popularity.
  • Another trend referred to two related areas – increased user-centeredness and increased inter-disciplinarity. Archive 2008-02-01
  • Despite their superficial similarity, submersion of minorities in English-only programs in the USA and Canadian immersion programs are different and they lead to different results.
  • The geography was utterly alien to Patrick, although his unfamiliarity with the picture could have been attributed to the gaps.
  • The fall in popularity of the death's head and the subsequent prevalence of the cherub was a reflection of the Great Awakening and the belief in the immortality of the soul: "Cherubs reflect a stress on resurrection, while death's heads emphasize the mortality of man. Headstones for Dummies, the New York Edition
  • It is true that, even at the time of the discovery of nitrobenzol, he pointed out the striking similarity of its smell to that of the oil of bitter almonds. The Art of Perfumery And Methods of Obtaining the Odors of Plants
  • Hunt thinks it unlikely that the currency will break parity with the dollar next year, and feels it is likely to settle around the $0.92 level.
  • Most often, this implies a life on city streets begging, panhandling, petty theft, and using charity and soup kitchens close to the drug source.
  • They stood, without any respect for regularity, on each side of a straggling kind of unpaved street, where children, almost in a primitive state of nakedness, lay sprawling, as if to be crushed by the hoofs of the first passing horse. The Waverley
  • We will show solidarity and we will obey the law. The Sun
  • But because Americans are not nearly as fond of dates as they are of coffee, java came out on top due to sheer popularity.
  • Boschi, who trained with Passignano in the late 1580s, is known today principally to specialists, but he enjoyed a considerable degree of popularity in the early seicento.
  • The arrival of the charity van set off a minor riot as villagers scrambled for a share of the aid.
  • Palpation of the nasal structures should be done to elicit any crepitus, indentation, or irregularity of the nasal bone.
  • Benedict, put simply, is living out what he spoke of in Deus Caritas Est, which is true charity: Can we simply exclude them, as representatives of a radical fringe, from our pursuit of reconciliation and unity? Ecumenism
  • Call me a moon-eyed dreamer: I still believe the work of the serious writer will be recognized for what it is, whether it takes place examples chosen only for clarity and expediency in Ambergris, or 351 West 52 St New York City Apt # D RIGHT NOW, dammit. Evil Monkey on Fantasy
  • Another feature of interest is the rarity with which axillary prolification is found in irregular gamopetalous blooms. Vegetable Teratology An Account of the Principal Deviations from the Usual Construction of Plants
  • However peculiarity is a characteristic of all things Royal, not to say outright barminess.
  • Dot and I took some manchets about the manor to sell for charity, although she did all the talking.
  • The soloist and orchestra achieve wonderful clarity and fine ensemble.
  • Vanessa raised hundreds of pounds for the charity by playing requests in exchange for donations to the appeal.
  • It had four wheels, but that was where the similarity to anything she had ever driven ended.
  • And in any case, there will be plenty of memories gained and stories to embellish after another extravaganza of Celtic solidarity.
  • Although the number of rural ponds is decreasing rapidly, garden ponds are gaining in popularity and are becoming increasingly important habitats for toads, says the trust.
  • Cash will be the vital ingredient as celebrity chefs cook up a special fundraising treat for charity.
  • While such drinks as the Sour Appletini have been getting lots of press lately, it seems the tried and true classics still lead the pack in popularity, at least according to the latest survey of bar managers and bartenders.
  • The Church and the laity were increasingly active in charity work.
  • His narrative has a circularity that makes the reader's head spin.
  • We do need to show that we can talk without contradiction of God's universal salvific will and the scandalous particularity of the incarnate and risen Lord.
  • If the problem is income disparity, then the answer must be income redistribution. Times, Sunday Times
  • The key to their popularity was government subsidy and regulation that obliged motorists and oil companies to use biofuels. Times, Sunday Times
  • This in some degree corresponds with Captain Cook's record of the irregularity of his compass when he passed near this part of the coast, in consequence of which he called the peaked island to the westward of the cape, Magnetical Island: this irregularity, however, was not noticed by me in my observations near the same spot; and the difference observed by him may very probably have been occasioned by the ship's local attraction, which in those days was unknown. Narrative of a Survey of the Intertropical and Western Coasts of Australia Performed between the years 1818 and 1822 — Volume 1
  • Their ability to conduct surprise raids presupposed close familiarity with currents, beaches, and locations of population centres.
  • The Year 9 mentors are trained by children's charity Childline and run lunchtime support clubs as well as a drop-in centre where younger students can call in for advice or help.
  • There she goes again with that faith, hope, charity, and creativity twaddle.
  • See it once and it will haunt your memory with the pleasant familiarity of an old friend.
  • Its popularity in 1948 with both schoolchildren and adults saw the Blossom Street picture house bursting at the seams during matinees and evening performances for weeks on end.
  • For example, consider the disparity in flight rates between Saturn 1B and Saturn V during the Skylab program or between the Soyuz and Proton in the Russian Salyut & Mir programs. Ares V - Ares 1 = Ares IV - NASA Watch
  • How often I have I known him affect an open brow and a jovial manner, joining in the games of the gentry, and even in the sports of the common people, in order to invest himself with a temporary degree of popularity; while, in fact, his heart was bursting to witness what he called the degeneracy of the times, the decay of activity among the aged, and the want of zeal in the rising generation. Redgauntlet
  • I wouldn't be surprised if as a result of his Liverpool trip he finds his popularity ratings soaring.
  • One of the primary objectives of the Calcutta celebration is to crystallize this counter-exemplarity in the very space where previous observers, including Projection, Patriotism, Surrogation: Handel in Calcutta
  • This easy way to avoid sales tax is one reason for the enormous popularity of mail order in the US and it means that US Internet e-tailers are used to not collecting sales tax too often.
  • What if it was expressive of the redundancy of these men's thoughts, their emptiness and circularity?
  • The two in fact are related: the ideas resonate differently in different parts of the world, exemplifying with remarkably clarity the issues introduced in the previous sections.
  • Raquel Welch was at the height of her popularity as a sex goddess.
  • The disparity seems further exaggerated by the size and blackness of the soldier's hat.
  • Whether you ride a moped or a Honda, a scooter or a vintage Hog, the organisers of the annual North Coast Children's Motorcycle Toy Run want you to join the ranks raising money for charity this weekend.
  • They performed well - many have sustained their popularity for years mainly because they give excellent performance for low cost.
  • That obvious familiarity of product and my jovial manner helped me pass through the whole security network unchecked. Corporate Cloak and Dagger
  • Charity begins at home, but should not end there. 
  • Sclavonic blood, or from the descendants of Rurik's companions, differ little in regularity of feature and expression of countenance from the handsomest races of Europe. Glimpses of Life and Manners in Persia
  • The Kensington High Street rag reckons chuggers—paid workers who stop you in the street and persuade you to give over your bank details for charity—are well on their way out.
  • Giving money to charity in your will is another handy way to sidestep the taxman. Times, Sunday Times
  • The size and familiarity of the little lamb is genuinely touching. Times, Sunday Times
  • The scandal of Christian theology, of Jesus' particularity, Keck argues, must be considered in view of Jesus' Jewishness.
  • The exact particulars of the similarity never came to light, but apparently the lady had, in a fit of high-minded inadvertence, had gone through the ceremony of marriage with, one quotes the unpublished discourse of Mr. Butteridge — “a white-livered skunk,” and this zoological aberration did in some legal and vexatious manner mar her social happines. The War in the Air
  • I should add that I am only really interested in results from the UK as we are a UK based charity and cannot help anyone outside of Scotland Testing Search Engine Page Ranking Techniques « Lorelle on WordPress
  • The charity added that birds that no longer performed had their necks wrung. Times, Sunday Times
  • They also hope for further union delegations to extend the links of international solidarity.
  • The similarity of the two fires suggests the possibility of malicious intent.
  • His appeal may lie in the disparity between the image projected in his interviews and the image perpetuated in his records.
  • A WordPress child theme is a theme that inherits the functionality of another theme form-a directory with a file named '' style. css '' make; itr equires only some familiarity with HTML and CSS, and no knowledge of PHP. Codex - Recent changes [en]
  • From the beginning, they have echoed their disinterest in matters like chart placings and mass popularity.
  • Lipatti s performance possesses a clarity of articulation, a depth of sonority and an energy that shine through the crackly recording.
  • This charity aims to help people to help themselves.
  • Nothing satisfies these people, because now they cannot abide clarity in anyone but themselves.
  • In contrast, Princess Sirindhorn, his sister, enjoys a saintly image as a patron of charity.
  • His stunt mimics magician David Blaine's attempt to survive 72 days in a glass box above London but Michael decided he would use the idea to raise cash for charity.
  • The similarity between their names is due to coincidence and European mispronunciation -- "Mahican" comes from the word Muheconneok, "from Drag to Playlist WN.com - Articles related to Ten tips for expectant mothers
  • Solidarity and diversity are both desirable objectives.
  • The charity also revealed it had cost £27,500 to kennel the dogs since they were confiscated in October, 2003.
  • In many respects, the development of international human rights is an example of the principle of subsidiarity - the international community only steps in when the State cannot or will not deal with the problem.
  • She ran away with the show as Liu, bringing clarity to both her deepest, most vociferous registers and to her challenging tremolos over sostenuto in the highest notes.
  • The guy really does have it all - girlfriend, popularity, and university scouts drooling over his breaststroke.
  • The absolute clarity of the orchestral texture allowed for the sometimes jarring harmonies and raucous percussion effects to be highlighted.
  • The disparity is played out on a bigger scale between cities. Times, Sunday Times
  • I was struck by the similarity of displays on many of their office pinboards.
  • A five-day week has found an immediate welcome and much popularity since it was officially adopted across the country.
  • When you laugh at politicians, all you do is channel righteous anger into passive hilarity. Times, Sunday Times
  • People who lack the clarity, courage, or determination to follow their own dreams will often find ways to discourage yours. Live your truth and don't EVER stop! Steve Maraboli 
  • Problem is, they're too busy raising money for charity or building an electric bike to care that their dad is holding out an olive branch. The Sun
  • Yorkshire folk turned prickly yesterday after a wild flower charity announced that the common harebell had replaced the white rose as the county's floral emblem.
  • Of critical importance, Du Bois wrote, is his financial success, his efforts to increase church membership, and his personal popularity. American Grace
  • The expression pervading the countenance of the one was vulgarity; of the other, that which is rarely found, except in persons of high birth. Jack Sheppard A Romance
  • We suspected that most people would not spontaneously think in terms of this curvilinearity and would, in fact, think that fuel consumption decreases as a linear function of MPG. The Miles Per Gallon Illusion | clusterflock
  • The charity also needs volunteers and furniture, clothes and food.
  • Its ills have largely been the result of the rapid growth in popularity of online movie rental and download services. Times, Sunday Times
  • Would you like to make a donation to our charity appeal?
  • Unfortunately, whatever mojo he worked in the mountains has reversed the Earth's cool polarity and Superman is temporarily cooler than Batman.
  • However, despite that the sport of surfing continues to grow in popularity.
  • Off to the Charity Ball is a firm favourite, with its livid pastels against bright white, the skulking figures throwing dark, tactile shadows onto the projecting shelf below.
  • Like a kid, Mr. Mailer was fascinated by his own naughtiness -- his earliest critics castigated him for the vulgarity of his language, though his editors insisted that he use the word "fug" in "The Naked and the Dead. A Boy's Life
  • It is the peculiarity of knowledge that those who really thirst for it always get it. 
  • Here various design moves unfold: nothing is what it seems, complexity unstitches singularity.
  • Edward's affair and subsequent marriage to divorced Mrs Simpson had left the family's popularity at an all-time low.
  • This notion of the singularity is the most popular (although by no means the only) current theory. Think Progress » Cheney: If You Don’t Support Everything I Do, You Aren’t Serious About Terrorism
  • The irritating lack of clarity about who holds what amount of debt has led to some ridiculous underpricing of risk. Times, Sunday Times
  • The charity aims to relieve poverty and distress caused by natural disasters.
  • The desire to cut taxes Governments gain popularity by cutting taxes, not by increasing them.
  • Conclusion: The leiomyomatous neoplasms are rich in vascularity. the benign and malignant tumor possess vascular feature.
  • But this can not, of course, explain the greater similarity in the striping of the rest of the body.
  • Clarity of diction is vital for a public speaker.
  • Similarity in a trait is measured with a value called concordance.
  • With the ideological polarity of the cold war, the UN procedures for collective security were still-born (as either of the superpowers and their allies would veto any action proposed by the other).
  • They would all see her go mental, and she would slowly but surly lose her popularity.
  • But the economic aims of the MFA guild would be unrealizable without its social aims, which perpetuate solidarity. Anis Shivani: Creative Writing Programs: Is The MFA System Corrupt And Undemocratic?
  • The company is filled with superb technologists who are prepared to obsolete products in their prime and to churn out new ones with clockwork regularity.
  • A local Burmese solidarity group wants you to think twice about the country of origin of your favourite soporific.
  • The early success and popularity of rural reforms encouraged the introduction of economic change in urban areas.
  • Did Charity lure him into her sticky web? The Sun
  • So, in contrast to the ACCORD subjects, these started with relatively healthy vascularity. More supporting evidence for the sugar hypothesis | The Blog of Michael R. Eades, M.D.
  • In theory, PLS is applied in situations of multicollinearity, but the MBH network has many series that are essentially white noise and thus the proxies are surprisingly close to being orthogonal in the early networks and there are blocks of orthogonal series in the later network. More on Bürger et al 2006 « Climate Audit
  • Moreover it seems to me atrocious that we who insist on seven millions of Catholics supporting a church they call heretical, should dare to talk of our scruples (conscientious scruples forsooth!) about assisting with a poor pittance of very insufficient charity their 'damnable idolatry.' The Letters of Elizabeth Barrett Browning
  • Wherefore, upon all these accounts, as well as for all the reasons before mentioned, youth stands in need of good government to manage it in the reading of poetry, that being free from all prejudicate opinions, and rather instructed beforehand in conformity thereunto, it may with more calmness, friendliness, and familiarity pass from thence to the study of philosophy. Essays and Miscellanies
  • The lawyer asked the jury to take cognizance of the defendant's generosity in giving to charity.
  • The disparity in halves hasn't escaped the coaching staff's attention. Washington Redskins are halfway there: First two quarters have been better than last two
  • Elsewhere she might have won sympathy and benefited from female solidarity. Times, Sunday Times
  • The difference and similarity between shadow moire fringe and Newtonian circlet are discussed from basic principles.
  • He also keeps himself fairly socially active, spearheading a charity to benefit inner-city youths of musical talent.
  • Someone makes a heartfelt, tear-jerking appeal on behalf of the charity, and then up pops some sweaty, half-cut minor-league celebrity who's a mate of someone on the committee.
  • The chief limitation on the number of fossil species studied was the rarity in museum collections of skulls with complete dentition, especially incisors.
  • Pelosi was non-committal when asked about how much this would cost, saying more clarity will come from congressional hearings before and after the November 4th U.S. presidential election.
  • Its ills have largely been the result of the rapid growth in popularity of online movie rental and download services. Times, Sunday Times
  • We urgently need to build a solidarity movement on the scale of those against South African apartheid and the Vietnam War in the past.
  • The necessary precondition for a functioning democracy is not just minimal outright poverty, but a reasonable degree of similarity between the life and life prospects of the citizens.
  • Depending on the irregularity of the terrain, the operator can adjust both the ground clearance of the machine and height of each step.
  • The charity will forward the letters to the foreign embassies to make them aware of the level of public support for the drivers.
  • Women workers are demanding parity with their male colleagues.
  • It wasn't the faux avuncularity we've come to expect from Stewart on "The Daily Show" but there, of course, he's playing a role. October 2004
  • The popularity of diversified operations promotes the origination and development of segment report.
  • There are other, smaller points of similarity; Emma's boredom with village life is parallelled in Cher's boredom with high school boys. Way Existential
  • The shop and cafe were once a thriving business and despite a recent upturn in fortunes, a three-year period of losses have led to charity chiefs deciding it is no longer financially viable.
  • His flat-tax fire, which burned hot for months, ultimately flickered out along with his popularity.
  • Employees make regular donations to charity.
  • It now has to become a modern social democratic party which can win because of the popularity of its vision.
  • Cordelia Carroll had pride, one daughter, and the desire to see the Hereford Carrolls retain some parity with the Charolais Dales.
  • In addition to supporting their validity, it provides a clearer sense of the relation between infinitude, singularity, and whole - part priority, and of the status of space and time as infinite ‘givens.’
  • A living will also allows a person to state with particularity the forms of treatment which are wanted and not wanted.
  • Nations. yep, it's pretty quaint stuff, couched in terms of newness and normalcy, of foreigness and familiarity. it describes the music as modern and "swingy" and yet timeless, as being of universal appeal - they belong to everyone - and yet "from a single nationality." i wonder whether the universalist rhetoric was meant to appeal to non-jews or simply to jews ambivalent about their jewishness? or am i simply being naive about midcentury, metropolitan jewishness? it is interesting to me also that, apparently, zionist discourse had not yet divorced the term palestinian from any association with jewish heritage. Wayneandwax.com
  • Any such definitive analysis, however, would need to respond, at the very least, both to his at once ‘avant- garde’ and hard-headedly commercial use of abstracted, deliberately over-stylised backgrounds and movements, and to the logical circularity which repeatedly dictates the emotional lives of his characters.
  • It planned for a mock battle, shammed unity, and were confused by the intransigence and solidarity of the other side.
  • It has also been boosted by the popularity of trainers and trend for wearing training kit outside the gym. The Sun
  • The early-twentieth-century cult of the wilderness further boosted the popularity of night air among the health-conscious.
  • Job seekers' experience and their familiarity with the Chinese market were the focal issues for headhunters.
  • You probably haven't noticed, but my surname bears a passing resemblance to a certain vulgarity.
  • When al Molqi took off, he was under the charge of Roman Catholic charity workers.
  • I wouldn't demean myself by asking for charity.
  • Perhaps worse still was the monotonous, mechanical regularity imposed on the worker by the factory system. Property and Prophets: The Evolution of Economic Institutions and Ideologies
  • In an age of crassness, vulgarity and self-indulgence, she has continued to be an icon of what we once were and of what we might yet become again.
  • Will it meet the expectations of nurses, who want the government to settle their claim for pay parity in the same way it did for teachers in 2002?
  • Given the circumstances, Bouder gave an incredibly polished rendition of the role, weaving the choreographic phrases into a dancerly whole with clarity and detail.
  • Collectors of everything from uncirculated coins to Parker shotguns agree that there are three criteria in determining the worth of a collector's item - rarity, authenticity and quality.
  • To determine the correct gene structure, we performed a sequence similarity search against the protein database.
  • Apart from the rainbows and browns, it is stocked with some cross-bred trout which seem to be gaining in popularity at fisheries.
  • Rather, the disparity can be traced to disparities in the socioeconomic status between segments of the American population. An Introduction to Community Health
  • Pleasing to the eye: Owing to the diffuse reflection of vermiculites , its flamboyant looking and tridimensional appearance, metal roofing tiles enjoy great popularity worldwide.
  • r is called the arity of the function f, i.e., the number of arguments that it takes. Computability and Complexity
  • The museum has a Saudi sculpture of a falcon on a perch, of inestimable value and stunning vulgarity, made from gold, quartz, rubies, emeralds, sapphires and 1,210 diamonds.
  • This utter tripe that is reality TV seems to be gaining in popularity.
  • Familiarity with danger makes a brave man braver but less daring
  • Marked terms show a polarity, like one pole of the magnet or one side of the coin.
  • They behave to one another as they do to a foreign armadillo, in spite of their genetic similarity.
  • The confessional language is stunning in its clarity: ‘I know my transgressions, and my sin is ever before me.’
  • 'Friend,' whispered he, 'for charity conduct us to some safe place where we may withdraw this bier from the sacrilegious eye of curiosity.' The Scottish Chiefs
  • His technical skill guarantees admirable clarity in the midst of complex counterpoints, and there is a delightful sense of well-being about the performances.
  • I ran my fingers along the carved wood, admiring the way the workman had managed to fit motifs from Inuit art into the design without muddying the clarity of the sign. How to Flirt with A Naked Werewolf
  • Charity dinners and celebrity dos for a cause are a trend these days - what better way to raise a big sum for a noble cause?
  • The assumption that gender parity in all things is inconducive to sustainable propagation arrives at the footstep of the ideas in Steve Sailer's article "The Return of Patriarchy?". The Audacious Epigone
  • Marziya knows with money you get sweets toys, but here she is aware that what she gives the Umbrella lady will not get her anything in return..but a sweet smile .. and this is the lesson I teach Marziya , giving charity without compulsion, I teach Marziya along with photography the meaning of humility... Archive 2009-08-01
  • Charity organizations have chastised the Government for not doing enough to prevent the latest famine in Africa.
  • Classical music, 14-18sNational Youth Orchestra, conducted by Semyon Bychkov, at the Royal Albert Hall, London, on 7 August by Sasha Millwood, 18The magical and mysterious quality imbued to the Dukas never came at the expense of the clarity of the virtuosic lines. Guardian young arts critic competition: 2010 winning entries
  • He, on the other hand, is impudent, and addresses the Lord with pert familiarity.
  • People become charity trustees for myriad reasons, often wanting to give something back to society. Times, Sunday Times
  • The latest opinion poll shows that the president's popularity has declined.
  • It is a potent time-release medication for relief of moderate to severe pain, known as hillbilly heroin because of black-market popularity in some rural areas.
  • It goes on and on, but I didn't want it to end, found myself sitting at the computer snorting and guffawing at the over-the-top shmaltzy spectacularity. 15 Minutes of Bliss
  • Line editing also known as copyediting is all about clarity and presentation, and is thus a great choice for a writer unfamiliar with the norms of submission or in question about grammar. Author! Author! » 2008 » December
  • The charity advises all people looking at their options to seek independent advice. Times, Sunday Times
  • It seemed that Alice was expiating her father's sins with her charity work.
  • The lawyer asked the jury to take cognizance of the defendant's generosity in giving to charity.
  • Gits Drummer Steve Moriarity Comments On Mia Zapata Killer's Reinstated Prison Sentence Butt Powder: Sitek should stop ripping off the early 4AD catalo ... The Tripwire
  • Due to its rarity and unique coloring, the python now commands fantastic prices.
  • Spurred by the growing popularity of judo, especially in European countries, a new generation of non-Japanese judoka are coming of age -- and they're changing the nature of the game. Judo power shift
  • Lewis found his métier in the new popularity of the film noir.
  • All an RDF (or "interlingua") proponent will say is that RDF can be even cheaper and less error prone, and much of the reason not to adopt it is down to developer preferences, lack of familiarity, tooling and so on - i.e., much the same reason developers don't adopt XSLT, summarising the issue as "XSLT sucking". Planet XML
  • The administration has enunciated this position with admirable clarity in its new national security strategy.
  • Even in our sensual days the strength of delight is in its seldomness or rarity, and sting in its satiety; mediocrity is its life, and immoderacy its confusion. A History of Elizabethan Literature
  • The reference to text messages provoked hilarity on the opposition benches. Times, Sunday Times
  • But the Spread Law and Cross Law are uncredited as equivalents of the sine and cosine rules, and the Triple Quad Formula for collinearity as an equivalent of Heron's formula (three points are collinear if they make a triangle of zero area).

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