ratioin a sentence

The ratio of width to height of typical computer displays is 4:3.
ratio = relative lengths

The golden ratio, also known as the divine proportion, is a special number (equal to about 1.618) that appears many times in geometry, art, an architecture.
ratio = relative magnitudes of two quantities

Three common business profit ratios that are measured are gross profit margin, operating profit margin, and net profit margin.
ratios = relative quantities

A relatively low ratio of the length of the index finger to the ring finger correlates with increased risk of prostate cancer in men.
ratio = relative measurement

There is much interesting study on the predictive value of the ratio of the length of the index finger to the ring finger within a given gender and race.
ratio = relative lengths

It featured a sentencetocorpse ratio of nearly 1:1, and I tore through it without ever looking up.
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ratio = measurement comparing relative quantities

Stanley weighed three times as much as the other boy. Mrs. Bell wrote the ratio on the board, 3:1, unaware of how much embarrassment she had caused both of them.
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ratio = the relative amount of two quantities

They looked at me with faint distaste—or perhaps even incomprehension—no doubt weighing up my fattomuscle ratio and finding it wanting.
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ratio = relative amounts

This changed the volume ratio of solid to liquid dramatically, which in turn made the aggregate act as a liquid.
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ratio = relative quantities

Their meat has a ratio of about 14 omega6 to 1 omega3.
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ratio = measurement of relative quantities

I learned about veneers and gilding, what a mortise and tenon was, the difference between ebonized wood and true ebony, between Newport and Connecticut and Philadelphia crest rails, how the blocky design and closecropped top of one Chippendale bureau rendered it inferior to another bracketfoot of the same vintage with its fluted quarter columns and what he liked to call the "exalted" proportions of the drawer ratio.
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ratio = relative sizes

Its six hundredfoot tall silos held the powders of aluminumsilicate, soda ash, limestone and silica sand, which were mixed in precise ratios called batches.
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ratios = relative quantities

The census has two objectives: First, to periodically adjust the ratio of representatives to inhabitants; the exception is that each State will have at least one representative.
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ratio = relative counts
show 187 more with this conextual meaning

We don't permit their magnesiumcalcium ratio to fall below what it was at thirty.
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ratio = relative quantities
 A few months after my return to California, I received a letter from Noelle letting me know that she had moved to New Caledonia, where, according to her, the ratio of men to women was five to one.† (source)
 For example, if you drew a line, I could always draw another line that would divide it into the golden ratio: 1.618.† (source)
 He was the first to show that the human body is literally made of building blocks whose proportional ratios always equal PHI.† (source)
 Suddenly there was real appeal in building a volcano or making my own neoprene or demonstrating the various scientific applications of gear ratios.† (source)
 Everything pointed to Aris's having come from another version of the Maze, set up in the same format except with the ratio of girls to boys being switched.† (source)
 Josie, who was presenting hers tomorrow, had polled her friends to see if there was a ratio between the number of hours you spent doing your homework and your grade point average.† (source)
 High ratio for what grade school taught us was an extinct country.† (source)
 He makes charts of Irish grammar, Irish history and algebra at home, hangs them on an easel and we have to chant our way through the cases, conjugations and declensions of Irish, famous names and battles, proportions, ratios, equations.† (source)
 We haven't run her diagnostics yet, but I think she's going to have a pretty high ratio.† (source)
 Using the ratio of infected to clean here at the base, we estimate that one out of every three surviving human beings on Earth is one of them.† (source)
 Blacks outnumbered whites by a ratio of more than ten to one.† (source)
 Immigrants have been reduced to costbenefit ratios.† (source)
 It was unusual for him to go there without getting several good shots and though he still often missed he had worked out a ratio of five to one: He seemed to get one rabbit for about every five shots on rabbits.† (source)
 The ratio of men to women in the University is about ten to one.† (source)
 We have already noted Descartes's affinity with Plato, who also observed that mathematics and numerical ratio give us more certainty than the evidence of our senses.† (source)
 Each year, right through until the mid1990s, they passed more and ran less until the ratios were almost exactly reversed: in 1995, NFL teams passed 59 percent of the time and ran 41 percent of the time.† (source)
 I'd make a decent lanyard in crafts, perfect the mayonnaiserelish ratio for the potato salad in the group kitchen, beat my father at Rummy, and sleep thickly through the night and wake up feeling rested, changed, like things were actually getting better.† (source)
 What does ultima ratio regum mean?† (source)
 Even with our high stafftopattent ratio, twotoones often meant restricted to the ward.† (source)
 He felt them cup the air, their aspect ratio dropping faster and faster.† (source)
 Ruth's bodyfat ratio was a healthy twentyfour percent.† (source)
 The ratio of misery to pleasure was greater by an order of magnitude than any other mountain I'd been on; I quickly came to understand that climbing Everest was primarily about enduring pain.† (source)
 "I fear the ratio of the mass of propellant added compared to the mass of the empty rocket will be too small," he said.† (source)
 I must have had a pee ratio of three to one in Nam versus the amount of times I had peed in Harlem.† (source)
 (Nicholas D. Kristof) The implication of the sex ratios, Professor Sen found, is that about 107 million females are missing from the globe today† (source)
 It has the largest walltolumen ratio of any tubular structure in the body, believe it or not.† (source)
 James asks, drawing ten hands out of the thirty attendees, a high ratio among the conscious.† (source)
 In terms of class size, teachers' education, and computertostudent ratio, the schools attended by blacks and whites are similar.† (source)
 I read somewhere once that people see the world and everything in it in direct ratio to how they see themselves.† (source)
 Eightyfive percent success ratio.† (source)
 To keep the ratio the same.† (source)
 Or whether each shall have a weight in proportion to its numbers, or wealth, or exports or imports, or a compound ratio of all?† (source)
 I don t know the ratio of muscle or fat in someone's body.† (source)
 Would he attain his assigned killratio of ten enemies before he was slaughtered?† (source)
 The lab is still working, but they have identified several of the ingredients, and their ratios.† (source)
 The ratios are all there.† (source)
 An outraged Mortenson offered to pay Ghulam's salary, and hire two more teachers to reduce Khanday's studentteacher ratio to a reasonable level.† (source)
 Maybe it was lucky, then, that my terrortoconfidence ratio was at an alltime low.† (source)
 Yahda, yahda, yahda, yahda, yah, carburetor, gear ratio, compression, yahdayah, piston, plugs, intake, yahdayah, on and on and on.† (source)
 He's in business solely to make a profitand his profits escalate in direct ratio to his reputation.† (source)
 0097 08 18 GET US THE DECAY RATIOS AS SOON AS POSSIBLE.† (source)
 The authorities normally preferred to have a ratio of one warder for every three prisoners.† (source)
 Ratio was tentoone or worse then.† (source)
 The long trip from factory to junkyard had weathered some pieces to certain proportions, small rods with elegant ratios of length and width, scarred old bolts with harmonious spacings between their dents.† (source)
 "The numerical ratio is not in our favor, and the country is vast and intricate," the lieutenant stated.† (source)
 The ratio of support to combat personnel was twelve to one.† (source)
 Budgets, metrics, research, and ratios: My form of expression became much more calculated.† (source)
 It's not that hard; you just need to know the ratios, and once you get those down you can play with it.† (source)
 Fivetoone kill ratio.† (source)
 It was a year when the malefemale ratio was out of balance, and most were mallard drakes, their green heads standing out sharply in the dark mass.† (source)
 That made a ratio of seventythree to one.† (source)
 However, to my surprise I observed that the density of caribou remains decreased in an almost geometric ratio to the distance from the cabin.† (source)
 Some balance wheel was misweighted, some gear out of ratio.† (source)
 I'm prepared to hold that ratio until we're relieved at 0800.† (source)
 I believe that since that time the Wells family has lived in fear of losing the place, and that their fear has grown in direct ratio to the value of the land.† (source)
 With my first letter I was instantaneously transformed from a number on a teacherratio chart to a labor problem.† (source)

On his last day of school, his math teacher... taught ratios.
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ratios = the relative magnitudes of two quantities (for example 1:2)

Representative/Constituent Ratio
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ratio = relative counts
 She packs a 20:1 thrust/weight ratio; most jets run at 7:1.† (source)
 And can you guess what the ratio is of each spiral's diameter to the next?† (source)
 She was talking about the squarecube ratio, though she didn't know what to call it.† (source)
 Without Daisy, the staffto patient ratio was higher than usual: five patients, three nurses.† (source)
 The ratio was seven to one on foolbirds.† (source)
 Ready the ratio detector, if you please.† (source)
 Everyone else sipped at mineral water, or checked the sweetener ratios on their Diet Cokes.† (source)
 Can you guess the ratio of each rotation's diameter to the next?† (source)
 The bottom of the screen was labeled: RATIO: 36.28%† (source)
 A counter along one wall held the same heartrate machines and ratio detectors as the other had.† (source)
 Her retina display informed her that she was now connected to RATIO DETECTOR 2.3.† (source)
 Ready the ratio detector, if you please.† (source)
 The meddroid was bustling around behind her, putting the ratio detector away.† (source)
 Someone she put in a cage for the duration would have the strongest revenge ratio.† (source)
 Plus the ratio in the classes of professors to students is really good.† (source)
 Infective ratio of .1% remainder too low to be harmful.† (source)
 The group's maternal mortality ratio was 872 per 100,000 live births.† (source)
 Last spring, 12 climbers died and 84 reached the summita ratio of one in seven.† (source)
 There are certain numbers and patterns and ratios that freak them out, basically.† (source)
 But still the ratio can't widen in their favor.† (source)
 ; some wanted to make it selective by "ethnic ratios."† (source)
 Perhaps there are ratios of wind pressure to velocity that can be mathematically calculated.† (source)
 Superiority is measured in ratios, not sums, yes?† (source)
 The most common measure is the maternal mortality ratio (MMR).† (source)
 If the Virginia ratio was the same as Rhode Island, Virginia would have 400500 representatives.† (source)
 Keeping the racial ratio the same and all?† (source)
 Great Britain: Citizens to Representative Ratio† (source)
 After compromising on the ratio of representation, a fresh struggle probably started.† (source)
 And the multiplication must be a ratio of the number of issues and the number of States.† (source)
 The number of votes each State gets is based on a compound ratio.† (source)
 And if Pennsylvania's ratio was used in Delaware, Delaware would have 78 representatives.† (source)
 The State legislatures have many different representativestopopulation ratios.† (source)
 Very large and very small populations should have different representative to constituent ratios.† (source)
 In my head, I was frantically trying to determine the ratios of positive emotion to negative emotion.† (source)
 Dunbar has actually developed an equation, which works for most primates, in which he plugs in what he calls the neocortex ratio of a particular species — the size of the neocortex relative to the size of the brain — and the equation spits out the expected maximum group size of the animal.† (source)
 Add to that the fact that we're losing Immunes left and right to whoknowswhere, decreasing our ratio each and every day, and things were bound to reach a boiling point eventually.† (source)
 Many, not understanding the prohibitive massratio problem, may even think we'll bring water from some other planet rich in it.† (source)
 His findings is that for a marriage to survive, the ratio of positive to negative emotion in a given encounter has to be at least five to one.† (source)
 mm hypervelocity railgun system Ng Security Industries, Inc. PRERELEASE VERSIONNOT FOR FIELD USE DO NOT TEST IN A POPULATED AREA — ULTIMA RATIO REGUMthe superstructure is slowly collapsing down into the hull like a botched souffle.† (source)
 Obsessed with bodyfat ratios.† (source)
 The nurses were less nervous on the street that day, spring fever making them careless—or perhaps the stafftopatient ratio was a more comfortable one for them.† (source)
 But when we listened closely to their interaction and measured the ratio of positive to negative emotions, we got a different story.† (source)
 Sex Ratio.† (source)
 On a technical level, she was measuring the amount of positive and negative emotion, because one of Gottman's findings is that for a marriage to survive, the ratio of positive to negative emotion in a given encounter has to be at least five to one.† (source)
 I sat squashed between Patrick and a man whose name appeared to be the Rutter, staring periodically at the horse brasses pinned to the oak beams above my head and the photographs of the castle that punctuated the joists, and tried to look even vaguely interested in the talk around me, which seemed to revolve chiefly around bodyfat ratios and carb loading.† (source)
 Plants, animals, and even human beings all possessed dimensional properties that adhered with eerie exactitude to the ratio of PHI to 1.† (source)
 Yes, the ratios of line segments in a pentacle all equal PHI, making this symbol the ultimate expression of the Divine Proportion.† (source)
 Yes, her ratio should be impressive.† (source)
 With a 6.4 percent ratio?† (source)
 To fill each necessary combat billet, one job to one officer, would call for a 5 per cent ratio of officers — but 3 per cent is all we've got.† (source)
 And while the dividends from Apollo continue to be good, the PE ratio would he much better if they weren't involving the company in this boondoggle.† (source)
 Calling it six, he divided it into the twelve thousand kilometers that he guessed stretched over the open sea to southern Argentina without a break, and determined that the mass of the sea, in all its unimaginable weight and volume, never expanded more than one part in two million, and, indeed, was more stable than that, for he had failed to consider the immense volume of the ocean, which would make the ratio much more severe.† (source)
 Over chilled herring, she questioned Doc about the future of socialized medicine, listening attentively as he discussed healthdelivery systems and doctorpatient ratios, Medicare versus Medicaid.† (source)
 She and Feeney had taken the time to swing past her office and use her computer for the probability ratio.† (source)
 I had good moments and bad, terrified thoughts and confident ones—though my terrortoconfidence ratio was pretty dismal at present, like threetoone, and in the terrified moments it felt like I was being pushed into a role I hadn't asked for; volunteered for frontline duty in a war, the full scope of which none of us yet knew.† (source)
 My interpretation of the definitions of specific impulse and mass ratio especially seemed to impress him.† (source)
 Or here's another way to look at it: between 1921 and May 1996, 144 people died and the peak was climbed some 630 timesa ratio Of one in four.† (source)
 Dess was also on some new navigation trip, doing star sightings with a homemade sextant, excited about some new numerological secret she was keeping from the rest of them, her mind wrapped up in the pure world of angles and ratios.† (source)
 Burton stood in the room that housed the spectrometer along with several other pieces of equipment for radioactivity assays, ratiodensity photometry, thermocoupling analysis, and preparation for Xray crystallography.† (source)
 Over the last half century, Sri Lanka has brought its maternal mortality ratio down from 550 maternal deaths for every 100,000 live births to just 58.† (source)
 I suspected there were dimensional relationships involved in rocket design, such as a proper ratio between the area of the guidancecontrolling fins to the area of the casement.† (source)
 It has been proposed, for example, that a guidetoclient ratio of one to one be established as the standard on Everesti. e each client would climb with his or her own personal guide and remain roped to that guide at all times.† (source)
 0097 11 35 Scoop, Houston Projection Group has confirmed orbital instability and decay ratios are now being passed by the data trunk to your station.† (source)
 Ratio.† (source)
 The sex ratio of newborns is 116 boys for every 100 girls, meaning that many poor men will never be able to marry; this will be a source of future instability.† (source)
 Every day I honed my spiel a little more so that I could quickly deliver a learned presentation on the mathematics of the design of De Laval nozzles, the calculations of specific impulse and mass ratios, and the trigonometry of altitudes needed for an amateur rocketry test range.† (source)
 Visitors to events where Mukhtar was honored saw a shy woman with a head scarf getting one standing ovation after another (when she appeared in Glamour, she set the magazine's alltime record for clothingtoskin ratio).† (source)
 Additionally, the number of States will probably increase and there is no provision for increasing the ratio of votes.† (source)
 Ratio Changes with Population† (source)
 Constituent/Legislator Ratios† (source)
 There was almost a quarter million cash on hand, a far higher ratio of cash than regulations required, but consistent with his conservative principles.† (source)
 Immediately after establishing a permanent base you will proceed, by means of canoe and utilizing waterways, to make an extensive general survey of the surrounding country to a depth, and in a manner, which will be significant in statistical terms, in order to determine the range 'population ratio of Canis lupus and in order to establish contact with the study species.... I was willing enough to carry on as per instructions, but the ice underfoot had a solidity about it which suggested that canoeing would have to be deferred for several weeks, if not forever.† (source)
 It consisted of three parts: first I had to make a collection of all the species of plants in the area; then I had to make a "cover degree" study, to determine the ratios of various plants one to the other; and finally I was expected to do a "content analysis," to determine the nutritional value of the vegetation from the point of view of the caribou.† (source)
 Right now the ratio between income tax and total income for the state gives an index that—† (source)
 Its value and its civilization are in inverse ratio to that extortion.† (source)
 Meanwhile, as though in inverse ratio to the vanishing voice, the invoked ghost of the man whom she could neither forgive nor revenge herself upon began to assume a quality almost of solidity, permanence.† (source)
 The stick still fell; as the progress of the horse slowed, the speed of the stick increased in exact ratio.† (source)
 Mae watched them get into the great truck, watched it lumber off in low gear, and heard the shift up the whining gears to cruising ratio.† (source)
 Anyone who looked more white folkish than herself was better than she was in her criteria, therefore it was right that they should be cruel to her at times, just as she was cruel to those more negroid than herself in direct ratio to their negroness.† (source)
 It was an inverse ratio in Scarret's calculations: every filthy adjective thrown at Dominique created sympathy for Wynand in the reader's mind; this fed Scarret's smear talent.† (source)
 She's sure ratio'd down.† (source)
 Wasn't she growing visibly older in ratio as Vida grew plumper and younger?† (source)
 Manufacturing property then does not extend its rights in the same ratio as its importance.† (source)
 Thus the ratio between the cost of production and the value of the produce is changed.† (source)
 The ratio between them was, therefore, about 36 to 100.† (source)
 People fled before this tortured thinker, for whoever he managed to buttonhole was subjected to a passionate torrent of words intended to awaken a deeper sensitivity to the hopeless irrationality of this mystical ratio and to its shameful defilement of the human spirit.† (source)
 I had taken note of the fact that, apart from her own kinsfolk, the sufferings of humanity inspired in her a pity which increased in direct ratio to the distance separating the sufferers from herself.† (source)
 That swing of the shoulders that had frozen the timid when he was but a lad had increased with his growth and education at the ratio of ten to one.† (source)
 He knew only one, dreadfully tedious topic of conversation: the ratio pi, that forlorn fraction, which a lesser genius of mental arithmetic named Zacharias Dase had once worked out to two hundred decimal places—a superfluous task, since even at two thousand places he would have had no greater prospect of approaching unattainable accuracy, indeed would not have been one whit closer to it.† (source)
 In the matter of wills, personal qualities were subordinate to the great fundamental fact of blood; and to be determined in the distribution of your property by caprice, and not make your legacies bear a direct ratio to degrees of kinship, was a prospective disgrace that would have embittered her life.† (source)
 So it isn't quite built on the tentoone ratio of your highspeed steamers; but its lines are sufficiently long, and their tapering gradual enough, so that the displaced water easily slips past and poses no obstacle to the ship's movements.† (source)
 It was altogether repulsive to him, and he never entered into any calculation of the ratio between the Vicar's income and his more or less necessary expenditure.† (source)
 The blaze, enlarging in a double ratio by his approach and its own increase, showed him as he drew nearer the outlines of ricks beside it, lighted up to great distinctness.† (source)
 In dirty upper casements, here and there, hazy little patches of candlelight reveal where some wise draughtsman and conveyancer yet toils for the entanglement of real estate in meshes of sheepskin, in the average ratio of about a dozen of sheep to an acre of land.† (source)
 That exactly in the ratio as they worked long and monotonously, the craving grew within them for some physical relief — some relaxation, encouraging good humour and good spirits, and giving them a vent — some recognized holiday, though it were but for an honest dance to a stirring band of music — some occasional light pie in which even M'Choakumchild had no finger — which craving must and would be satisfied aright, or must and would inevitably go wrong, until the laws of the Creation were repealed?† (source)
 His property increased in a tenfold ratio, and he was already ranked among the most wealthy and important of his countrymen.† (source)
 The dangers of the elective system increase, therefore, in the exact ratio of the influence exercised by the executive power in the affairs of State.† (source)
 Still—if I have read religious history aright—faith, hope, and charity have not always been found in a direct ratio with a sensibility to the three concords, and it is possible—thank Heaven!† (source)
 In fact, the facility with which I shall arrive, or have arrived, at the solution of this mystery, is in the direct ratio of its apparent insolubility in the eyes of the police.† (source)
 If men are to remain civilized, or to become so, the art of associating together must grow and improve in the same ratio in which the equality of conditions is increased.† (source)
 This equation does not give us the value of the unknown factor but gives us a ratio between two unknowns.† (source)
 Mr Clennam did not increase in favour with the Father of the Marshalsea in the ratio of his increasing visits.† (source)
 The Hospital was to be reserved for fever in all its forms; Lydgate was to be chief medical superintendent, that he might have free authority to pursue all comparative investigations which his studies, particularly in Paris, had shown him the importance of, the other medical visitors having a consultative influence, but no power to contravene Lydgate's ultimate decisions; and the general management was to be lodged exclusively in the hands of five directors associated with Mr. Bulstrode, who were to have votes in the ratio of their contributions, the Board itself filling up any vacancy in its numbers, and no mob of small contributors being admitted to a share of government.† (source)
 And if I'm not mistaken, the submerged part of this Ice Bank is in a fourtoone ratio to its emerging part.† (source)
 Only when we have admitted the conception of the infinitely small, and the resulting geometrical progression with a common ratio of one tenth, and have found the sum of this progression to infinity, do we reach a solution of the problem.† (source)
 Men grow more alike in the one—more different in the other; and inequality increases in the less numerous class in the same ratio in which it decreases in the community.† (source)
 During the war of independence, which lasted eight years, the population continued to increase without intermission in the same ratio.† (source)
 But nothing is gained by increasing the army amongst a democratic people, because the number of aspirants always rises in exactly the same ratio as the army itself.† (source)
 Egotism is a vice as old as the world, which does not belong to one form of society more than to another: individualism is of democratic origin, and it threatens to spread in the same ratio as the equality of conditions.† (source)
 In the year 1832 the ratio between the foreign and British ships which entered the ports of Great Britain was 29 to 100.† (source)
 Thenceforward the number of negroes could only increase according to the ratio of the natural increase of population.† (source)
 Thus the jurisdiction of the tribunals of the Union extends and narrows its limits exactly in the same ratio as the sovereignty of the Union augments or decreases.† (source)
 I have already spoken of the natural defects of democratic institutions, and they all of them increase at the exact ratio of the power of the majority.† (source)
 [Footnote i: The tonnage of the vessels which entered all the ports of the Union in the years 1829, 1830, and 1831, amounted to 3,307,719 tons, of which 544,571 tons were foreign vessels; they stood, therefore, to the American vessels in a ratio of about 16 to 100† (source)
 The extension of judicial power in the political world ought therefore to be in the exact ratio of the extension of elective offices: if these two institutions do not go hand in hand, the State must fall into anarchy or into subjection.† (source)
 Thus, if the increase of the population of the lesser country be to that of the greater in an exact inverse ratio of the proportion between the new and the old numbers of all the representatives, the number of the representatives of Virginia will remain stationary; and if the increase of the Virginian population be to that of the whole Union in a feeblerratio than the new number of the representatives of the Union to the old number, the number of the representatives of Virginia must decrease.† (source)
 In all former confederations the privileges of the Union furnished more elements of discord than of power, since they multiplied the claims of the nation without augmenting the means of enforcing them: and in accordance with this fact it may be remarked that the real weakness of federal governments has almost always been in the exact ratio of their nominal power.† (source)
 However, Hebrew school had one thing going for it: a terrific boygirl ratio.† (source)
 In 1936 when Bloom would be 70 and Stephen 54 their ages initially in the ratio of 16 to 0 would be as 17 1/2 to 13 1/2, the proportion increasing and the disparity diminishing according as arbitrary future years were added, for if the proportion existing in 1883 had continued immutable, conceiving that to be possible, till then 1904 when Stephen was 22 Bloom would be 374 and in 1920 when Stephen would be 38, as Bloom the† (source)
 The Latines called Accounts of mony Rationes, and accounting, Ratiocinatio: and that which we in bills or books of account call Items, they called Nomina; that is, Names: and thence it seems to proceed, that they extended the word Ratio, to the faculty of Reckoning in all other things.† (source)
 However, she had, on such occasions, the advantage of concealing her blushes from the eyes of men; and De non apparentibus, et non existentibus eadem est ratio—in English, "When a woman is not seen to blush, she doth not blush at all."† (source)
 In addition to this, it is to be observed that there is a probability of an increase in the number of States, and no provision for a proportional augmentation of the ratio of votes.† (source)
 The degree of that multiplication must evidently be in a ratio to the number of particulars and the number of parties.† (source)
 They would not, therefore, in this mode alone contribute to the public treasury in a ratio to their abilities.† (source)
 On the other hand, the ratio of Pennsylvania, if applied to the State of Delaware, would reduce the representative assembly of the latter to seven or eight members.† (source)
 The votes allotted to them are in a compound ratio, which considers them partly as distinct and coequal societies, partly as unequal members of the same society.† (source)
 Another general remark to be made is, that the ratio between the representatives and the people ought not to be the same where the latter are very numerous as where they are very few.† (source)
 All this is admitted, it will perhaps be said; but does it follow, from an admission of numbers for the measure of representation, or of slaves combined with free citizens as a ratio of taxation, that slaves ought to be included in the numerical rule of representation?† (source)
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