Nihil potest esse diuturnum cui non subest ratio.
The Imperial Gazetteer of India reported the intensification of the urban character of Madras in the early twentieth century, noting that 30 percent of the city’s population was between the ages of twenty and forty and that the sex ratio was 98/100.Mary Hancock
The Eudemian Summary says that Eudoxus "first increased the number of general theorems, added to the three proportions three more, and raised to a considerable quantity the learning, begun by Plato, on the subject of the section, to which he applied the analytical method." By this 'section' is meant, no doubt, the "golden section" ( sectio aurea ), which cuts a line in extreme and mean ratio. The first five propositions in Euclid XIII. relate to lines cut by this section, and are generally attributed to Eudoxus.
Official dignity tends to increase in inverse ratio to the importance of the country in which the office is held.
I verily believe that a man’s way with women is in inverse ratio to his prowess among men. The weakling and the saphead have often great ability to charm the fair sex, while the fighting man who can face a thousand real dangers unafraid, sits hiding in the shadows like some frightened child.Edgar Rice Burroughs
Religion exalts mystery as an unknowable secret that must be sealed in glass like the corpse of an enchanted princess and fearfully worshipped from afar. Initiation, on the other hand, requires direct participation and demands each of us to smash the casket and press mad lips to mystery, wooing her as a lover who will offer up her treasurers in a succession of sweet surrenders. This she will do, but only in exact ratio to our evolving ability and worthiness to receive them.lon milo duquette
Auctoritas siquidem ex vera ratione processit, ratio vero nequaquam ex auctoritate. Omnis enim auctoritas, quae vera ratione non approbatur, infirma videtur esse. Vera autem ratio, quum virtutibus suis rata atque immutabilis munitur, nullius auctoritatis adstipulatione roborari indigent.johannes scotus eriugena
Geometry has two great treasures; one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel.johannes kepler
Materiae ne quaere modum; sed perspice viresQuas ratio, non pondus habet; ratio omnia vincit.marcus manilius
Quippe res dei ratio quia deus omnium conditor nihil non ratione providit disposuit ordinavit, nihil [enim] non ratione tractari intellegique voluit.  Igitur ignorantes quique deum rem quoque eius ignorent necesse est quia nullius omnino thesaurus extraneis patet. Itaque universam vitae conversationem sine gubernaculo rationis transfretantes inminentem saeculo procellam evitare non norunt.tertullian
Behind every man now alive stand 30 ghosts , for that is the ratio by which the dead outnumber the living.arthur c. clarke
A promise is binding in the inverse ratio of the numbers to whom it is made.thomas de quincey
The American farmer, whose holdings were not so extensive as those of the grandee nor so tiny as those of the peasant, whose psychology was Protestant and bourgeois, and whose politics were petty-capitalist rather than traditionalist, had no reason to share the social outlook of the rural classes of Europe. In Europe land was limited and dear, while labor was abundant and relatively cheap; in America the ratio between land and labor was inverted.Richard Hofstadter
The life of man is made up of action and endurance; and life is fruitful in the ratio in which it is laid out in noble action or in patient perseverance.
Population, when unchecked, increases in a geometrical ratio, Subsistence, increases only in an arithmetical ratio.
Had population and food increased in the same ratio, it is probable that man might never have emerged from the savage state.
The following are the other extant works generally attributed to Euclid: Phœnomena , a work on spherical geometry and astronomy; Optics , which develops the hypothesis that light proceeds from the eye, and not from the object seen; Catoptrica , containing propositions on reflections from mirrors; De Divisionibus , a treatise on the division of plane figures into parts having to one another a given ratio; Sectio Canonis , a work on musical intervals.
This solidarity can grow only in inverse ratio to personality.... Solidarity which comes from likenesses is at its maximum when the collective conscience completely envelops our whole conscience and coincides in all points with it.... when this solidarity exercises its force, our personality vanishes, as our definition permits us to say, for we are no longer ourselves, but the collective life.Émile durkheim
Materiae ne quaere modum; sed perspice vires Quas ratio, non pondus habet; ratio omnia vincit.
[Japanese defenses threatened] to grow to [the] point where we attack on a ratio of one (1) to one (1) which is not a recipe for victory.
Est quidem vera Lex recta ratio, naturae congruens, diffusa in omnes, constans, sempiterna, quae vocet ad officium jubendo, vetando a fraude deterreat.cicero
Est quidem vera Lex recta ratio, naturae congruens, diffusa in omnes, constans, sempiterna, quae vocet ad officium jubendo, vetando a fraude deterreat.