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.
The quality of moral behaviour varies in inverse ratio to the number of human beings involved.
Population, when unchecked, increases in geometrical ratio. Subsistence only increases in arithmetical ratio.
Reason, or the ratio of all we have already known, is not the same that it shall be when we know more.william blake
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
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.henry parry liddon
Population, when unchecked, increases in a geometrical ratio, Subsistence, increases only in an arithmetical ratio.thomas malthus
Had population and food increased in the same ratio, it is probable that man might never have emerged from the savage state.thomas malthus
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
A silly society is a youth-obsessed society: To the Chinese, who appreciate the value of experience, the greater the ratio in a team of grey ‘hairs and no-hairs’ to ‘black hairs’ the faster and better a task will be completed. The opposite assumption obtains in the youth-obsessed U.S.ilana mercer
Bullialdus wrote that all force respecting ye Sun as its center & depending on matter must be reciprocally in a duplicate ratio of ye distance from ye center.isaac newton
Common sense in matters medical is rare, and is usually in inverse ratio to the degree of education.william osler
Had population and food increased in the same ratio, it is probable that man might never have emerged from the savage state.
The last decade has seen a steady increase in the application of concepts from the theory of games to the study of evolution . Fields as diverse as sex ratio theory, animal distribution, contest behaviour and reciprocal altruism have contributed to what is now emerging as a universal way of thinking about phenotypic evolution... Paradoxically, it has turned out that game theory is more readily applied to biology than to the field of economic behavior for which it was originally designed
Qui fit, Mæcenas, ut nemo quam sibi sortem, Seu ratio dederit, seu fors objecerit, illa Contentus vivat? laudet diversa sequentes.
A silly society is a youth-obsessed society: To the Chinese, who appreciate the value of experience, the greater the ratio in a team of grey ‘hairs and no-hairs’ to ‘black hairs’ the faster and better a task will be completed. The opposite assumption obtains in the youth-obsessed U.S.
Population, when unchecked, increases in a geometrical ratio, Subsistence, increases only in an arithmetical ratio.
Materiae ne quaere modum; sed perspice vires Quas ratio, non pondus habet; ratio omnia vincit.
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.
Dis proximus ille est, quem ratio non ira movet.
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.
Est quidem vera Lex recta ratio, naturae congruens, diffusa in omnes, constans, sempiterna, quae vocet ad officium jubendo, vetando a fraude deterreat.