Ratio Quotes - page 4

For reasons of security, our submarine operations throughout the Pacific can be discussed only in very general terms. No branch of the naval service, however, has acquitted itself more creditably. Submarine commanding officers are skillful, daring and resourceful. Their crews are well trained and efficient. Their morale is high, and in direct ratio to the success of submarine operations. Materially our submarines are in excellent shape, and we have kept up to the minute in all features of design and scientific development and research. The versatility of our submarines has been so repeatedly demonstrated throughout the war that the Japanese know only too well that in no part of the Pacific Ocean are they safe from submarine attack. When the full story can be told, it will constitute one of the most stirring chapters in the annals of naval warfare. (Ernest King)

Though Wallis was advanced for his times and accepted negative numbers, he thought they were larger than infinity but not less than zero. In his Arithmetica Infinitorum (1655), he argued that since the ratio a/0, when a is positive, is infinite, then, when the denominator is changed to a negative number, as in a/b with b negative, the ratio must be greater than infinity.

Morris Kline

The concept-systems of antithesis are concepts that are indeed thoroughly determined by negative predicates but are not positively representable. Just because a precise and complete representation of these concept-systems is impossible, they are inaccessible to direct investigation and elaboration by our reflection. They may, however, be regarded as lying at the limit of the representable, i. e., we can form a concept-system lying within the representable, which passes over into the given system by simple change of magnitude ratio. By abstracting from the ratios of the quantities, the concept-system remains unchanged in case of transition to the limit. At the limit itself, however, some of the correlative concepts of the system lose their susceptibility of being represented, and those, indeed, that mediate the relation between other concepts.

Bernhard Riemann

Proposition 14. The straight line joined from the centre of the earth to the centre of the moon has to the straight line cut off from the axis towards the centre of the moon by the straight line subtending the (circumference) within the earth's shadow a ratio greater than that which 675 has to 1.

Aristarchus of Samos

Proposition 13. The straight line subtending the portion intercepted within the earth's shadow of the circumference of the circle in which the extremities of the diameter of the circle dividing the dark and the bright portions in the moon move is less than double of the diameter of the moon, but has to it a ratio greater than that which 88 has to 45; and it is less than 1/9th part of the diameter of the sun, but has to it a ratio greater than that which 22 has to 225. But it has to the straight line drawn from the centre of the sun at right angles to the axis and meeting the sides of the cone a ratio greater than that which 979 has to 10125.

Aristarchus of Samos

Proposition 18. The earth is to the moon in a ratio greater than that which 1259712 has to 79507, but less than that which 216000 has to 6859.

Aristarchus of Samos

We are now in a position to prove the following propositions : - 1. The distance of the sun from the earth is greater than eighteen times, but less than twenty times, the distance of the moon (from the earth); this follows from the hypothesis about the halved moon. 2. The diameter of the sun has the same ratio (as aforesaid) to the diameter of the moon. 3. The diameter of the sun has to the diameter of the earth a ratio greater than that which 19 has to 3, but less than that which 43 has to 6; this follows from the ratio thus discovered between the distances, the hypothesis about the shadow, and the hypothesis that the moon subtends one fifteenth part of a sign of the zodiac.

Aristarchus of Samos

Proposition 12. The diameter of the circle which divides the dark and the bright portions in the moon is less than the diameter of the moon, but has to it a ratio greater than that which 89 has to 90.

Aristarchus of Samos

There is generally, therefore, an inverse ratio between the worship of goddesses and the granting of rights to human women. Nor are the goddesses by and large compassionate; they are generally a pretty bloodthirsty lot. Goddesses are not the solution.

Wendy Doniger

The Pythagoreans discovered the existence of incommensurable lines, or of irrationals. This was, doubtless, first discovered with reference to the diagonal of a square which is incommensurable with the side, being in the ratio to it of √2 to 1. The Pythagorean proof of this particular case survives in Aristotle and in a proposition interpolated in Euclid's Book X.; it is by a reductio ad absurdum proving that, if the diagonal is commensurable with the side, the same number must be both odd and even. This discovery of the incommensurable... showed that the theory of proportion invented by Pythagoras was not of universal application and therefore that propositions proved by means of it were not really established.... The fatal flaw thus revealed in the body of geometry was not removed till Eudoxus discovered the great theory of proportion (expounded in Euclid's Book V.), which is applicable to incommensurable as well as to commensurable magnitudes.

Thomas Little Heath

Archimedes is said to have requested his friends and relatives to place upon his tomb a representation of a cylinder circumscribing a sphere within it, together with the inscription giving the ratio (3/2) which the cylinder bears to the sphere; from which we may infer that he himself regarded the discovery of this ration as his greatest achievement. (Thomas Little Heath)

We show that it is natural to introduce the concept of black-hole entropy as the measure of information about a black-hole interior which is inaccessible to an exterior observer. Considerations of simplicity and consistency, and dimensional arguments indicate that the black-hole entropy is equal to the ratio of the black-hole area to the square of the Planck length times a dimensionless constant of order unity. A different approach making use of the specific properties of Kerr black holes and of concepts from information theory leads to the same conclusion, and suggests a definite value for the constant.

Jacob Bekenstein

There were so many great music and political scenes going on in the late '60s in Cambridge. The ratio of guys to girls at Harvard was four to one, so all of those things were playing in my mind.

Bonnie Raitt

I enjoy comedic things. People don't understand it's the hardest thing to do. We have a ratio of 25-to-1 between good dramatic actors and people who are considered good comic actors.

Charles Grodin

When you are a writer the assist-to-turnover ratio...there are a lot more turnovers than assists. It's just the nature of the beast.

Jeff Baena

For a manager to be perceived as a positive manager, they need a four to one positive to negative contact ratio.

Ken Blanchard

The thinner a newspaper or magazine is - due to reduced revenue from advertising dollars - the less editorial content because of the standard ad-to-editorial ratio, and the less money there is to support investigative journalism.

Lynda Resnick

It becomes a giant's task to compute the result when the effect of cross seas, wind at all angles and ever varying force, arched surfaces, head resistance, ratio of weight to area, and the intelligence of the guiding power crop up.

Lawrence Hargrave

If you read the memoirs of slave-owning families, you'd be hard pressed to find evidence of black people in the lives of the whites, even though for most of the time on the plantations black people outnumbered whites by a ratio of seven to one.

Edward Ball

I always say that life is not easy for anybody. People hear about the young actors who have a rough life, but there are plenty of other kids who aren't actors who have a rough time, too, and I don't know if the ratio is any different.

Johnny Crawford

We have lost one shuttle for every 57 flights and that is not a good ratio. I do believe we need to continue space flights, but maybe we can follow the example of the Russians and use unmanned vehicles to transport hardware into space. (Lincoln Davis)

Nominally, there is one executive for every eight federal employees, a ratio that would bankrupt many private industries.

Martin L. Gross

I am involved with 'Write Girl,' which is such a great organization, because they go into inner city schools and work with underprivileged girls to pair them up with other writers. And it gets them learning to express themselves and become familiar with their own voice. They have a 100% success ratio getting those girls into college.

Melissa Rosenberg

At Reliance Foundation schools, we lay special emphasis on value-based education, sports, and overall development of students. That is why the teacher-students ratio is kept at a healthy 1:20 so that all children get proper attention in class.

Nita Ambani

I have this ratio that if you divide age of entrepreneur by market cap of company. For Facebook it's one. Every year of his life Zuckerberg has been making $1 billion for investors.

Yuri Milner

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