“The development of Indian trigonometry, based on sine as against chord of the Greeks, a necessity for astronomical calculations with his own concise notation which expresses the full sine table in just one couplet for easy remembrance. One of the two methods suggested by him for the sine table is based on the property that the second order sine differences were proportional to sines themselves.”

— Aryabhata

In, P.245.
Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures

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Aryabhata 11

Indian mathematician-astronomer 476–550

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“A Logarithmic Table is a small table by the use of which we can obtain a knowledge of all geometrical dimensions and motions in space, by a very easy calculation. It is deservedly called very small, because it does not exceed in size a table of sines; very easy, because by it all multiplications, divisions, and the more difficult extractions of roots are avoided; for by only a very few most easy additions, subtractions, and divisions by two, it measures quite generally all figures and motions.”

John Napier (1550–1617) Scottish mathematician

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“Soul-serving requires a heart that beats hard against the ribs. It requires a soul full of the milk of human kindness. This is the sine qua non of success.”

Charles Spurgeon (1834–1892) British preacher, author, pastor and evangelist

The Soul-Winner (1895)

“And if any number of equals to a first sine be multiplied together producing a second, just so many equals to the Logarithm of the first added together produce the Logarithm of the second.”

John Napier (1550–1617) Scottish mathematician

Appendix, The relations of Logarithms & their natural numbers to each other
The Construction of the Wonderful Canon of Logarithms (1889)

“Our intention in this Disme is to worke all by whole numbers: for seing that in any affayres, men reckon not of the thousandth part of a mite, grayne, &c. as the like is also used of the principall Geometricians, and Astronomers, in computacions of great consequence, as Ptolome & Johannes Monta-regio have not described their Tables of Arches, Chords, or Sines, in extreme perfection (as possibly they might have done by Multinomiall numbers,) because that imperfection (considering the scope and end of those Tables) is more convenient then such perfection.”

Simon Stevin (1548–1620) Flemish scientist, mathematician and military engineer

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“If a first sine be multiplied into a second producing a third, the Logarithm of the first added to the Logarithm of the second produces the Logarithm of the third. So in division, the Logarithm of the divisor subtracted from the Logarithm of the dividend leaves the Logarithm of the quotient.”

John Napier (1550–1617) Scottish mathematician

Appendix, The relations of Logarithms & their natural numbers to each other
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“Unfortunately, all life on earth - the only life we know - represents, for all its current variety, the results of a single experiment, for every earthly species evolved from the common ancestry of a single origin. We desperately need a repetition of the experiment (several would be better, but let's not be greedy!) in order to make a judgement. Mars represents our first real hope for a second experiment - the sine qua non”

Stephen Jay Gould book Leonardo's Mountain of Clams and the Diet of Worms

for any proper answer for the question of questions.
"War of the Worldviews", p. 353
Leonardo's Mountain of Clams and the Diet of Worms (1998)

“I have lately spent some Thoughts relative to the Nature of Light, whether it be subject to the common Laws of Motion. In this particular Newton seems to contradict himself. For in his Principia Sect. 14th he applies the common Laws of Motion to account for Reflection and Refraction, as he does also in one Part of his Optics where he proves the Sine of Incid. to Sine Refr, in a given in a given Ratio. But in another Part he says, “nothing more is requisite for producing all the Variety of Colours and Degrees of Refrangibility than that the Rays of Light be Bodies of different Sizes, the least of which may make Violet, and the Greatest the Red"; this manifestly is not consistent with the Theory of Motion applied to Bodies, where the Magnitude of the Bodies is of no Consequence. Now it is evident that if the common Theory of Motion can be applied to Light, the Red Light must have had the greatest Velocity before Incidence, as it suffers the least Deviation, for if the Vels of all the Difft colour'd Light were equal before Incidence, they must by Newton's Principia Sect. Sect. 8. Prop. 1. have continued equal after, and therefore must have suffered the same Deviation. The Determination of this Point seems to be of considerable Importance, as we so often apply the Theory of Motion to Light.”

Samuel Vince (1749–1821) British mathematician, astronomer and physicist

As quoted in: Russell McCormmach (2011) Weighing the World: The Reverend John Michell of Thornhill. p. 193

“Though patriotism includes a sentimental, as it were a family, feeling for place, we can distinguish the ethical motive from the sentimental. At certain times in certain countries there has been a moral urgency to be patriotic when the actual or ideal policy of a man’s nation has been a sine qua non for his conscience. But to-day patriotism, in so far as it means subordination to a specifically national policy, is superannuated. This war, we assume, is not being fought-not by most of us-for any merely national end; we are fighting it, primarily and clearly, for our lives, and secondarily, and, alas! vaguely, for a new international order.”

Louis MacNeice (1907–1963) poet

"Traveller's Return", in Horizon, February 1941, Reprinted in David Pierce Irish Writing in the Twentieth Century: A Reader. Cork University Press, 2000.

“The difficulty, as in all this work, is to find a notation which is both concise and intelligible to at least two people of whom one may be the author.”

Paul Taunton Matthews (1919–1987) British scientist

with Abdus Salam. [1951, October, The Renormalization of Meson Theories, Reviews of Modern Physics, 23, 4, 311-314] About the difficulty to express renormalization in quantum field theories. Also known as the Salam criterion.

“But how shall this love be demonstrated? After what method shall it be expressed? Not by secret musings alone; not by the chanting of religious sonnets alone; not by grateful remembrances of Him — at His table only — but by deeds of love towards those who in a real sense represent Him, because partakers of that nature, our common humanity, which He condescended to assume.”

William Adams (1706–1789) Fellow and Master of Pembroke College, Oxford

Source: Dictionary of Burning Words of Brilliant Writers (1895), P. 396.

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Aryabhata 11

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