Quotes about chapter
page 4

François Viète photo

“On symbolic use of equalities and proportions. Chapter II.
The analytical method accepts as proven the most famous [ as known from Euclid ] symbolic use of equalities and proportions that are found in items such as:
1. The whole is equal to the sum of its parts.
2. Quantities being equal to the same quantity have equality between themselves. [a = c & b = c => a = b]
3. If equal quantities are added to equal quantities the resulting sums are equal.
4. If equals are subtracted from equal quantities the remains are equal.
5. If equal equal amounts are multiplied by equal amounts the products are equal.
6. If equal amounts are divided by equal amounts, the quotients are equal.
7. If the quantities are in direct proportion so also are they are in inverse and alternate proportion. [a:b::c:d=>b:a::d:c & a:c::b:d]
8. If the quantities in the same proportion are added likewise to amounts in the same proportion, the sums are in proportion. [a:b::c:d => (a+c):(b+d)::c:d]
9. If the quantities in the same proportion are subtracted likewise from amounts in the same proportion, the differences are in proportion. [a:b::c:d => (a-c):(b-d)::c:d]
10. If proportional quantities are multiplied by proportional quantities the products are in proportion. [a:b::c:d & e:f::g:h => ae:bf::cg:dh]
11. If proportional quantities are divided by proportional quantities the quotients are in proportion. [a:b::c:d & e:f::g:h => a/e:b/f::c/g:d/h]
12. A common multiplier or divisor does not change an equality nor a proportion. [a:b::ka:kb & a:b::(a/k):(b/k)]
13. The product of different parts of the same number is equal to the product of the sum of these parts by the same number. [ka + kb = k(a+b)]
14. The result of successive multiplications or divisions of a magnitude by several others is the same regardless of the sequential order of quantities multiplied times or divided into that magnitude.
But the masterful symbolic use of equalities and proportions which the analyst may apply any time is the following:
15. If we have three or four magnitudes and the product of the extremes is equal to the product means, they are in proportion. [ad=bc => a:b::c:d OR ac=b2 => a:b::b:c]
And conversely
10. If we have three or four magnitudes and the first is to the second as the second or the third is to the last, the product of the extremes is equal to that of means. [a:b::c:d => ad=bc OR a:b::b:c => ac=b2]
We can call a proportion the establishment of an equality [equation] and an equality [equation] the resolution of a proportion.”

François Viète (1540–1603) French mathematician

From Frédéric Louis Ritter's French Tr. Introduction à l'art Analytique (1868) utilizing Google translate with reference to English translation in Jacob Klein, Greek Mathematical Thought and the Origin of Algebra (1968) Appendix
In artem analyticem Isagoge (1591)

Malcolm Muggeridge photo

“One scarcely knows whether to laugh or cry. The spectacle presented, in Cynthia Russett's splendid book, of nineteenth-century white male scientists and thinkers earnestly trying to prove women inferior to men--thereby providing, along with "savages" and "idiots," an evolutionary buffer between men and animals--is by turns appalling, amusing, and saddening. Surveying the work of real scientists as well as the products of more dubious minds, Russett has produced a learned yet immensely enjoyable chapter in the annals of human folly.
At the turn of the century science was successfully challenging the social authority of religion; scientists wielded a power no other group commanded. Unfortunately, as Russett demonstrates, in Victorian sexual science, empiricism tangled with prior belief, and scientists' delineation of the mental and physical differences between men and women was directed to show how and why women were inferior to men. These men were not necessarily misogynists. This was an unsettling time, when the social order was threatened by wars, fierce economic competition, racial and industrial conflict, and the failure of society to ameliorate poverty, vice, crime, illnesses. Just when men needed the psychic lift an adoring dependent woman could give, she was demanding the vote, higher education, and the opportunity to become a wage earner!”

Cynthia Eagle Russett (1937–2013) American historian

Cynthia Eagle Russett. Sexual Science: The Victorian Construction of Womanhood. Harvard University Press, 2009. Abstract

Thomas Little Heath photo
William Kingdon Clifford photo
Gabrielle Giffords photo
Alan Watts photo
Robert Chambers (publisher, born 1802) photo

“The first chapter of the Mosaic record is”

Source: Vestiges of the Natural History of Creation (1844), p. 155
Context: The first chapter of the Mosaic record is not only not in harmony with the ordinary ideas of mankind respecting cosmical and organic creation, but is opposed to them, and only in accordance with the views here taken. When we carefully peruse it with awakened minds, we find that all the procedure is represented primarily and pre-eminently as flowing from commands and expressions of will, not from direct acts.... Thus the scriptural objection quickly vanishes, and the prevalent ideas about the organic creation appear only as a mistaken inference from the text, formed at a time when man's ignorance prevented him from drawing therefrom a just conclusion.

Al Gore photo

“We Americans write our own history. And the chapters of which we're proudest are the ones where we had the courage to change.”

Al Gore (1948) 45th Vice President of the United States

Speech at the Democratic National Convention (28 August 1996) http://www.pbs.org/newshour/convention96/floor_speeches/gore_8-28.html.
Context: We Americans write our own history. And the chapters of which we're proudest are the ones where we had the courage to change. Time and again, Americans have seen the need for change, and have taken the initiative to bring that change to life.

“chapter 'Caption', p. 84”

Per Kirkeby (1938–2018) Danish artist

1965 - 1995, Bravura', Per Kirkeby, (1982)

P. J. O'Rourke photo
Thomas Hobbes photo

“And because the condition of Man, (as hath been declared in the precedent Chapter) is a condition of Warre of every one against everyone”

The First Part, Chapter 14, p. 64.
Leviathan (1651)
Context: And because the condition of Man, (as hath been declared in the precedent Chapter) is a condition of Warre of every one against everyone; in which case every one is governed by his own Reason; and there is nothing he can make use of, that may not be a help unto him, in preserving his life against his enemyes; It followeth, that in such a condition, every man has a Right to every thing; even to one anothers body.

John Heywood photo

“Part I, chapter 7.”

John Heywood (1497–1580) English writer known for plays, poems and a collection of proverbs

Proverbs (1546), Bartlett's Familiar Quotations, 10th ed. (1919)

P. J. O'Rourke photo
James Mill photo

“A certain immense aggregate of operations, is subservient to the production of the commodities useful and agreeable to man. It is of the highest importance that this aggregate should be divided into portions, consisting, each, of as small a number of operations as possible, in order that every operation may be the more quickly and perfectly, performed. If each man could, by the more frequent repetition thus occasioned, perform two of these operations, instead of one, and also perform each of them better, the powers of the community, in producing articles useful and agreeable to them, would, upon this supposition, be more than doubled. Not only would they be doubled in quantity, but a great advantage would be gained in point of quality.
This subject has been fully illustrated by Dr. Smith, in the first chapter of the first book of the "Inquiry into the Nature and Causes of the Wealth of Nations," where the extraordinary effect of the division of labour in increasing its productive powers, in the more complicated cases, is displayed in some very remarkable instances. He states that a boy, who has been accustomed to make nothing but nails, can make-upwards of two thousand three hundred in a day; while a common blacksmith, whose operations are nevertheless so much akin to those of the nailer, cannot make above three hundred, and those very bad ones.”

James Mill (1773–1836) Scottish historian, economist, political theorist and philosopher

Ch 1 : Production
Elements of Political Economy (1821)

Albert Hofmann photo

“The cultural-historical meaning of the Eleusinian Mysteries, their influence on European intellectual history, can scarcely be overestimated. Here suffering humankind found a cure for its rational, objective, cleft intellect, in a mystical totality experience, that let it believe in immortality, in an everlasting existence.
This belief had survived in early Christianity, although with other symbols. It is found as a promise, even in particular passages of the Gospels, most clearly in the Gospel according to John, as in Chapter 14:16-20. Jesus speaks to his disciples, as he takes leave of them:
And I will pray the Father, and he shall give you another Comforter, that he may abide with you forever; Even the Spirit of truth; whom the world cannot receive, because it seeth him not, neither knoweth him: but ye know him; for he dwelleth with you, and shall be in you.
I will not leave you comfortless: I will come to you. Yet a little while, and the world seeth me no more; but ye see me: because I live, ye shall live also.
At that day ye shalt know that I am in my Father, and ye in me, and I in you.”

Albert Hofmann (1906–2008) Swiss chemist

'This promise constitutes the heart of my Christian beliefs and my call to natural-scientific research: we will attain to knowledge of the universe through the spirit of truth, and thereby to understanding of our being one with the deepest, most comprehensive reality, God.'
Source: LSD : My Problem Child (1980), Ch. 11 : LSD Experience and Reality

Carl Van Doren photo

“The most momentous chapter in American history is the story of the making and ratifying of the Constitution of the United States. The Constitution has so long been rooted so deeply in American life — or American life rooted so deeply in it — that the drama of its origins is often overlooked.”

Carl Van Doren (1885–1950) American biographer

Preface
The Great Rehearsal (1948)
Context: The most momentous chapter in American history is the story of the making and ratifying of the Constitution of the United States. The Constitution has so long been rooted so deeply in American life — or American life rooted so deeply in it — that the drama of its origins is often overlooked. Even historical novelists, who hunt everywhere for memorable events to celebrate, have hardly touched the event without which there would have been a United States very different from the one that now exists; or might have been no United States at all.
The prevailing conceptions of those origins have varied with the times. In the early days of the Republic it was held, by devout friends of the Constitution, that its makers had received it somewhat as Moses received the Tables of the Law on Sinai. During the years of conflict which led to the Civil War the Constitution was regarded, by one party or the other, as the rule of order or the misrule of tyranny. In still later generations the Federal Convention of 1787 has been accused of evolving a scheme for the support of special economic interests, or even a conspiracy for depriving the majority of the people of their liberties. Opinion has swung back and forth, while the Constitution itself has grown into a strong yet flexible organism, generally, if now and then slowly, responsive to the national circumstances and necessities.

George H. W. Bush photo

“The new breeze blows, a page turns, the story unfolds. And so today a chapter begins, a small and stately story of unity, diversity, and generosity — shared, and written, together.”

George H. W. Bush (1924–2018) American politician, 41st President of the United States

Inaugural Address (1989)
Context: I do not mistrust the future; I do not fear what is ahead. For our problems are large, but our heart is larger. Our challenges are great, but our will is greater. And if our flaws are endless, God's love is truly boundless.
Some see leadership as high drama, and the sound of trumpets calling, and sometimes it is that. But I see history as a book with many pages, and each day we fill a page with acts of hopefulness and meaning. The new breeze blows, a page turns, the story unfolds. And so today a chapter begins, a small and stately story of unity, diversity, and generosity — shared, and written, together.

Walter Rauschenbusch photo

“The words are part of the first chapter of Isaiah”

Walter Rauschenbusch (1861–1918) United States Baptist theologian

Source: Christianity and the Social Crisis (1907), Ch.1 The Historical Roots of Christianity the Hebrew Prophets, p. 10
Context: The words are part of the first chapter of Isaiah to which reference has been made. The prophet throughout the chapter deals with the national condition of the kingdom of Judah and its capital.... he urges... the abolition of social oppression and injustice as the only way of regaining God's favor for the nation. If they would vindicate the cause of the helpless and oppressed, then he would freely pardon; then their scarlet and crimson guilt would be washed away. The familiar text is followed by the very material promise of economic prosperity and the threat of continued war: "If ye be willing and obedient, ye shall eat the good of the land; but if ye refuse and rebel, ye shall be devoured with the sword."

William James photo

“The pivot round which the religious life… revolves, is the interest of the individual in his private personal destiny. Religion, in short, is a monumental chapter in the history of human egotism.”

William James (1842–1910) American philosopher, psychologist, and pragmatist

Lecture XX, "Conclusions"
1900s, The Varieties of Religious Experience (1902)
Context: The pivot round which the religious life... revolves, is the interest of the individual in his private personal destiny. Religion, in short, is a monumental chapter in the history of human egotism. The gods believed in—whether by crude savages or by men disciplined intellectually—agree with each other in recognizing personal calls. Religious thought is carried on in terms of personality, this being, in the world of religion, the one fundamental fact. To-day, quite as much as at any previous age, the religious individual tells you that the divine meets him on the basis of his personal concerns.

Carl Sagan photo

“By exploring other worlds we safeguard this one. By itself, I think this fact more than justifies the money our species has spent in sending ships to other worlds. It is our fate to live during one of the most perilous and, at the same time, one of the most hopeful chapters in human history.
Our science and our technology have posed us a profound question. Will we learn to use these tools with wisdom and foresight before it's too late?”

Carl Sagan (1934–1996) American astrophysicist, cosmologist, author and science educator

55 min 20 sec
Cosmos: A Personal Voyage (1990 Update), Who Speaks for Earth? [Episode 13]
Context: Since this series' maiden voyage, the impossible has come to pass: Mighty walls that maintained insuperable ideological differences have come tumbling down; deadly enemies have embraced and begun to work together. The imperative to cherish the Earth and protect the global environment that sustains all of us has become widely accepted, and we've begun, finally, the process of reducing the obscene number of weapons of mass destruction. Perhaps we have, after all, decided to choose life. But we still have light years to go to ensure that choice. Even after the summits and the ceremonies and the treaties, there are still some 50,000 nuclear weapons in the world — and it would require the detonation of only a tiny fraction of them to produce a nuclear winter, the predicted global climatic catastrophe that would result from the smoke and the dust lifted into the atmosphere by burning cities and petroleum facilities.
The world scientific community has begun to sound the alarm about the grave dangers posed by depleting the protective ozone shield and by greenhouse warming, and again we're taking some mitigating steps, but again those steps are too small and too slow. The discovery that such a thing as nuclear winter was really possible evolved out of the studies of Martian dust storms. The surface of Mars, fried by ultraviolet light, is also a reminder of why it's important to keep our ozone layer intact. The runaway greenhouse effect on Venus is a valuable reminder that we must take the increasing greenhouse effect on Earth seriously.
Important lessons about our environment have come from spacecraft missions to the planets. By exploring other worlds we safeguard this one. By itself, I think this fact more than justifies the money our species has spent in sending ships to other worlds. It is our fate to live during one of the most perilous and, at the same time, one of the most hopeful chapters in human history.
Our science and our technology have posed us a profound question. Will we learn to use these tools with wisdom and foresight before it's too late? Will we see our species safely through this difficult passage so that our children and grandchildren will continue the great journey of discovery still deeper into the mysteries of the Cosmos? That same rocket and nuclear and computer technology that sends our ships past the farthest known planet can also be used to destroy our global civilization. Exactly the same technology can be used for good and for evil. It is as if there were a God who said to us, “I set before you two ways: You can use your technology to destroy yourselves or to carry you to the planets and the stars. It's up to you.”

George Adamski photo
Frederick Cornwallis Conybeare photo
Ernest King photo
Franz Bardon photo
Franz Bardon photo
Sören Kierkegaard photo
Donald J. Trump photo
Winston S. Churchill photo

“Chapter 11 (The Mamund Valley).”

https://books.google.com/books?id=ooFGl74WbXsC&pg=PT149
My Early Life: A Roving Commission (1930)

Carl Sagan photo
Tony Benn photo
Buckminster Fuller photo

“Selected quotes from the chapter on Synergy onwards…”

Buckminster Fuller (1895–1983) American architect, systems theorist, author, designer, inventor and futurist

1970s, Synergetics: Explorations in the Geometry of Thinking (1975), "Synergy" onwards

Lucy Maud Montgomery photo
Jean Froissart photo

“His chapters inspire me with more enthusiasm than even poetry itself. And the noble canon, with what true chivalrous feeling he confines his beautiful expressions of sorrow to the death of the gallant and high-bred knight, of whom it was a pity to see the fall, such was his loyalty to his king, pure faith to his religion, hardihood towards his enemy, and fidelity to his lady-love!”

Jean Froissart (1337–1405) French writer

Ah, benedicite! how he will mourn over the fall of such a pearl of knighthood, be it on the side he happens to favour, or on the other. But, truly, for sweeping from the face of the earth some few hundreds of villain churls, who are born but to plough it, the high-born and inquisitive historian has marvellous little sympathy.
Claverhouse, in Walter Scott's Old Mortality (1816), ch. 35.
Criticism

Margaret Mead photo

“With the exception of the few cases to be discussed in the next chapter, adolescence represented no period of crisis or stress, but was instead an orderly developing of a set of slowly maturing interests and activities.”

Margaret Mead (1901–1978) American anthropologist

The girls' minds were perplexed by no conflicts, troubled by no philosophical queries, beset by no remote ambitions. To live as a girl with many lovers as long as possible and then to marry in one's own village, near one's own relatives, and to have many children, these were uniform and satisfying ambitions.
Source: 1920s, Coming of Age in Samoa (1928), p. 107

William of Ockham photo

“The Holy Spirit through blessed John the evangelist makes a terrible threat against those who add anything to or take anything from divine scripture when he says in the last chapter of Revelations [22:18–9], "If any man shall add to these things, God shall add unto him the plagues which are in this book. And if any man shall take away from the words of the book of this prophecy, God shall take his part out of the book of life and out of the holy city, and from these things that are written in this book."”

William of Ockham (1285–1349) medieval philosopher and theologian

We clearly gather from all these that nothing should be added to sacred scripture nor anything removed from it. To decide by way of teaching, therefore, which assertion should be considered catholic, which heretical, chiefly pertains to theologians, the experts on divine scripture.
You see that I have set out opposing assertions in response to your question and I have touched on quite strong arguments in support of each position. Therefore consider now which seems the more probable to you.
Vol. I, Book 1, Ch. 2.
Dialogus (1494)

Arthur C. Clarke photo

“I am afraid that this chapter will amply demonstrate the truth of Clarke's 69th Law, viz., "Reading computer manuals without the hardware is as frustrating as reading sex manuals without the software."”

Arthur C. Clarke (1917–2008) British science fiction writer, science writer, inventor, undersea explorer, and television series host

In both cases the cure is simple though usually very expensive.
"Appendix II: MITE for Morons," The Odyssey File (1984), p. 123
1960s, Clarke's Three Laws, et al (1962; 1973…)

Christopher Poole photo

“I can’t wait to contribute my own experience from a dozen years of building online communities, and to begin the next chapter of my career at such an incredible company”

Christopher Poole (1988) American Internet entrepreneur, founder of 4chan

Source: 7 March 2016 https://variety.com/2016/digital/news/google-hires-4chan-founder-chris-poole-moot-1201724308/

Marilyn Ferguson photo
Marilyn Ferguson photo
David Hilbert photo
William Blum photo
Arun Shourie photo
Colin Powell photo
Helena Roerich photo
Prosanta Chakrabarty photo
Leopold II of Belgium photo
Massad Ayoob photo
John Steinbeck photo
Laurence Tribe photo

“We... devote... Chapter five to the proposition that there is too much loose impeachment talk, and we think that impeachment... needs to be cautiously and carefully approached.”

Laurence Tribe (1941) American lawyer and law school professor

Laurence Tribe on To End a Presidency (2018)
Source: 13:54 https://www.c-span.org/video/?446316-3/washington-journal-laurence-tribe-discusses-presidential-impeachment&start=834

Alastair Reynolds photo

“Nature shouldn’t be able to do this, Sunday thought. It shouldn’t be able to produce something that resembled the work of directed intelligence, something artful, when the only factors involved were unthinking physics and obscene, spendthrift quantities of time. Time to lay down the sediments, in deluge after deluge, entire epochs in the impossibly distant past when Mars had been both warm and wet, a world deluded into thinking it had a future. Time for cosmic happenstance to hurl a fist from the sky, punching down through these carefully superimposed layers, drilling through these carefully superimposed layers, drilling the geological chapters like a bullet through a book. And then yesterday more time—countless millions of years—for wind and dust to work their callous handiwork, scouring and abrading, wearing the exposed layers back at subtly different rates depending on hardness and chemistry, util these deliberate-looking right-angled steps and contours began to assume grand and imperial solidity, rising from the depths like the stairways of the gods.
Awe-inspiring, yesterday. Sometimes it was entirely right and proper to be awed. And recognising the physics in these formations, the hand of time and matter and the nuclear forces underpinning all things, did not lessen that feeling. What was she, ultimately, but the end product of physics and matter? And what was her art but the product of physics and matter working on itself?”

Source: Blue Remembered Earth (2012), Chapter 17 (pp. 292-293)

Frank Lloyd Wright photo
Isabella Rossellini photo

“I’m not there now to represent beauty; I’m there to represent a different dream. It may be defined as joyfulness; life goes on and there are many chapters. I think that’s why they keep me.”

Isabella Rossellini (1952) Italian actress and filmmaker

On what she feels like she symbolizes now for Lancôme in “Isabella Rossellini: ‘Ageing brings a lot of happiness. You get fatter – but there is freedom’” https://www.theguardian.com/film/2020/oct/13/isabella-rossellini-ageing-brings-a-lot-of-happiness-you-get-fatter-but-there-is-freedom in The Guardian (2020 Oct 13)