“This principle, which is thus made the foundation of the operations and results of Symbolical Algebra, has been called "The principle of the permanence of equivalent forms", and may be stated as follows:
"Whatever algebraical forms are equivalent, when the symbols are general in form but specific in value, will be equivalent likewise when the symbols are general in value as well as in form."”

—  George Peacock

Vol. II: On Symbolical Algebra and its Applications to the Geometry of Position (1845) Ch. XV, p. 59
A Treatise on Algebra (1842)

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Scottish mathematician 1791–1858

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“Symbolical algebra adopts the rules of arithmetical algebra, but removes altogether their restrictions: thus symbolical subtraction differs from the same operation in arithmetical algebra in being possible for all relations of value of the symbols or expressions employed… all the results of arithmetical algebra which are deduced by the application of its rules, and which are general in form, though particular in value, are results likewise of symbolical algebra, where they are general in value as well as in form: thus the product of a^{m} and a^{n}, which is a^{m+n} when m and n are whole numbers, and therefore general in form though particular in value, will be their product likewise when m and n are general in value as well as in form: the series for (a+b)^{n}, determined by the principles of arithmetical algebra, when n is any whole number, if it be exhibited in a general form, without reference to a final term, may be shewn, upon the same principle, to the equivalent series for (a+b)^n, when n is general both in form and value.”

George Peacock (1791–1858) Scottish mathematician

Vol. I: Arithmetical Algebra Preface, p. vi-vii
A Treatise on Algebra (1842)

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“I have endeavoured… to present the principles and applications of Symbolical, in immediate sequence to those of Arithmetical, Algebra, and at the same time to preserve that strict logical order and simplicity of form and statement which is essential to an elementary work. This is a task of no ordinary difficulty, more particularly when the great generality of the language of Symbolical Algebra and the wide range of its applications are considered, and this difficulty has not been a little increased, in the present instance, by the wide departure of my own views of its principles from those which have been commonly entertained.”

George Peacock (1791–1858) Scottish mathematician

Vol. II: On Symbolical Algebra and its Applications to the Geometry of Position (1845) Preface, p. iii
A Treatise on Algebra (1842)

George Peacock photo

“I have separated arithmetical from symbolical algebra, and I have devoted the present volume entirely to the exposition of the principles of the former science and their application to the theory of numbers and of arithmetical processes: the second volume, which is now in the press, will embrace the principles of symbolical algebra: it will be followed, if other and higher duties should allow me the leisure to complete them, by other works, embracing all the more important departments of analysis, with the view of presenting their principles in such a form, as may make them component parts of one uniform and connected system.”

George Peacock (1791–1858) Scottish mathematician

Vol. I: Arithmetical Algebra Preface, p. iii
A Treatise on Algebra (1842)

George Boole photo

“Let us conceive, then, of an algebra in which the symbols x, y z etc. admit indifferently of the values 0 and 1, and of these values alone The laws, the axioms, and the processes, of such an Algebra will be identical in their whole extend with the laws, the axioms, and the processes of an Algebra of Logic. Difference of interpretation will alone divide them. Upon this principle the method of the following work is established.”

George Boole (1815–1864) English mathematician, philosopher and logician

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 37; Cited in: William Torrey Harris (1879) The Journal of Speculative Philosophy, p. 109

“With regard to the principle [of using symbols to represent sounds], it matters little whether the symbol is an elaborately detailed picture, a slightly stylized drawing, or a drastically abbreviated symbol of essentially abstract form. What is crucial is to recognize that the diverse forms perform the same function in representing sound. To see that writing has the form of pictures and to conclude that it is pictographic is correct in only one sense -- that of the form, but not the function, of the symbols. We can put it this way:
QUESTION: When is a pictograph not a pictograph?
ANSWER: When it represents a sound.”

John DeFrancis book The Chinese Language: Fact and Fantasy

The Chinese Language: Fact and Fantasy (1984, p. 140) http://www.pinyin.info/readings/texts/ideographic_myth.html
The Chinese Language: Fact and Fantasy (1984)

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“There are many ways in which the intuition can be drawn into activity, and one of the most useful and potent is the study and interpretation of symbols. Symbols are the outer and visible forms of the inner spiritual realities, and when facility in discovering the reality behind any specific form has been gained, that very fact will indicate the awakening of the intuition.”

Alice A. Bailey (1880–1949) esoteric, theosophist, writer

Source: Glamour: A World Problem (1950), Certain Preliminary Clarifications

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“Perhaps the least inadequate description of the general scope of modern Pure Mathematics—I will not call it a definition—would be to say that it deals with form, in a very general sense of the term; this would include algebraic form, functional relationship, the relations of order in any ordered set of entities such as numbers, and the analysis of the peculiarities of form of groups of operations.”

E. W. Hobson (1856–1933) British mathematician

Source: Presidential Address British Association for the Advancement of Science, Section A (1910), p. 287; Cited in: Robert Edouard Moritz. Memorabilia mathematica; or, The philomath's quotation-book https://archive.org/stream/memorabiliamathe00moriiala#page/4/mode/2up, (1914), p. 5: Definitions and objects of mathematics.

“Greek thought was essentially non-algebraic, because it was so concrete. The abstract operations of algebra, which deal with objects that have been purposely stripped of their physical content, could not occur to minds which were so intently interested in the objects themselves. The symbol is not a mere formality; it is the very essence of algebra. Without the symbol the object is a human perception and reflects all the phases under which the human senses grasp it; replaced by a symbol the object becomes a complete abstraction, a mere operand subject to certain indicated operations.”

Tobias Dantzig (1884–1956) American mathematician

p, 125
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“Honour both spirit and form, the sentiment within as well as the symbol without.”

Ramakrishna (1836–1886) Indian mystic and religious preacher

Source: Sayings of Sri Ramakrishna (1960), p. 308

“The Irish… developed a form of confession that was exclusively private and that had no equivalent on the continent.”

Thomas Cahill book How the Irish Saved Civilization

Source: How the Irish Saved Civilization (1995), Ch. VI What Was Found
Context: The Irish... developed a form of confession that was exclusively private and that had no equivalent on the continent. In the ancient church, confession of one's sins—and the subsequent penance... had always been public.... one did not necessarily choose one's "priest" from among ordained professionals: the act of confession was too personal and too important for such a limitation. One looked for an anmchara, a soul-friend, someone to be trusted over a whole lifetime.

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