Frases de John Wallis (34 citas)

“I did at last overcome the Difficulty; but with so much Paines and Expense of Time as I am not willing to mention; though yet I did not repent of that Labour, when I had discovered thereby, that it was a Businesse, which though with much Difficulty, was yet capable to bee effected.”

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John Wallis

An Essay on the Art of Decyphering (1737)
Contexto: Partly out of my owne Curiosity, partly to satisfy the Gentleman's Importunity that did request it, I resolved to try what I could do in it: And having projected the best Methods I could think of for the effecting it, I found yet so hard a Task, that I did divers Times give it over as desperate: Yet, after some Intermissions, resuming it againe, I did at last overcome the Difficulty; but with so much Paines and Expense of Time as I am not willing to mention; though yet I did not repent of that Labour, when I had discovered thereby, that it was a Businesse, which though with much Difficulty, was yet capable to bee effected.<!--p.13

“The invention was greedily embraced (and deservedly) by Learned Men”

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John Wallis

Of Logarithms, Their Invention and Use (1685)
Contexto: Logarithms was first of all Invented (without any Example of any before him, that I know of) by John Neper... And soon after by himself (with the assistance of Henry Briggs...) reduced to a better form, and perfected. The invention was greedily embraced (and deservedly) by Learned Men.... in a short time, it became generally known, and greedily embraced in all Parts, as of unspeakable Advantage; especially for Ease and Expedition in Trigonometrical Calculations.

“I found no difficulty to understand it, and I was very well pleased with it: and thought it ten days or a fortnight well spent. This was my first insight into Mathematicks; and all the Teaching I had.”

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John Wallis

Dr. Wallis's Account of some Passages of his own Life (1696)
Contexto: At Christmass 1631, (a season of the year when Boys use to have a vacancy from School,) I was, for about a fortnight, at home with my Mother at Ashford. I there found that a younger Brother of mine (in Order to a Trade) had, for about 3 Months, been learning (as they call'd it) to Write and Cipher, or Cast account, (and he was a good proficient for that time,) When I had been there a few days; I was inquisitive to know what it was, they so called. And (to satisfie my curiosity) my Brother did (during the Remainder of my stay there before I return'd to School) shew me what he had been Learning in those 3 Months. Which was (besides the writing a fair hand) the Practical part of Common Arithmetick in Numeration, Addition, Substraction, Multiplication, Division, The Rule of Three (Direct and Inverse) the Rule of Fellowship (with and without, Time) the Pule of False-Position, Rules of Practise and Reduction of Coins, and some other little things. Which when he had shewed me by steps, in the same method that he had learned them; and I had wrought over all the Examples which he before had done in his book; I found no difficulty to understand it, and I was very well pleased with it: and thought it ten days or a fortnight well spent. This was my first insight into Mathematicks; and all the Teaching I had.<!--pp. cxlvi-cxlvii

“I had the opportunity of being acquainted with divers worthy Persons, inquisitive into Natural Philosophy, and other parts of Humane Learning; And particularly of what hath been called the New Philosophy or Experimental Philosophy. We did by agreement, divers of us, meet weekly in London on a certain day, to treat and discourse of such affairs”

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John Wallis

Dr. Wallis's Account of some Passages of his own Life (1696)
Contexto: About the year 1645 while, I lived in London (at a time, when, by our Civil Wars, Academical Studies were much interrupted in both our Universities:) beside the Conversation of divers eminent Divines, as to matters Theological; I had the opportunity of being acquainted with divers worthy Persons, inquisitive into Natural Philosophy, and other parts of Humane Learning; And particularly of what hath been called the New Philosophy or Experimental Philosophy. We did by agreement, divers of us, meet weekly in London on a certain day, to treat and discourse of such affairs.... Some of which were then but New Discoveries, and others not so generally known and imbraced, as now they are, with other things appertaining to what hath been called The New Philosophy; which, from the times of Galileo at Florence, and Sr. Francis Bacon (Lord Verulam) in England, hath been much cultivated in Italy, France, Germany, and other Parts abroad, as well as with us in England. About the year 1648, 1649, some of our company being removed to Oxford (first Dr. Wilkins, then I, and soon after Dr. Goddard) our company divided. Those in London continued to meet there as before... Those meetings in London continued, and (after the King's Return in 1660) were increased with the accession of divers worthy and Honorable Persons; and were afterwards incorporated by the name of the Royal Society, &c. and so continue to this day.

“It hath been my Lot to live in a time, wherein have been many and great Changes and Alterations. It hath been my endeavour all along, to act by moderate Principles, between the Extremities on either hand, in a moderate compliance with the Powers in being,”

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John Wallis

Dr. Wallis's Account of some Passages of his own Life (1696)
Contexto: It hath been my Lot to live in a time, wherein have been many and great Changes and Alterations. It hath been my endeavour all along, to act by moderate Principles, between the Extremities on either hand, in a moderate compliance with the Powers in being, in those places, where it hath been my Lot to live, without the fierce and violent animosities usual in such Cases, against all, that did not act just as I did, knowing that there were many worthy Persons engaged on either side. And willing whatever side was upmost, to promote (as I was able) any good design for the true Interest of Religion, of Learning, and the publick good; and ready so to do good Offices, as there was Opportunity; And, if things could not be just, as I could wish, to make the best of what is: And hereby, (thro' God's gracious Providence) have been able to live easy, and useful, though not Great.<!--p. clxix

“I leave to the Judgement of those who have thought it worth their while to peruse what I have published”

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John Wallis

Dr. Wallis's Account of some Passages of his own Life (1696)
Contexto: I made it my business to examine things to the bottom; and reduce effects to their first principles and original causes. Thereby the better to understand the true ground of what hath been delivered to us from the Antients, and to make further improvements of it. What proficiency I made therein, I leave to the Judgement of those who have thought it worth their while to peruse what I have published therein from time to time; and the favorable opinion of those skilled therein, at home and abroad. <!--p. clxv

“Thus in Compliance with your repeated desires, I have given you a short account of divers passages of my life, 'till I have now come to more than fourscore years of age. How well I have acquitted my self in each, is for others rather to say, than for Your friend and servant John Wallis.”

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John Wallis

Oxford January 29. 1696, 7.
Dr. Wallis's Account of some Passages of his own Life (1696)

“These Exponents they call Logarithms”

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John Wallis

Of Logarithms, Their Invention and Use (1685)
Contexto: These Exponents they call Logarithms, which are Artificial Numbers, so answering to the Natural Numbers, as that the addition and Subtraction of these, answers to the Multiplication and Division of the Natural Numbers. By this means, (the Tables being once made) the Work of Multiplication and Division is performed by Addition and Subtraction; and consequently that of Squaring and Cubing, by Duplication and Triplication; and that of Extracting the Square and Cubic Root, by Bisection and Trisection; and the like in the higher Powers.

“But hee that will do any Thing in it, must first furnish himself with Patience and Sagacity”

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John Wallis

An Essay on the Art of Decyphering (1737)
Contexto: I saw, there was little or no Help to bee exspected from others; but that if I should have further Occasions of that Kind, I must trust to my owne Industry, and such Observations as the present Case should afford. And indeed the Nature of the Thing is scarce capable of any other Directions; every new Cipher allmost being contrived in a new Way, which doth not admit any constant Method for the finding of it out: But hee that will do any Thing in it, must first furnish himself with Patience and Sagacity, as well as hee may, and then Consilium in arenâ capere, and make the best Conjectures hee can, till hee shall happen upon something that hee may conclude for Truth.<!--p.14

“It was always my affectation even from a child”

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John Wallis

Dr. Wallis's Account of some Passages of his own Life (1696)
Contexto: It was always my affectation even from a child, in all pieces of Learning or Knowledge, not merely to learn by rote, which is soon forgotten, but to know the grounds or reasons of what I learn; to inform my Judgement, as well as furnish my Memory; and thereby, make a better Impression on both.<!--p. cxliv

“I must trust to my owne Industry, and such Observations as the present Case should afford. And indeed the Nature of the Thing is scarce capable of any other Directions”

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John Wallis

An Essay on the Art of Decyphering (1737)
Contexto: I saw, there was little or no Help to bee exspected from others; but that if I should have further Occasions of that Kind, I must trust to my owne Industry, and such Observations as the present Case should afford. And indeed the Nature of the Thing is scarce capable of any other Directions; every new Cipher allmost being contrived in a new Way, which doth not admit any constant Method for the finding of it out: But hee that will do any Thing in it, must first furnish himself with Patience and Sagacity, as well as hee may, and then Consilium in arenâ capere, and make the best Conjectures hee can, till hee shall happen upon something that hee may conclude for Truth.<!--p.14

“I saw, there was little or no Help to bee exspected from others; but”

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John Wallis

An Essay on the Art of Decyphering (1737)
Contexto: I saw, there was little or no Help to bee exspected from others; but that if I should have further Occasions of that Kind, I must trust to my owne Industry, and such Observations as the present Case should afford. And indeed the Nature of the Thing is scarce capable of any other Directions; every new Cipher allmost being contrived in a new Way, which doth not admit any constant Method for the finding of it out: But hee that will do any Thing in it, must first furnish himself with Patience and Sagacity, as well as hee may, and then Consilium in arenâ capere, and make the best Conjectures hee can, till hee shall happen upon something that hee may conclude for Truth.<!--p.14

“The Issue of which War, proved very different from what was said to be at first intended. As is usual in such cases; the power of the sword frequently passing from hand to hand and those who begin a War, not being able to foresee where it wil end.”

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John Wallis

Dr. Wallis's Account of some Passages of his own Life (1696)
Contexto: The Occasion of that Assembly was this; The Parliament which then was, (or the prevailing part of them,) were ingaged in a War with the King.... The Issue of which War, proved very different from what was said to be at first intended. As is usual in such cases; the power of the sword frequently passing from hand to hand and those who begin a War, not being able to foresee where it wil end.<!--pp. cliii-cliv

“I was… informed, that Baptista Porta, and one or two more, had written somewhat of that Subject, upon this Information I was willing to see whether I might from any of them find any Directions, that might help mee, if I should afterwards have the like Occasion: But I found very little in any of them for my Purpose. Their Businesse being for the most Part, onely to shew how to write in Cipher, (which was not my Work,) and that Things so written were beyond the Skill of Men to decipher. Onely in Baptista Porta (who alone if I mistake not, hath written any Thing to Purpose about deciphering, and was it seemes famous in his Time for his Abilities that Way;) I found that there were some general Directions, such as were obvious from the Nature of the Thing, and which I had before of myself taken Notice of, and made use of so far as the Nature of an intricate Cipher would permit. But the Truth of it is, there are scarce any of his Rules, which the present Way of Cipher (which is now much improved, beyond what, it seemes, it was in his Days) doth not in a Manner wholly elude…”

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John Wallis

p, 125
An Essay on the Art of Decyphering (1737)

“In the year 1660 being importuned by some friends of his, I undertook so to teach Mr. Daniel Whalley of Northampton, who had been Deaf and Dumb from a Child. I began the work in 1661, and in little more than a year's time, I had taught him to pronounce distinctly any words, so as I directed him… and in good measure to understand a Language and express his own mind in writing; And he had in that time read over to me distinctly (the whole or greatest part of) the English Bible; and did pretty well understand (at least) the Historical part of it. In the year 1662 I did the like for Mr. Alexander Popham… I have since that time (upon the same account) taught divers Persons (and some of them very considerable) to speak plain and distinctly, who did before hesitate and stutter very much; and others, to pronounce such words or letters, as before they thought impossible for them to do: by teaching them how to rectify such mistakes in the formation, as by some natural impediment, or acquired Custome, they had been subject to.”

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John Wallis

p, 125
Dr. Wallis's Account of some Passages of his own Life (1696)

“Around 1650 I came across the mathematical writings of Torricelli, where among other things, he expounds the geometry of indivisibles of Cavalieri. …His method, as taught by Torricelli… was indeed all the more welcome to me because I do not know that anything of that kind was observed in the thinking of almost any mathematician I had previously met.”

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John Wallis

Arithmetica Infinitorum (1656)

“About the beginning of our Civil Wars, in the year 1642, a Chaplain of Sr. Will. Waller's (one evening as we were sitting down to Supper at the Lady Vere's in London, with whom I then dwelt,) shewed me an intercepted Letter written in Cipher. He shewed it me as a Curiosity (and it was indeed the first thing I had ever seen written in Cipher.) And asked me between jeast and earnest, whether I could make any thing of it. And he was surprised when I said (upon the first view) perhaps I might, if it proved no more but a new Alphabet. It was about ten a clock when we rose from Supper. I then withdrew to my chamber to consider of it. And by the number of different Characters therein, (not above 22 or 23:) I judged that it could not be more than a new Alphabet, and in about 2 hours time (before I went to bed) I had deciphered it; and I sent a Copy of it (so deciphered) the next morning to him from whom I had it. And this was my first attempt at Deciphering.”

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John Wallis

p, 125
Dr. Wallis's Account of some Passages of his own Life (1696)

“Let as many Numbers, as you please, be proposed to be Combined: Suppose Five, which we will call a b c d e. Put, in so many Lines, Numbers, in duple proportion, beginning with 1. The Sum (31) is the Number of Sumptions, or Elections; wherein, one or more of them, may several ways be taken. Hence subduct (5) the Number of the Numbers proposed; because each of them may once be taken singly. And the Remainder (26) shews how many ways they may be taken in Combination; (namely, Two or more at once.) And, consequently, how many Products may be had by the Multiplication of any two or more of them so taken. But the same Sum (31) without such Subduction, shews how many Aliquot Parts there are in the greatest of those Products, (that is, in the Number made by the continual Multiplication of all the Numbers proposed,) a b c d e. For every one of those Sumptions, are Aliquot Parts of a b c d e, except the last, (which is the whole,) and instead thereof, 1 is also an Aliquot Part; which makes the number of Aliquot Parts, the same with the Number of Sumptions. Only here is to be understood, (which the Rule should have intimated;) that, all the Numbers proposed, are to be Prime Numbers, and each distinct from the other. For if any of them be Compound Numbers, or any Two of them be the same, the Rule for Aliquot Parts will not hold.”

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John Wallis

Fuente: A Discourse of Combinations, Alterations, and Aliquot Parts (1685), Ch.I Of the variety of Elections, or Choice, in taking or leaving One or more, out of a certain Number of things proposed.

“This method of mine takes its beginnings where Cavalieri ends his Method of indivisibles…. for as his was the Geometry of indivisibles, so I have chosen to call my method the Arithmetic of infinitesimals.”

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John Wallis

Arithmetica Infinitorum (1656)

“On March 4. 1644, 5. I married Susanna daughter of John and Rachel Glyde of Northjam in Sussex; born there about the end of January 1621, 2. and baptised Feb. 3 following. By whom I have (beside other children who died young) a Son and two Daughters now surviving; John born Dec. 26 1650. Anne born June 4. 1656. and Elizabeth born Sept. 23 1658…. My Wife died at Oxford Mar. 17. 1686, 7. after we had been married more than 42 years. ”

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John Wallis

p, 125
Dr. Wallis's Account of some Passages of his own Life (1696)

“Being encouraged by… success, beyond expectation; I afterwards ventured on many others and scarce missed of any, that I undertook, for many years, during our civil Wars, and afterwards. But of late years, the French Methods of Cipher are grown so intricate beyond what it was wont to be, that I have failed of many; tho' I have master'd divers of them. Of such deciphered Letters, there be copies of divers remaining in the Archives of the Bodleyan Library in Oxford; and many more in my own Custody, and with the Secretaries of State.”

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John Wallis

Dr. Wallis's Account of some Passages of his own Life (1696)

“[Mathematics were] scarce looked upon as Academical studies but rather Mechanical… And among more than two hundred students (at that time) in our college, I do not know of any two (perhaps not any) who had more of Mathematicks than I, (if so much) which was then but little; and but very few, in that whole university. For the study of Mathematicks was at that time more cultivated in London than in the universities.”

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John Wallis

(1635) as quoted by W. W. Rouse Ball, A History of the Study of Mathematics at Cambridge https://books.google.com/books?id=Pl32YkKFIhsC (1889) pp. 41-42.

“[W]hereas Nature, in propriety of Speech, doth not admit more than Three (Local) Dimensions, (Length, Breadth and Thickness, in Lines, Surfaces and Solids;) it may justly seem improper to talk of a Solid (of three Dimensions) drawn into a Fourth, Fifth, Sixth, or further Dimension.
A Line drawn into a Line, shall make a Plane or Surface; this drawn into a Line, shall make a Solid. But if this Solid be drawn into a Line, or this Plane into a Plane, what shall it make? A Plano-plane? This is a Monster in Nature, and less possible than a Chimera or a Centaure. For Length, Breadth and Thickness, take up the whole of Space.”

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John Wallis

Nor can our Fansie imagine how there should be a Fourth Local Dimension beyond these Three.
Treatise of Algebra (1685)

“This suiting my humor so well; I did thenceforth prosecute it, (at School and in the University) not as a formal Study, but as a pleasing Diversion, at spare hours; as books of Arithmetick or others Mathematical fel occasionally in my way. For I had none to direct me, what books to read, or what to seek, or in what Method to proceed. For Mathematicks, (at that time, with us) were scarce looked upon as Academical Studies, but rather Mechanical; as the business of Traders, Merchants, Seamen, Carpenters, Surveyors of Lands, or the like; and perhaps some Almanack-makers in London.”

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John Wallis

Dr. Wallis's Account of some Passages of his own Life (1696)

“Upon this Occasion many Methods have been invented of secret Writing, or Writing in Cipher, a Thing heretofore scarce known to any but the Secretaries of Princes, or others of like Condition; but of late Years, during our Commotions and civill Wars in England, grown very common and familiar, so that now there is scarce a Person of Quality, but is more or lesse acquainted with it, and doth as there is Occasion, make use of it.”

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John Wallis

p, 125
An Essay on the Art of Decyphering (1737)

“Suppose we a certain Number of things exposed, different each from other, as a, b, c, d, e, &c.; The question is, how many ways the order of these may be varied? as, for instance, how many changes may be Rung upon a certain Number of Bells; or, how many ways (by way of Anagram) a certain Number of (different) Letters may be differently ordered?
Alt.1,21) If the thing exposed be but One, as a, it is certain, that the order can be but one. That is 1.
2) If Two be exposed, as a, b, it is also manifest, that they may be taken in a double order, as ab, ba, and no more. That is 1 x 2 = 2. Alt.3
3) If Three be exposed; as a, b, c: Then, beginning with a, the other two b, c, may (by art. 2,) be disposed according to Two different orders, as bc, cb; whence arise Two Changes (or varieties of order) beginning with a as abc, acb: And, in like manner it may be shewed, that there be as many beginning with b; because the other two, a, c, may be so varied, as bac, bca. And again as many beginning with c as cab, cba. And therefore, in all, Three times Two. That is 1 x 2, x 3 = 6.
Alt.34) If Four be exposed as a, b, c, d; Then, beginning with a, the other Three may (by art. preceeding) be disposed six several ways. And (by the same reason) as many beginning with b, and as many beginning with c, and as many beginning with d. And therefore, in all, Four times six, or 24. That is, the Number answering to the case next foregoing, so many times taken as is the Number of things here exposed. That is 1 x 2 x 3, x 4 = 6 x 4 = 24.
5) And in like manner it may be shewed, that this Number 24 Multiplied by 5, that is 120 = 24 x 5 = 1 x 2 x 3 x 4 x 5, is the number of alternations (or changes of order) of Five things exposed. (Or, the Number of Changes on Five Bells.) For each of these five being put in the first place, the other four will (by art. preceeding) admit of 24 varieties, that is, in all, five times 24. And in like manner, this Number 120 Multiplied by 6, shews the Number of Alternations of 6 things exposed; and so onward, by continual Multiplication by the conse quent Numbers 7, 8, 9, &c.;
6) That is, how many so ever of Numbers, in their natural Consecution, beginning from 1, being continually Multiplied, give us the Number of Alternations (or Change of order) of which so many things are capable as is the last of the Numbers so Multiplied. As for instance, the Number of Changes in Ringing Five Bells, is 1 x 2 x 3 x 4 x 5 = 120. In Six Bells, 1 x 2 x 3 x 4 x 5 x 6 = 120 x 6 = 720. In Seven Bells, 720 x 7 = 5040. In Eight Bells, 5040 x 8 = 40320, And so onward, as far as we please.”

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John Wallis

Fuente: A Discourse of Combinations, Alterations, and Aliquot Parts (1685), Ch.II Of Alternations, or the different Change of Order, in any Number of Things proposed.