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A Budget of Paradoxes, Volume II
A Budget of Paradoxes, Volume II

Chapter VIII

Chapter 8 of A Budget of Paradoxes, Volume II is here in full — 358 sentences across 72 reading sections, with audio for every sentence and word.

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Context Illustration Reading 1/71 · 5 lines
English subtitles · tap any word to listen 1 / 5
{212} 1.
Take any diameter, double it, take 1-3d of that double, 2-5ths of the last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so on.
The sum of all is the circumference of that diameter.
The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.
Here 200 etc. is double of the diameter; 666 etc. is 1-3rd of 200 etc.; 266 etc. is 2-5ths of 666 etc.; 114 etc. is 3-7ths of 266 etc.; 507 etc. is 4-9ths of 114 etc.; and so on.
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LEARNER DICTIONARY
Archivist
/ˈɑːrkɪvɪst/
Editorial verification pending

A keeper or guardian of historical records and memories.

A Budget of Paradoxes, Volume II

Chapter VIII

Chapter 8 of A Budget of Paradoxes, Volume II is here in full — 358 sentences across 72 reading sections, with audio for every sentence and word.

Reading 1/71 · 5 reading units · Lines 1–5

Line 1
{212} 1.
Line 2
Take any diameter, double it, take 1-3d of that double, 2-5ths of the last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so on.
Line 3
The sum of all is the circumference of that diameter.
/ðə sʌm ʌv ɔːl ɪz ðə ˌsɜːrˈkʌmfrəns ʌv ðæt daɪˈæmətər/
Line 4
The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.
/ðə priˈsiːdɪŋ ɪz ðə ˈprɑːses wen ðə daɪˈæmətər ɪz ə ˈhʌndrəd ˈmɪljənz ðə ˈerərz ərˈaɪzɪŋ frʌm rɪˈdʒekʃən ʌv ˈfrækʃənz ˈbiːɪŋ ˈlesənd baɪ prəˈsiːdɪŋ ɑːn ə ˈθaʊzənd ˈmɪljənz ənd ˈstraɪkɪŋ ɔːf wʌn ˈfɪɡjər/
Line 5
Here 200 etc. is double of the diameter; 666 etc. is 1-3rd of 200 etc.; 266 etc. is 2-5ths of 666 etc.; 114 etc. is 3-7ths of 266 etc.; 507 etc. is 4-9ths of 114 etc.; and so on.

Learner Dictionary

These definitions explain words found in the current reading and keep every example grounded in its original sentence.

Oxford-style entry order: headword, part of speech, US IPA, concise definition, contextual example, and audio.

arising verb US /ərˈaɪzɪŋ/

-ing form of “arise” — come into existence; take on form or shape

From this reading “The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.”

circumference noun US /ˌsɜːrˈkʌmfrəns/

the size of something as given by the distance around it

From this reading “The sum of all is the circumference of that diameter.”

diameter noun US /daɪˈæmətər/

the length of a straight line passing through the center of a circle and connecting two points on the circumference

From this reading “Take any diameter, double it, take 1-3d of that double, 2-5ths of the last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so on.”

errors noun US /ˈerərz/

plural of “error” — a wrong action attributable to bad judgment or ignorance or inattention

From this reading “The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.”

fractions noun US /ˈfrækʃənz/

plural of “fraction” — a component of a mixture that has been separated by a fractional process

From this reading “The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.”

lessened adjective US /ˈlesənd/

impaired by diminution

From this reading “The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.”

rejection noun US /rɪˈdʒekʃən/

the act of rejecting something

From this reading “The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.”

ths noun US /θs/

plural of “th” — the fifth day of the week; the fourth working day

Word partnerships in these lines

English keeps certain words together, and knowing the pair is worth more than knowing each word alone. Every partnership below was counted across our whole published library, and earns its place by appearing far more often than two unrelated words of the same frequency would.

Shown as this reading writes them, with the form the library counts, what kind of pairing it is, and how often it occurs.

hundred millions noun + noun counted as “hundred million”

In this reading “The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.”

arising from verb + particle counted as “arise from”

In this reading “The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.”

thousand millions noun + noun counted as “thousand million”

In this reading “The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.”

All words in this reading · 55

Every word in these five lines is listed here, and every one of them can be played on its own.

Dictionary details are shown only when verified; these are not licensed Oxford entries.

1

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading {212} 1.

11

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Take any diameter, double it, take 1-3d of that double, 2-5ths of the last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so on.

114

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Here 200 etc. is double of the diameter; 666 etc. is 1-3rd of 200 etc.; 266 etc. is 2-5ths of 666 etc.; 114 etc. is 3-7ths of 266 etc.; 507 etc. is 4-9ths of 114 etc.; and so on.

2

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Take any diameter, double it, take 1-3d of that double, 2-5ths of the last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so on.

200

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Here 200 etc. is double of the diameter; 666 etc. is 1-3rd of 200 etc.; 266 etc. is 2-5ths of 666 etc.; 114 etc. is 3-7ths of 266 etc.; 507 etc. is 4-9ths of 114 etc.; and so on.

212

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading {212} 1.

266

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Here 200 etc. is double of the diameter; 666 etc. is 1-3rd of 200 etc.; 266 etc. is 2-5ths of 666 etc.; 114 etc. is 3-7ths of 266 etc.; 507 etc. is 4-9ths of 114 etc.; and so on.

3

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Take any diameter, double it, take 1-3d of that double, 2-5ths of the last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so on.

3rd

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Here 200 etc. is double of the diameter; 666 etc. is 1-3rd of 200 etc.; 266 etc. is 2-5ths of 666 etc.; 114 etc. is 3-7ths of 266 etc.; 507 etc. is 4-9ths of 114 etc.; and so on.

4

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Take any diameter, double it, take 1-3d of that double, 2-5ths of the last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so on.

5

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Take any diameter, double it, take 1-3d of that double, 2-5ths of the last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so on.

507

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Here 200 etc. is double of the diameter; 666 etc. is 1-3rd of 200 etc.; 266 etc. is 2-5ths of 666 etc.; 114 etc. is 3-7ths of 266 etc.; 507 etc. is 4-9ths of 114 etc.; and so on.

666

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Here 200 etc. is double of the diameter; 666 etc. is 1-3rd of 200 etc.; 266 etc. is 2-5ths of 666 etc.; 114 etc. is 3-7ths of 266 etc.; 507 etc. is 4-9ths of 114 etc.; and so on.

7

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Take any diameter, double it, take 1-3d of that double, 2-5ths of the last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so on.

9

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Take any diameter, double it, take 1-3d of that double, 2-5ths of the last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so on.

adeterminerUS /ə/

used before a singular noun to mean one of a group, when it is not a particular one

From this reading The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.

alladjectiveUS /ɔːl/

(quantifier) used with either mass or count nouns to indicate the whole number or amount of or every one of a class

From this reading The sum of all is the circumference of that diameter.

andconjunctionUS /ənd/

used to join words or parts of a sentence that go together

From this reading Take any diameter, double it, take 1-3d of that double, 2-5ths of the last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so on.

anyadjectiveUS /ˈeni/

one or some or every or all without specification

From this reading Take any diameter, double it, take 1-3d of that double, 2-5ths of the last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so on.

arisingverbUS /ərˈaɪzɪŋ/

-ing form of “arise” — come into existence; take on form or shape

From this reading The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.

beingauxiliary verbUS /ˈbiːɪŋ/

the -ing form of “be”

From this reading The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.

byprepositionUS /baɪ/

showing who or what does the action

From this reading The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.

circumferencenounUS /ˌsɜːrˈkʌmfrəns/

the size of something as given by the distance around it

From this reading The sum of all is the circumference of that diameter.

dnounUS /diː/

a fat-soluble vitamin that prevents rickets

From this reading Take any diameter, double it, take 1-3d of that double, 2-5ths of the last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so on.

diameternounUS /daɪˈæmətər/

the length of a straight line passing through the center of a circle and connecting two points on the circumference

From this reading Take any diameter, double it, take 1-3d of that double, 2-5ths of the last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so on.

doubleverbUS /ˈdʌbəl/

increase twofold

From this reading Take any diameter, double it, take 1-3d of that double, 2-5ths of the last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so on.

errorsnounUS /ˈerərz/

plural of “error” — a wrong action attributable to bad judgment or ignorance or inattention

From this reading The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.

etc

Dictionary entry pending editorial verification. Tap Listen to hear the word.

From this reading Here 200 etc. is double of the diameter; 666 etc. is 1-3rd of 200 etc.; 266 etc. is 2-5ths of 666 etc.; 114 etc. is 3-7ths of 266 etc.; 507 etc. is 4-9ths of 114 etc.; and so on.

figurenounUS /ˈfɪɡjər/

a diagram or picture illustrating textual material

From this reading The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.

fractionsnounUS /ˈfrækʃənz/

plural of “fraction” — a component of a mixture that has been separated by a fractional process

From this reading The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.

fromprepositionUS /frʌm/

showing where something starts, or who sent it

From this reading The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.

HereadverbUS /hiːr/

in or at this place; where the speaker or writer is

From this reading Here 200 etc. is double of the diameter; 666 etc. is 1-3rd of 200 etc.; 266 etc. is 2-5ths of 666 etc.; 114 etc. is 3-7ths of 266 etc.; 507 etc. is 4-9ths of 114 etc.; and so on.

hundrednounUS /ˈhʌndrəd/

ten 10s

From this reading The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.

isauxiliary verbUS /ɪz/

the form of “be” used with he, she, it, or a singular noun

From this reading The sum of all is the circumference of that diameter.

itpronounUS /ɪt/

a thing, animal, or idea already mentioned

From this reading Take any diameter, double it, take 1-3d of that double, 2-5ths of the last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so on.

lastadjectiveUS /læst/

immediately past

From this reading Take any diameter, double it, take 1-3d of that double, 2-5ths of the last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so on.

lessenedadjectiveUS /ˈlesənd/

impaired by diminution

From this reading The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.

millionsnounUS /ˈmɪljənz/

plural of “million” — the number that is represented as a one followed by 6 zeros

From this reading The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.

ofprepositionUS /ʌv/

belonging to, or connected with, somebody or something

From this reading Take any diameter, double it, take 1-3d of that double, 2-5ths of the last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so on.

offadverbUS /ɔːf/

from a particular thing or place or position (“forth” is obsolete)

From this reading The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.

onprepositionUS /ɑːn/

touching and supported by a surface

From this reading Take any diameter, double it, take 1-3d of that double, 2-5ths of the last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so on.

onepronounUS /wʌn/

used to mean any person in general, including the speaker

From this reading The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.

precedingadjectiveUS /priˈsiːdɪŋ/

existing or coming before

From this reading The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.

proceedingnounUS /prəˈsiːdɪŋ/

(law) the institution of a sequence of steps by which legal judgments are invoked

From this reading The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.

processverbUS /ˈprɑːses/

subject to a process or treatment, with the aim of readying for some purpose, improving, or remedying a condition

From this reading The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.

rejectionnounUS /rɪˈdʒekʃən/

the act of rejecting something

From this reading The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.

soconjunctionUS /soʊ/

for that reason; with the result that

From this reading Take any diameter, double it, take 1-3d of that double, 2-5ths of the last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so on.

strikingadjectiveUS /ˈstraɪkɪŋ/

sensational in appearance or thrilling in effect

From this reading The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.

sumnounUS /sʌm/

a quantity of money

From this reading The sum of all is the circumference of that diameter.

TakeverbUS /teɪk/

carry out

From this reading Take any diameter, double it, take 1-3d of that double, 2-5ths of the last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so on.

thatconjunctionUS /ðæt/

used to introduce what somebody said, thought, or felt

From this reading Take any diameter, double it, take 1-3d of that double, 2-5ths of the last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so on.

thedeterminerUS /ðə/

used before a noun that is already known, already mentioned, or the only one of its kind

From this reading Take any diameter, double it, take 1-3d of that double, 2-5ths of the last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so on.

thousandnounUS /ˈθaʊzənd/

the cardinal number that is the product of 10 and 100

From this reading The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.

thsnounUS /θs/

plural of “th” — the fifth day of the week; the fourth working day

From this reading Take any diameter, double it, take 1-3d of that double, 2-5ths of the last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so on.

whenconjunctionUS /wen/

at the time that

From this reading The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure.

Chapter 8 of A Budget of Paradoxes, Volume II by Augustus De Morgan holds 358 sentences, grouped into 72 reading sections of at most 5 sentences. The text is the source edition, unabridged, and the chapter records which sentences cover which part of the work so that nothing is dropped. Every word can be tapped for its pronunciation and dictionary entry.

What does chapter 8 of A Budget of Paradoxes, Volume II contain?

Chapter 8 holds 358 sentences of A Budget of Paradoxes, Volume II, unabridged, divided into 72 reading sections.

This page carries chapter 8 of A Budget of Paradoxes, Volume II by Augustus De Morgan exactly as it stands in the source edition, without abridgement. It runs to 358 sentences, grouped into 72 sections of at most 5 sentences so that a reader can take the chapter in steady, finishable pieces. The chapter also stores a coverage record mapping every one of its sentences to a part of the work, which is how the edition demonstrates that no line was dropped.

How do I study chapter 8 of A Budget of Paradoxes, Volume II?

Work through the 72 sections in order, replaying any sentence and tapping unfamiliar words for their entries.

Each of the 72 sections in this chapter is short enough to read once, hear once, and then re-read with the vocabulary in view. Tapping a word plays it alone and opens its dictionary entry with IPA, part of speech and meaning, so the reader is never forced to guess a pronunciation from spelling. Working section by section keeps a long chapter from becoming an undifferentiated wall of text, which is the usual reason a reader abandons a work of this period.

Can chapter 8 be read aloud to me?

Yes — every sentence and every individual word in chapter 8 can be played aloud in United States English.

Audio covers the whole chapter: any sentence can be played, and any single word within it can be played on its own. The voice uses United States English. For a work of this period that matters, because spelling is an unreliable guide to pronunciation for vocabulary that has fallen out of daily use, and a learner who guesses wrong tends to keep the error. Hearing the word in its own sentence, and then alone, settles it.

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Project Gutenberg eBook #26408, unabridged. The Project Gutenberg header, footer and licence are removed.

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About 587 minutes of reading across 1410 sections of 5 sentences each, at an unhurried pace.

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Vocabulary met early in A Budget of Paradoxes, Volume II

Words and structures a reader meets early in A Budget of Paradoxes, Volume II, each tappable for pronunciation and meaning.

Typographical
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Errors
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Corrected
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