幾何原本

Metadata

name content
dcterms:identifier ECHO:7lettersPlusChecksum.xml
dcterms:creator Ricci, Matteo
dcterms:contributor Xu Guangqi
dcterms:contributor Clavius, Christophorus
dcterms:contributor Euclid
dcterms:title 幾何原本
dcterms:alternative Jihe yuanben
dcterms:language zho-Hant
dcterms:date 1607
dcterms:rights open access
dcterms:license http://echo.mpiwg-berlin.mpg.de/policy/oa_basics/declaration
dcterms:accessRights free
dcterms:description This Chinese translation of Euclid's Elements is based on the Greek original and on Clavius' commented Latin edition.
stylesheet www.echo.mpiwg-berlin.mpg.de/stylesheet/echo-stylesheet.xsl
stylesheet www.echo.mpiwg-berlin.mpg.de/stylesheet/echo-stylesheet.css
echolink www.echo.mpiwg-berlin.mpg.de?titleID=02NT95YF
dcterms:description The metadata in this file belongs to Euclid (1966), while the text simply tests all features of the schema.
dcterms:description Special Instruction for another text: Characters with the old shape of the Grass radical have not been marked as < R> since this radical occurs very often in the text.
dcterms:spatial Berlin
dcterms:spatial Germany
dcterms:temporal 1900-1950

Table of Contents

volume 1 . . . . . . . . . . . . . 1
    body . . . . . . . . . . . . . 1
        chapter 1 . . . . . . . . . . . . . 1
        chapter 2 . . . . . . . . . . . . . 1
        chapter 3 . . . . . . . . . . . . . 1
            murp 1 . . . . . . . . . . . . . 1
        chapter 4 . . . . . . . . . . . . . 1
            section 1 . . . . . . . . . . . . . 1
            float . . . . . . . . . . . . . 1
        chapter 5 . . . . . . . . . . . . . 1
            section 1 . . . . . . . . . . . . . 1
            section 2 . . . . . . . . . . . . . 1
            section 3 . . . . . . . . . . . . . 1
        chapter 6 . . . . . . . . . . . . . 1
        chapter 7 . . . . . . . . . . . . . 1
        chapter 8 . . . . . . . . . . . . . 1
        chapter 9 . . . . . . . . . . . . . 1
        chapter 10 . . . . . . . . . . . . . 1
        chapter 11 . . . . . . . . . . . . . 1
            section 1 . . . . . . . . . . . . . 1
            section 2 . . . . . . . . . . . . . 1
        chapter 12 . . . . . . . . . . . . . 5
        chapter 13 . . . . . . . . . . . . . 5
        chapter 14 . . . . . . . . . . . . . 5
        chapter 15 . . . . . . . . . . . . . 5
        chapter 16 . . . . . . . . . . . . . 5
        chapter 17 . . . . . . . . . . . . . 5
            section 1 . . . . . . . . . . . . . 5
            section 2 . . . . . . . . . . . . . 5
        chapter 18 . . . . . . . . . . . . . 5

Text

volume 1

body

chapter 1

echo-start

chapter 2

echo-metadata

chapter 3

echo-div

murp 1

This is the only sentence in the only paragraph in a div with type="other" and type-free="murp".

chapter 4

echo-block

section 4.1

A Heading in Upright Shape

A paragraph in italics. A paragraph in italics. A paragraph in italics.

A sentence in upright shape.

A Heading in Italics

A sentence in upright shape. A sentence in italics, which occurs once in Benedetti (1585). A sentence in upright shape.

float

a very short note

Short note, sentence 1. Short note, sentence 2.

Long note, paragraph 1, sentence 1. Long note, paragraph 1, sentence 2.

Long note, paragraph 2, sentence 1. Long note, paragraph 2, sentence 2. Long note, paragraph 2, sentence 3.

chapter 5

echo-content

section 5.1

elements with plaintext model

The Roman number vii and the vulgar fraction ½. The line AB. The regularized form acutiſſimisque.

section 5.2

elements with inline model

This sentence contains a word in italics, a bold word, the combination of bold and italics, a word in Small Caps, a word in subscript, a word in superscript, a word in smaller font size, an underlined word, an overlined word, a struck-through word, a word in red, and a word in Sperrung. (The German word Sperrung is marked by <foreign> in the xml, but not in the xhtml.) The elements in the inline model do not need their own xml:space attribute because they inherit it from <s xml:space="preserve">.

This paragraph is in Fraktur if “Lucida Blackletter” is inſtalled. Note that this font has problems with the long s and does not contain the obligatory ligatures. (Engliſh is rarely written in Fraktur, though.)

section 5.3

quotes

This sentence contains an “inline quote”. This sentence contains a set-off

“inline quote within a sentence”,
after which the sentence continues. The paragraph ends here.

A new paragraph starts here. This sentence does not contain a set-off.

“ Quote within a paragraph, but not within a sentence. ”
Ths is a new sentence. Another sentence. The paragraph ends here.

A new paragraph starts here. A normal sentence. “ This quote within a paragraph is one sentence long. ” A normal sentence. “ This quote within a paragraph is more than one sentence long. It ends here. ” This paragraph also contains the following set-off blockquote:

This set-off quote within a paragraph is three sentences long. This sentence contains a bold word. This set-off quote within a paragraph is three sentences long.
The paragraph ends here.

This is a short blockquote. It it is not within a paragraph. Short means that it consists of a single paragraph, or more precisely some <s> without an enclosing <p>, i.e. it is on the same level as a paragraph.

A paragraph with a single sentence between two blockquotes.

This is a long blockquote, which consists of two paragraphs. This is the second sentence of the first paragraph.

This is the first sentence of the second paragraph. This is the second sentence of the second paragraph.

chapter 6

echo-gap

chapter 7

echo-de

xy

chapter 8

echo-figure

chapter 9

echo-handwritten

a short handwritten text text

chapter 10

echo-float

chapter 11

echo-milestone

The following note contains the soft hyphen U+00AD, which is not displayed.

Plutar
chus in
commẽ
tario de
dæmo­
nio So­
cratis.

The following note contains the normal hyphen U+002D.

Plutar
chus in
commẽ
tario de
dæmo-
nio So-
cratis.

The typesetter did not use a hyphen in Plutarchus or commẽtario (ẽ stands for en).

section 11.1

linebreaks at different positions

Blah blah blah. A linebreak in the middle
of the sentence. Blah blah blah. A linebreak in the mid-
dle of a word. Blah blah blah.
A linebreak at the beginning of the <s> (bad). Blah blah blah. A linebreak at the end of the <s>, after the period (also bad).
Blah blah blah. Instead, linebreaks at the beginning or end of a sentence should be moved out, as between this and the next sentence.
However, the schema accepts all three versions, and in your browser you will see no difference.

Since it's only a convention which doesn't change the semantics of the text, one could ask whether it would make sense to move linebreaks into the sentence rather than moving them out. When post-processing the transcription, the period and "return" can be replaced either by

... .</s><lb/>
<s>...
or by
... .<lb/></s>
<s>...
The former is more natural, but the latter is better for the tree representation of the XML since it makes linebreak tags as unintrusive as possible. A linebreak at the beginning of a sentence as a consequence of the post-processing, i.e.
... .</s>
<s><lb/>...
would be very unusual.

section 11.2

pagebreaks at different positions

Blah blah blah. A pagebreak in the middle

(page 1)

of the sentence. Blah blah blah. A pagebreak in the mid-

(page 2)

dle of a word. Blah blah blah.

(page 3)

A pagebreak at the beginning of the <s> (bad). Blah blah blah. A pagebreak at the end of the <s>, after the period (also bad).

(page 4)

Blah blah blah. Instead, pagebreaks at the beginning or end of a sentence should be moved out, as between this and the next sentence.

(page 5)

However, the schema accepts all three versions, and in your browser you will see no difference.

For pagebreaks the situation is slightly different than for linebreaks. The arguments of "natural" versus "better for the tree representation" are the same; the "natural" argument is perhaps even stronger than in the case of linebreaks because the typists are instructed to type the entire contents of one page before going on to the next page. In addition, when an XML fragment of a page is created, a pagebreak within a sentence or paragraph would create an artifact sentence or paragraph at the beginning of the next page, unless the script takes this situation into account. However, a strong argument for one pagebreak at the beginning of <div> is that the <pb> tag contains the running head. (This applies when the div starts at the top of the page; if the div starts in the middle of the page and the running head alerady gives the name of the new div, there is nothing one can do.)

chapter 12

echo-attribute

chapter 13

echo-datatype

chapter 14

echo-chinese-text

叢書集成簡編

亦
能使人無疑。

幾何原本第一卷之首界說三十六 求作四
公論十九

chapter 15

echo-mathematics

The Roman number vii and the vulgar fraction ½. The line AB.

Text small
text
text.

chapter 16

echo-import-xhtml

A simple table:

(back to anchor) row 1, column 1 row 1, column 2 row 2, column 1 a formula within a table:
x = − b ± b 2 − 4 ⁢ a ⁢ c 2 ⁢ a

A table with an <s> in one cell:

(back to anchor) row 1, column 1 row 1, column 2 row 2, column 1 A table cell with <s>.

A table with two <p> in one cell:

(back to anchor) row 1, column 1 row 1, column 2 row 2, column 1

A table cell with <s>. A table cell with <s>.

A table cell with <s>. A table cell with <s>.

A table with some large cells and

(back to anchor) a very very very long caption cell a 2x3 cell
with some text
cell
cell cell cell cell cell cell cell

A table from Benedetti (1585)

(back to anchor) Trabucha. pedes. vnciæ. 3. 2. 3. 2. 3. 2. 6. 4. 6. 1. 3. 1. 6. 1. 6. 8. 1. 8. 3. 2. 3.

Part of the errata in Benedetti (1585)

(back to anchor) Pag. Lin. Errata Correcta 3 29 æqualis æquali 8 35 maius maior 9 15 in vnitate ſuperficialis, erit ac in vnitate, ſupreficialis erit, ac

chapter 17

echo-import-mathml

This sentence contains a short mathematical term in the verbose MathML language, namely x = − b ± b 2 − 4 ⁢ a ⁢ c 2 ⁢ a , and thus looks very long in the XML file. The formula is taken from wikipedia (see http://en.wikipedia.org/wiki/Mathml). &minus; has been replaced by − (minus sign, U+2212), &PlusMinus; by ± (plus-minus sign, U+00B1), and &InvisibleTimes; by "invisible times" (U+2062); these replacements are not necessary, however. In addition, mode="display" in <math> has been removed. In display mode, the formula would look like this: x = − b ± b 2 − 4 ⁢ a ⁢ c 2 ⁢ a

The MathML formula x = - b ± b 2 - 4 a c 2 a has been generated by LaTeXMathML.pl (see http://pillars.che.pitt.edu/LaTeXMathML/) from the LaTex version $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. A typical command is

perl LaTeXMathML/LaTeXMathML.pl inputfile ./lichtenberg.xhtml outputfile lichtenberg-result.xhtml
The Perl script seems to do its work only inside of <(x)html> tags, e.g.
<xhtml><body>$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$</body></xhtml>.
The superfluous namespaces xmlns="http://www.w3.org/1998/Math/MathML" and xmlns:default="http://www.w3.org/1998/Math/MathML" in the result have been stripped (only the namespace in <math> remains), and a comment containing the original LaTeX formula has been added directly after <math>.

Note that the automatically created version uses the normal minus sign (U+002D), &PlusMinus; is written as &#xB1;, and <mo>&InvisibleTimes;</mo> is missing altogether. Also, the first <mrow> is now <mstyle>, the form="prefix" attribute for the first minus sign in is missing, and it uses two extra <mrow> elements. However, the resulting formulas look identical in Firefox 3.5.

Also note that the ECHO schema currently only checks that all elements inside <math> have the MathML namespace. The element names themselves, their attributes and their content are not checked. We simply assume that automatically created formulas are valid MathML. (Actually, Oxygen automatically checks MathML formulas even though the Schema does not!)

section 17.1

Test with a note by Georg Christoph Lichtenberg:

Sind wohl alle Wurzeln aus dem Unendlichen als zum Beispiel [ m ] ∞ n rational oder sind es nur die [ m ] ∞ m n wo m und n ganze Zahlen bedeuten? Ich sollte denken, denn da [ m ] 0 n gewiß = 0 und folglich rational ist, so wird auch [ m ] 1 ∞ n = 0 rational und folglich [ m ] ∞ - n und da n eine verneinte Zahl ausdrücken kann auch [ m ] ∞ n . (L 824)

The result is somewhat disappointing. In the second version, all formulas representing single variables have been replaced by <var>, and the “= 0” has been replaced by a normal = and a <num> tag:

Sind wohl alle Wurzeln aus dem Unendlichen als zum Beispiel [ m ] ∞ n rational oder sind es nur die [ m ] ∞ m n wo m und n ganze Zahlen bedeuten? Ich sollte denken, denn da [ m ] 0 n gewiß = 0 und folglich rational ist, so wird auch [ m ] 1 ∞ n = 0 rational und folglich [ m ] ∞ - n und da n eine verneinte Zahl ausdrücken kann auch [ m ] ∞ n . (L 824)

In the third version, the m-th roots have been removed:

Sind wohl alle Wurzeln aus dem Unendlichen als zum Beispiel ∞ n rational oder sind es nur die ∞ m n wo m und n ganze Zahlen bedeuten? Ich sollte denken, denn da 0 n gewiß = 0 und folglich rational ist, so wird auch 1 ∞ n = 0 rational und folglich ∞ - n und da n eine verneinte Zahl ausdrücken kann auch ∞ n . (L 824)

In the last version, the <msqrt> has been replaced by <mroot> with additional <mi>m</mi>:

Sind wohl alle Wurzeln aus dem Unendlichen als zum Beispiel ∞ n m rational oder sind es nur die ∞ m n m wo m und n ganze Zahlen bedeuten? Ich sollte denken, denn da 0 n m gewiß = 0 und folglich rational ist, so wird auch 1 ∞ n m = 0 rational und folglich ∞ - n m und da n eine verneinte Zahl ausdrücken kann auch ∞ n m . (L 824)

section 17.2

This is the same text with TexX4ht. One still has to re-format the result and fill in the LaTeX formula in the comment, but apart from that it seems to work well. However, it sometimes produces slightly illegal MathML; I had to insert <mstyle> in the two formulas with an = sign.

Sind wohl alle Wurzel[n] aus dem Unendlichen als zum Beispiel ∞ n m rational oder sind es nur die ∞ m n m wo m und n ganze Zahlen bedeuten? Ich sollte denken, denn da 0 n m gewiss = 0 und folglich rational ist, so wird auch 1 ∞ n m = 0 rational und folglich ∞ − n m und da n eine verneinte Zahl ausdruecken kann auch ∞ n m . (L 824)

chapter 18

echo-gis (experimental)

Im Januar 1923 lief Anton nach Berlijn.