Mixing
Origin of infix notation
$begingroup$
Wondering where the infix notation of things like 1 + 2 came from, when roughly it came about, and if it was before/after prefix or postfix notation. I know the summation and function notation came about potentially from Euler, but I haven't seen where infix notation comes from. Maybe if it's top of mind, knowing about if there were any controversies or competitions regarding which became the standard practice for math, that would be interesting.
notation math-history
asked Jan 11 at 8:10
Lance PollardLance Pollard
1,231824
$endgroup$
add a comment |
$begingroup$
Wondering where the infix notation of things like 1 + 2 came from, when roughly it came about, and if it was before/after prefix or postfix notation. I know the summation and function notation came about potentially from Euler, but I haven't seen where infix notation comes from. Maybe if it's top of mind, knowing about if there were any controversies or competitions regarding which became the standard practice for math, that would be interesting.
notation math-history
asked Jan 11 at 8:10
Lance PollardLance Pollard
1,231824
$endgroup$
$begingroup$
You can see Earliest Uses of Various Mathematical Symbols : very useful.
$endgroup$
– Mauro ALLEGRANZA
Jan 11 at 8:29
$begingroup$
The "standard" source is still Cajori.
$endgroup$
– Mauro ALLEGRANZA
Jan 11 at 8:29
add a comment |
$begingroup$
Wondering where the infix notation of things like 1 + 2 came from, when roughly it came about, and if it was before/after prefix or postfix notation. I know the summation and function notation came about potentially from Euler, but I haven't seen where infix notation comes from. Maybe if it's top of mind, knowing about if there were any controversies or competitions regarding which became the standard practice for math, that would be interesting.
notation math-history
asked Jan 11 at 8:10
Lance PollardLance Pollard
1,231824
$endgroup$
Wondering where the infix notation of things like 1 + 2 came from, when roughly it came about, and if it was before/after prefix or postfix notation. I know the summation and function notation came about potentially from Euler, but I haven't seen where infix notation comes from. Maybe if it's top of mind, knowing about if there were any controversies or competitions regarding which became the standard practice for math, that would be interesting.
notation math-history
notation math-history
asked Jan 11 at 8:10
Lance PollardLance Pollard
1,231824
asked Jan 11 at 8:10
Lance PollardLance Pollard
1,231824
asked Jan 11 at 8:10
Lance PollardLance Pollard
1,231824
asked Jan 11 at 8:10
Lance PollardLance Pollard
1,231824
asked Jan 11 at 8:10
Lance PollardLance Pollard
1,231824
1,231824
$begingroup$
You can see Earliest Uses of Various Mathematical Symbols : very useful.
$endgroup$
– Mauro ALLEGRANZA
Jan 11 at 8:29
$begingroup$
The "standard" source is still Cajori.
$endgroup$
– Mauro ALLEGRANZA
Jan 11 at 8:29
add a comment |
$begingroup$
You can see Earliest Uses of Various Mathematical Symbols : very useful.
$endgroup$
– Mauro ALLEGRANZA
Jan 11 at 8:29
$begingroup$
The "standard" source is still Cajori.
$endgroup$
– Mauro ALLEGRANZA
Jan 11 at 8:29
$begingroup$
You can see Earliest Uses of Various Mathematical Symbols : very useful.
$endgroup$
– Mauro ALLEGRANZA
Jan 11 at 8:29
$begingroup$
You can see Earliest Uses of Various Mathematical Symbols : very useful.
$endgroup$
– Mauro ALLEGRANZA
Jan 11 at 8:29
$begingroup$
The "standard" source is still Cajori.
$endgroup$
– Mauro ALLEGRANZA
Jan 11 at 8:29
$begingroup$
The "standard" source is still Cajori.
$endgroup$
– Mauro ALLEGRANZA
Jan 11 at 8:29
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The process of writing "equations" in symbols was very long.
We can start from an Ancient Greece specimen, due to Diophantus :
$Delta beta M alpha pitchfork ς gamma iota^{sigma} M delta$
that reads approximately as : $2 Delta +1 - 3 x = 4$, where $alpha, beta, gamma, delta, ldots$ are the naturals : $1,2,3,4,ldots$
$Delta$ is square, $M$ stand for units and $ς$ is the unknown. $pitchfork$ is subtracts and $iota^{sigma}$ is equals.
Justapoxition is sum and negative terms are collected, so that a single $pitchfork$ suffices for all terms following it.
In moder symbols : $2x^2-3x+1=4$.
We can see some Medieval and Renaissance examples into Victor Katz, A History of Mathematics: An Introduction (Addison-Wesley, 2009).
Page 386 :
Paolo Gerardi, in his Libro di ragioni of 1328, gave the rule for adding the fractions $dfrac {100} {x}$ and $dfrac {100} {(x + 5)}$:
You place $100$ opposite one cosa [$x$], and then you place $100$ opposite one cosa and $5$. Multiply crosswise as you see indicated, and you say...
and page 405 for Rafael Bombelli (1526 1572) :
he used R.q. to denote the square root, R.c. to denote the cube root, and similar expressions to denote higher roots. He used $downharpoonright$ $downharpoonleft$ as parentheses to enclose long expressions, as in $R.c. downharpoonright 2 p R.q.21 downharpoonleft$, but kept the standard Italian abbreviations of $p$ for plus and $m$ for minus. His major notational innovation was the use of a semicircle around a number $n$ to denote the $n$ th power of the unknown. Thus, $x^3 + 6x^2 − 3x$ would be
written as
$1^{frac 3 ˘} text { p } 6^{frac 2 ˘} text { m } 3^{frac 1 ˘}$.
In conclusion, IMO, in Western mathematics the infix notation was an obvious choice, because it rised slowly from writing "descriptions" in abbreviated form.
For further examples, see also : Jens Hoyrup, Jacopo da Firenze and the beginning of Italian vernacular algebra, HistMat (2006), regarding the Tractatus algorismi, written in 1307 in Montpellier by a certain Jacopo da Firenze, that contains the earliest extant algebra in a European vernacular and probably, the first algebra in vernacular Italian.
answered Jan 14 at 14:10
Mauro ALLEGRANZAMauro ALLEGRANZA
65.8k449114
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3069597%2forigin-of-infix-notation%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The process of writing "equations" in symbols was very long.
We can start from an Ancient Greece specimen, due to Diophantus :
$Delta beta M alpha pitchfork ς gamma iota^{sigma} M delta$
that reads approximately as : $2 Delta +1 - 3 x = 4$, where $alpha, beta, gamma, delta, ldots$ are the naturals : $1,2,3,4,ldots$
$Delta$ is square, $M$ stand for units and $ς$ is the unknown. $pitchfork$ is subtracts and $iota^{sigma}$ is equals.
Justapoxition is sum and negative terms are collected, so that a single $pitchfork$ suffices for all terms following it.
In moder symbols : $2x^2-3x+1=4$.
We can see some Medieval and Renaissance examples into Victor Katz, A History of Mathematics: An Introduction (Addison-Wesley, 2009).
Page 386 :
Paolo Gerardi, in his Libro di ragioni of 1328, gave the rule for adding the fractions $dfrac {100} {x}$ and $dfrac {100} {(x + 5)}$:
You place $100$ opposite one cosa [$x$], and then you place $100$ opposite one cosa and $5$. Multiply crosswise as you see indicated, and you say...
and page 405 for Rafael Bombelli (1526 1572) :
he used R.q. to denote the square root, R.c. to denote the cube root, and similar expressions to denote higher roots. He used $downharpoonright$ $downharpoonleft$ as parentheses to enclose long expressions, as in $R.c. downharpoonright 2 p R.q.21 downharpoonleft$, but kept the standard Italian abbreviations of $p$ for plus and $m$ for minus. His major notational innovation was the use of a semicircle around a number $n$ to denote the $n$ th power of the unknown. Thus, $x^3 + 6x^2 − 3x$ would be
written as
$1^{frac 3 ˘} text { p } 6^{frac 2 ˘} text { m } 3^{frac 1 ˘}$.
In conclusion, IMO, in Western mathematics the infix notation was an obvious choice, because it rised slowly from writing "descriptions" in abbreviated form.
For further examples, see also : Jens Hoyrup, Jacopo da Firenze and the beginning of Italian vernacular algebra, HistMat (2006), regarding the Tractatus algorismi, written in 1307 in Montpellier by a certain Jacopo da Firenze, that contains the earliest extant algebra in a European vernacular and probably, the first algebra in vernacular Italian.
answered Jan 14 at 14:10
Mauro ALLEGRANZAMauro ALLEGRANZA
65.8k449114
$endgroup$
add a comment |
$begingroup$
The process of writing "equations" in symbols was very long.
We can start from an Ancient Greece specimen, due to Diophantus :
$Delta beta M alpha pitchfork ς gamma iota^{sigma} M delta$
that reads approximately as : $2 Delta +1 - 3 x = 4$, where $alpha, beta, gamma, delta, ldots$ are the naturals : $1,2,3,4,ldots$
$Delta$ is square, $M$ stand for units and $ς$ is the unknown. $pitchfork$ is subtracts and $iota^{sigma}$ is equals.
Justapoxition is sum and negative terms are collected, so that a single $pitchfork$ suffices for all terms following it.
In moder symbols : $2x^2-3x+1=4$.
We can see some Medieval and Renaissance examples into Victor Katz, A History of Mathematics: An Introduction (Addison-Wesley, 2009).
Page 386 :
Paolo Gerardi, in his Libro di ragioni of 1328, gave the rule for adding the fractions $dfrac {100} {x}$ and $dfrac {100} {(x + 5)}$:
You place $100$ opposite one cosa [$x$], and then you place $100$ opposite one cosa and $5$. Multiply crosswise as you see indicated, and you say...
and page 405 for Rafael Bombelli (1526 1572) :
he used R.q. to denote the square root, R.c. to denote the cube root, and similar expressions to denote higher roots. He used $downharpoonright$ $downharpoonleft$ as parentheses to enclose long expressions, as in $R.c. downharpoonright 2 p R.q.21 downharpoonleft$, but kept the standard Italian abbreviations of $p$ for plus and $m$ for minus. His major notational innovation was the use of a semicircle around a number $n$ to denote the $n$ th power of the unknown. Thus, $x^3 + 6x^2 − 3x$ would be
written as
$1^{frac 3 ˘} text { p } 6^{frac 2 ˘} text { m } 3^{frac 1 ˘}$.
In conclusion, IMO, in Western mathematics the infix notation was an obvious choice, because it rised slowly from writing "descriptions" in abbreviated form.
For further examples, see also : Jens Hoyrup, Jacopo da Firenze and the beginning of Italian vernacular algebra, HistMat (2006), regarding the Tractatus algorismi, written in 1307 in Montpellier by a certain Jacopo da Firenze, that contains the earliest extant algebra in a European vernacular and probably, the first algebra in vernacular Italian.
answered Jan 14 at 14:10
Mauro ALLEGRANZAMauro ALLEGRANZA
65.8k449114
$endgroup$
add a comment |
$begingroup$
The process of writing "equations" in symbols was very long.
We can start from an Ancient Greece specimen, due to Diophantus :
$Delta beta M alpha pitchfork ς gamma iota^{sigma} M delta$
that reads approximately as : $2 Delta +1 - 3 x = 4$, where $alpha, beta, gamma, delta, ldots$ are the naturals : $1,2,3,4,ldots$
$Delta$ is square, $M$ stand for units and $ς$ is the unknown. $pitchfork$ is subtracts and $iota^{sigma}$ is equals.
Justapoxition is sum and negative terms are collected, so that a single $pitchfork$ suffices for all terms following it.
In moder symbols : $2x^2-3x+1=4$.
We can see some Medieval and Renaissance examples into Victor Katz, A History of Mathematics: An Introduction (Addison-Wesley, 2009).
Page 386 :
Paolo Gerardi, in his Libro di ragioni of 1328, gave the rule for adding the fractions $dfrac {100} {x}$ and $dfrac {100} {(x + 5)}$:
You place $100$ opposite one cosa [$x$], and then you place $100$ opposite one cosa and $5$. Multiply crosswise as you see indicated, and you say...
and page 405 for Rafael Bombelli (1526 1572) :
he used R.q. to denote the square root, R.c. to denote the cube root, and similar expressions to denote higher roots. He used $downharpoonright$ $downharpoonleft$ as parentheses to enclose long expressions, as in $R.c. downharpoonright 2 p R.q.21 downharpoonleft$, but kept the standard Italian abbreviations of $p$ for plus and $m$ for minus. His major notational innovation was the use of a semicircle around a number $n$ to denote the $n$ th power of the unknown. Thus, $x^3 + 6x^2 − 3x$ would be
written as
$1^{frac 3 ˘} text { p } 6^{frac 2 ˘} text { m } 3^{frac 1 ˘}$.
In conclusion, IMO, in Western mathematics the infix notation was an obvious choice, because it rised slowly from writing "descriptions" in abbreviated form.
For further examples, see also : Jens Hoyrup, Jacopo da Firenze and the beginning of Italian vernacular algebra, HistMat (2006), regarding the Tractatus algorismi, written in 1307 in Montpellier by a certain Jacopo da Firenze, that contains the earliest extant algebra in a European vernacular and probably, the first algebra in vernacular Italian.
answered Jan 14 at 14:10
Mauro ALLEGRANZAMauro ALLEGRANZA
65.8k449114
$endgroup$
The process of writing "equations" in symbols was very long.
We can start from an Ancient Greece specimen, due to Diophantus :
$Delta beta M alpha pitchfork ς gamma iota^{sigma} M delta$
that reads approximately as : $2 Delta +1 - 3 x = 4$, where $alpha, beta, gamma, delta, ldots$ are the naturals : $1,2,3,4,ldots$
$Delta$ is square, $M$ stand for units and $ς$ is the unknown. $pitchfork$ is subtracts and $iota^{sigma}$ is equals.
Justapoxition is sum and negative terms are collected, so that a single $pitchfork$ suffices for all terms following it.
In moder symbols : $2x^2-3x+1=4$.
We can see some Medieval and Renaissance examples into Victor Katz, A History of Mathematics: An Introduction (Addison-Wesley, 2009).
Page 386 :
Paolo Gerardi, in his Libro di ragioni of 1328, gave the rule for adding the fractions $dfrac {100} {x}$ and $dfrac {100} {(x + 5)}$:
You place $100$ opposite one cosa [$x$], and then you place $100$ opposite one cosa and $5$. Multiply crosswise as you see indicated, and you say...
and page 405 for Rafael Bombelli (1526 1572) :
he used R.q. to denote the square root, R.c. to denote the cube root, and similar expressions to denote higher roots. He used $downharpoonright$ $downharpoonleft$ as parentheses to enclose long expressions, as in $R.c. downharpoonright 2 p R.q.21 downharpoonleft$, but kept the standard Italian abbreviations of $p$ for plus and $m$ for minus. His major notational innovation was the use of a semicircle around a number $n$ to denote the $n$ th power of the unknown. Thus, $x^3 + 6x^2 − 3x$ would be
written as
$1^{frac 3 ˘} text { p } 6^{frac 2 ˘} text { m } 3^{frac 1 ˘}$.
In conclusion, IMO, in Western mathematics the infix notation was an obvious choice, because it rised slowly from writing "descriptions" in abbreviated form.
For further examples, see also : Jens Hoyrup, Jacopo da Firenze and the beginning of Italian vernacular algebra, HistMat (2006), regarding the Tractatus algorismi, written in 1307 in Montpellier by a certain Jacopo da Firenze, that contains the earliest extant algebra in a European vernacular and probably, the first algebra in vernacular Italian.
answered Jan 14 at 14:10
Mauro ALLEGRANZAMauro ALLEGRANZA
65.8k449114
answered Jan 14 at 14:10
Mauro ALLEGRANZAMauro ALLEGRANZA
65.8k449114
answered Jan 14 at 14:10
Mauro ALLEGRANZAMauro ALLEGRANZA
65.8k449114
answered Jan 14 at 14:10
Mauro ALLEGRANZAMauro ALLEGRANZA
65.8k449114
65.8k449114
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3069597%2forigin-of-infix-notation%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
You can see Earliest Uses of Various Mathematical Symbols : very useful.
$endgroup$
– Mauro ALLEGRANZA
Jan 11 at 8:29
$begingroup$
The "standard" source is still Cajori.
$endgroup$
– Mauro ALLEGRANZA
Jan 11 at 8:29