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**Hannibal lecter****Member**- Registered: 2016-02-11
- Posts: 392

Besides this, there is another rule for accuracy ; that is to say, when an unknown or incommensurable quantity is included between numerical limits not differing by many

units.

Thus if the diameter of a circle contain 497

parts, since it is not possible to ascertain precisely

of how many parts the circumference consists, the

more experienced, in accordance with the views of

Archimedes, have enclosed it within limits, namely

1562 and 1561. Again, if the side of a square

contain 1000 parts, the diagonal will be the square

root of the number 2000000. Since this is an in- commensurable number, we seek for its limits by

extraction of the square root, namely 1415 the

greater limit and 1414 the less limit, or more

accurately 1414(604/2828) greater, and 1414 (604/2829)

I searched a lot but I didn't find these what is 1562 greater limit and 1561 less limit

also what is 1414(604/2828) greater, and 1414 (604/2829)

if the side of square contain 1000 parts the diagonal will be the square root of number 2000?

isn't that should be 1 * square root of 2

why he put six zeros?

that book is talking about accuracy right now

also what is these numbers the 1414? and the 1561

*Last edited by Hannibal lecter (2023-06-23 05:11:32)*

Wisdom is a tree which grows in the heart and fruits on the tongue

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**Hannibal lecter****Member**- Registered: 2016-02-11
- Posts: 392

also allow me to quote this :-

Arithmetical progressions : 1, 2, 3, 4, 5, 6, 7,

&c. ; or 2, 4, 6, 8, 10, 12, 14, 16,

Geometrical progressions: 1, 2, 4, 8, 16, 32, 64,

or 243,81, 27, 9, 3, 1.

in these progressions we require accuracy and ease in

working. Accuracy is obtained by taking large numbers

for a basis ; but large numbers are most easily made from

small by adding cyphers,

Thus instead of 100000, which the less experienced make the greatest sine, the more learned

put 10.000.000, whereby the difference of all sines

is better expressed. Wherefore also we use the

same for radius and for the greatest of our geometrical proportional.

what does he put? he just increase the zeros it's mean he changed the number is that accuracy?

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,464

Please give a reference for this book.

B

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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**Hannibal lecter****Member**- Registered: 2016-02-11
- Posts: 392

this is the book shared bia google drive

https://drive.google.com/file/d/1eYeHtD4H-hnJdYAVTAxtSB_DY4zkhpS7/view?usp=sharing

I don't know if you can download it I found it on web

it's a translated version for the original book of john napier

Wisdom is a tree which grows in the heart and fruits on the tongue

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**Bob****Administrator**- Registered: 2010-06-20
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I've got the book. What page are you asking about?

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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**Hannibal lecter****Member**- Registered: 2016-02-11
- Posts: 392

it's page 9 he is talking about 1562 and 1561

Wisdom is a tree which grows in the heart and fruits on the tongue

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,464

Ok found it. Napier's language is not modern so it's tricky to follow what he is talking about. He seems to be talking in general terms about how accurately you might want to calculate something. So he uses examples where he leaves off the least significant digits without seriously affecting the quality of the result. In the Archimedes example he has a diameter divided into 497 parts ( =N say) so he reasons that the circumference should be divided into pi times N parts. If you take pi as 3.141 you get an answer that lies between 1562 and 1561.

Bob

ps. If you want to learn about logarithms (maybe after sines!) then look at MIF to get more up to date language.

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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**Hannibal lecter****Member**- Registered: 2016-02-11
- Posts: 392

Bob wrote:

Ok found it. Napier's language is not modern so it's tricky to follow what he is talking about. He seems to be talking in general terms about how accurately you might want to calculate something. So he uses examples where he leaves off the least significant digits without seriously affecting the quality of the result. In the Archimedes example he has a diameter divided into 497 parts ( =N say) so he reasons that the circumference should be divided into pi times N parts. If you take pi as 3.141 you get an answer that lies between 1562 and 1561.

Bob

ps. If you want to learn about logarithms (maybe after sines!) then look at MIF to get more up to date language.

when I do pi * 497 I find it's equal to 1561.37154883 to 1562

also in the book he is talking about a table which is that table? where can I find it

mr bob this book translation by WILLIAM RAE MACDONALD,

is there another better translation that understandable by students give me any another translation please

Wisdom is a tree which grows in the heart and fruits on the tongue

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,464

Napier is credited with the invention of logarithms. He wrote that book in Latin and Macdonald translated it into English. But the style and language is Napier's.

The table is a list of logarithmic values. Before the invention of computers and calculators, logarithms were used to enable calculations without the need for long multiplication and division. When I was at school we were given such a table and taught how to use them.

There's a page about him in Wiki: https://en.wikipedia.org/wiki/John_Napier

If you want to learn about logs then I recommend the MIF page:

https://www.mathsisfun.com/algebra/logarithms.html

Hope that helps,

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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**Hannibal lecter****Member**- Registered: 2016-02-11
- Posts: 392

Bob wrote:

Napier is credited with the invention of logarithms. He wrote that book in Latin and Macdonald translated it into English. But the style and language is Napier's.

The table is a list of logarithmic values. Before the invention of computers and calculators, logarithms were used to enable calculations without the need for long multiplication and division. When I was at school we were given such a table and taught how to use them.

There's a page about him in Wiki: https://en.wikipedia.org/wiki/John_Napier

If you want to learn about logs then I recommend the MIF page:

https://www.mathsisfun.com/algebra/logarithms.htmlHope that helps,

Bob

I didn't found the table in MIF can you send it to me here please

Wisdom is a tree which grows in the heart and fruits on the tongue

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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Here's the link.

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Hannibal lecter****Member**- Registered: 2016-02-11
- Posts: 392

Jai Ganesh wrote:

Here's the link.

yes but there is a table where is that table the book is talking about table of logarithm

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**Hannibal lecter****Member**- Registered: 2016-02-11
- Posts: 392

Bob wrote:

Napier is credited with the invention of logarithms. He wrote that book in Latin and Macdonald translated it into English. But the style and language is Napier's.

The table is a list of logarithmic values. Before the invention of computers and calculators, logarithms were used to enable calculations without the need for long multiplication and division. When I was at school we were given such a table and taught how to use them.

There's a page about him in Wiki: https://en.wikipedia.org/wiki/John_Napier

If you want to learn about logs then I recommend the MIF page:

https://www.mathsisfun.com/algebra/logarithms.htmlHope that helps,

Bob

Mr bob where can I found that table it's not there in MIF and tutorial for how to use it

Wisdom is a tree which grows in the heart and fruits on the tongue

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,464

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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**Hannibal lecter****Member**- Registered: 2016-02-11
- Posts: 392

Bob wrote:

Mr Bob it's a useful book thank you so much

Wisdom is a tree which grows in the heart and fruits on the tongue

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