Difference between revisions of "Anonymous text from Latin"

Addition

4 4 8 9 6   2 6 1 3

4 8 9 6 7 8 1 2

1 2 7 0 8

Multiplication

8 10 12 12 16 18		4 5 6 7 8 9	2 times
9 12 15 18 21 24 27		3 4 5 6 7 8 9	3 times
16 20 24 28 [32] 36		4 5 6 7 8 9	4 times
25 30 35 40 45		5 6 7 8 9	5 times

36 42 48 54		6 7 8 9	6 times
49 56 63		7 8 9	7 times
64 [7]2		8 9	8 times
81		9	9 times

• 2 times 2 is obtained from 20 minus 2 times 8.

• 2 times 3 is obtained from 30 minus 3 times 8.

• 2 times 4 is obtained from 40 minus 4 times 8.

• 2 times 5 is obtained from 50 minus 5 times 8.

• 2 times 6 is obtained from 60 minus 6 times 8.

• 2 times 7 is obtained from 70 minus 7 times 8.

9 8 7 6 5 4 3 2 1 0

9 8 7 6 5   4 3 2 1 0 9 8 7 6 5 0

9 8 7 6 5       4 3 2 1 0     9 8 7 6 5 0 1 9 7 5 3 0

9 4 5 6 5         4 3 2 1 0       9 8 7 6 5 0   1 9 7 5 3 0     [2] 9 6 2 9 5

9 8 7 6 5           4 3 2 1 0         9 8 7 6 5 0     1 9 7 5 3 0       [2] 9 6 2 9 5       3 9 5 0 [6] 0         4 2 [6] 7 6 3 5 6 5 0

Subtraction

4 8 5 3 6 4

9 8 2 7 6 5 0 5

9 8 2 7 6 5 0 5 3 3 2 2

9 7 2 1 6 8 9 2

9 7 2 1 6 8 9 2 2 8 2 9

Division

3 9 6   3 6

3 5 6   3 6

3 5 6   3 6

3     8 2 3 5 6   3 6

9

3 2 1 0   3 2 2     3

1 8 2 9 2 2     2 0 1

0     1 8 2 9 2 2   2 0 1       2 0

9

1 8 2 9 2 2   2 0 1 1       2 0

0   1 1 8 2 9 2 2   2 0 1 1       2 0

91

1 8 2 9 2 2   2 0 1 1 1     2 0 0         2

Progression

Austrian Measurement

Fuder[20] 32 Hin Dreiling[21] 24 Hin Eimer 32 Achtring[22] Seidel[23] 4 אנטרינג

Hungarian Coin

פשיטי‫' ‫00א זהוב חלשין ב פשי‫'

Proportions

Fractions

• Example: , the 3 is the numerator and the 4 is the denominator.

Fractions of Fractions

Chapter on Addition

• If the denominators are equal, sum the numerators together, with one denominator beneath them.

• If not, multiply the first numerator by the denominator of the other and vice versa, then sum the two [products] together, with the product of the denominators by each other beneath.

Sum 8, 5 and 11 together; the result is 24. Write beneath it 13.

It looks like this:

Or:

Or:

Subtraction of Fractions

Doubling

Halving

Multiplication of Fractions

Division

Proportions

• If one asks, for example: one has 248 Hungarian gold coins and the question is how much are they worth in Rheinos gold coins?

Multiply 248 by 10; the result is 2480. Divide them by 8; the result is 310 Rheinos gold coins.

• Example: you have 310 Rheinos gold coins and you wish to know how much are they worth in Hungarian gold coins?

Multiply 310 gold coins by 8 dinar; the result is 2480. Divide them by 10; the required is 248 Hungarian gold coins.

• Example: one has 360 Hungarian gold coins, the rate of a Hungarian gold coin is 11 dinar and the exchange rate is 12 pašuṭim. The question is how many Rheinos gold coins is this amount of Hungarian gold coins worth?

Multiply these 3[6]0 gold coins by 11 dinar; the result is 3960 dinar. Multiply them also by 12 pašuṭim; the result is 4320 pašuṭim. Divide them by the dinar; the result is 144 dinar. Add them to the 3960 dinar and divide the whole sum, which is 4104, by 8; the result is 513 Rheinos gold coins.

כפלם עוד על בא פשיטי' ויצמח 0בגד פשי‫'
חלקם לדינרי' והצומח הוא דדא ‫^[57]הוא דדא דינרי' חברם על 0וטג דינרי' וחלק הסך כולו כגון ד0אד דינר' בח' ועולה מורה גאה זהו' רינוס במטבע

• I bought 24 cubits for 9610 in the city of Vienna [at a rate of] a cubit for 4 Rheinos gold coins and when they were brought to Ofen [= Buda] in the country of Hungary, I sold one cubit for 4 Hungarian gold coins. of a cubit in Vienna is one cubit in Ofen. I ask: how much is the profit?

Say: at 4 Rheinos gold coins [for one cubit], how much is the price of 24 cubits? The result is 96 Rheinos gold coins.

Seek also how many cubits of Ofen are 24 cubits of Vienna:

Say: 3 cubits of Vienna are 4 cubits of Ofen, how many are 24 cubits of Vienna? The result is 32 cubits of Ofen.

Say also: at 1 cubit for 4 Hungarian gold coins, how much are 32 cubits worth? 128 Hungarian gold coins , which are 160 Rheinos gold coins .

Subtract the 96 Rheinos gold coins from them; you are left with 64 Rheinos gold coins and this is the profit.

• I bought 6 cubits of cloth for wearing; the width of the cubit is cubits; and I wish to buy another cloth instead of cubits. The question is how much of that cloth should be taken instead of the garment?

Barter

Partnership

Currency calculations

1 zaquq = 16 lot

1 lot = 4 quenten

1 quenten = 4 pešiṭim

• A piece of silver weighs 12 zequqim, 13 lot, 3 quenten, and 1 pašuṭ. When you remove the slag from it and melt it, there is in a refined pure silver zaquq 14 lot, 3 quenten, 2 pešiṭim.

How much pure silver is included in 12 zequqim, 13 lot, 3 quenten, and 1 pašuṭ?

The result is: 11 zequqim, 15 lot, 1 quenten, and pešiṭim

1 zahuv = 8 dinar

1 dinar = 30 pešiṭim

• A piece of silver weighs 20 zequqim, 12 lot, 2 quenten, and 2 pešiṭim.

Each lot is worth 5 Austrian dinar. How much is the price of the whole [piece of] silver?

Say: [If] 1 lot is worth 5 dinar, how much [is the price of] 20 zequqim, 12 lot, 2 quenten, and 2 pešiṭim?

The result is: 207 zehuvim, 7 dinar, and pešiṭim

24 carat = 1 marc

4 gran = 1 carat

• If one asks: 384 zequqim, 13 lot, 3 quenten of pure silver.

You bought the zaquq for 8 zehuvim.

The price is 3078 [zehuvim] 17 dinar, and 6 halusim.

This calculation is for Frankfurt dinars

1 zahuv = 20 dinar

1 dinar = 12 halish

• You bought 1256 zaquq at one lot of pure silver; the zaquq contains 9 lot and 3 quenten of pure silver. You bought one zaquq of pure silver for 8 zehuvim and 3 dinar; the result is 62641 zehuvim, 10 dinar, 7 halish and 14 parts of 63.

כפלהו וכתוב המחלק תחתיו כזה הזחַחַז0ג משקלי פשי' כסף מזוקק תוסיף עוד דו לאמר זקוק כסף מזוקק עולה דמיו זהו' בכמה ה משקלי פשי' ראשי' השיטה תעשה משקלי פשוט ותוליך שני השברי' ע"י אמצעי' שברהו על עצמו ואחרי' השיטה תעמיד המספר הכוללי ותעביר הפרטיי מעל פני וזה תבניתו

• One bought scraps of gold weighing 25 zequqin, 13 lot, and 3 quenten.

One zaquq is 18 carat and 3 gran of pure gold.

The price of one carat is 3 zehuvim, 10 dinar and 9 halushim.

The result is: 1715 [zehuvim], 4 dinar, 0 halishim, and

Say: one zaquq contains 18 carat and 3 gran, how much are 25 zequqim, 13 lot, and 3 quenten worth?

Write the beginning and the end of the line and in the middle [the conversion of] carat to gran. Its diagram is as follows:

1655 — [parts of] — 64

Multiply and divide; the result is gran. Convert to carat:

The result is: 484 carat, 3 gran, and

124125 — 849 pešiṭim — 256

• Scraps of gold weighing 21 zequqin, 14 lot, 3 quenten, and 3 pešiṭim.

One zaquq weighs 22 carat and 3 gran of pure gold.

The price of one lot of pure gold is 5 zehuvim and 5 dinar.

The result is: 1746 zehuvim, 9 dinar, 2 halishim

91 — 5615 — 96

510965 — 105 — 153[6]