MAT 118 Spring 2013

Here is Fibonacci's 1202 text with *my translation.
*

Qvidam posuit unum par cuniculorum in quodam loco, qui erat undique

parium

1

primus

2

Secundus

3

tercius

5

Quartus

8

Quintus

13

Sestus

21

Septimus

34

Octauus

55

Nonus

89

Decimus

144

Undecimus

233

Duodecimus

377

Quot paria coniculorum in uno anno ex uno pario germinentur.

*
How many pairs of rabbits will spring in one year from one pair.*

* A person put one pair of rabbits in a certain place, which was on all sides*

pariete circundatus, ut sciret, quot ex eo paria germinarentur in uno anno : cum

* surrounded by a wall, so as to know, how many would be engendered by that pair in a year: since*

natura eorum sit per singulum mensem aliud par germinare ; et in secundo

* it is their nature to give birth to another pair after one month; and to give *

mense ab eorum natiuitate germinant. Quia suprascriptum par in primo mense

* birth during the second month after birth. Because the above-mentioned pair gives birth*

germinat, duplicabis ipsum, erunt paria duo in uno mense. Ex quibus unum,

* during the first month, you will double it; there will be two pairs after one month. Of these one,*

scilicet primum, in secundo mense geminat ; et sic sunt in secundo mense paria

* say the first, will give birth during the second month: and so there are after the second month*

3 ; ex quibus in uno mense duo pregnantur ; et, gemitiantur in tercio mense* 3 pairs; of which during one month two get pregnant; and give birth in the third month
to *

paria 2 coniculorum ; et sic sunt paria 5 in ipso mense ; ex quibus in ipso* 2 pairs of rabbits; and so there are 5 pairs after that month; of which during the same month*

pregnantur paria 3 ; et sunt in quarto mense paria 8 ; ex quibus paria 5

* 3 pairs get pregnant; and after the forth month there are 8 pairs; of which 5 pairs*

geminant alia paria 5 : quibus additis cum parijs 8, faciunt paria 13 in quinto

* give birth to another 5 pairs: which added to the 8 pairs, make 13 pairs after the fifth*

mense ; ex quibus paria 5, que geminata fuerunt in ipso mense, non concipiunt

* month; of which 5 pairs, which were born in that same month, do not conceive*

in ipso mense ; sed alia 8 paria pregnantur ; et sic sunt in sexto mense paria 21 ;

* during that same month; but the other 8 pairs get pregnant; and so there are in six months 21 pairs;*

cum quibus additis parijs 13, que geminantur in septimo, erunt in ipso paria

* when to those are added the 13 pairs, that are born in the seventh month, there will be after that month*

34 ; cum quibus additis parijs 21, que geminantur in octauo mense, erunt in* 34 pairs; when to those are added the 21 pairs, that are born during the eighth month, there will be after*

ipso paria 55 ; cum quibus additis parijs 34, que geminantur in nono mense,* that month 55 pairs; when to those are added the 34 pairs, that are born during the ninth month,*

erunt in ipso paria 89 ; cum quibus additis rursum parijs 55, que geminantur in

* there will be after that month 89 pairs; when to those are added in turn the 55 pairs, that are born during *

decimo, erunt in ipso paria 144 ; cum quibus additis rursum parijs 89, que

* the tenth, there will be after that month 144 pairs; when to those are added in turn the 89 pairs, that*

geminantur in undecimo mense, erunt in ipso paria 233. Cum quibus etiam

* are born during the eleventh month, there will be after that month 233 pairs. When to those, furthermore,*

additis parijs 144, que geminantur in ultimo mense, erunt paria 377 ; et tot

* are added the 144 pairs, that are born during the last month, there will be 377 pairs; and all*

paria peperit suprascriptum par in prefato loco in capite unius anni. Potes enim

* the pairs have been engendered by the abovementioned pair in the described place in the course of one year. You can in fact*

uidere in hac margine, qualiter hoc operati fuimus, scilicet quod iunximus

* see in this margin how we worked, to wit: we added *

primum numerum cum secundo, uidelicet 1 cum 2 ; et secundum cum tercio ;

* the first number to the second, that is, 1 to 2; and the second to the third;*

et tercium cum quarto ; et quartum cum quinto, et sic deinceps, donec iunximus

* and the third to the fourth; and the fourth to the fifth, and thus successively, until we reached*

decimum cum undecimo, uidelicet 144 cum 233; et habuimus suprascriptorum

* the tenth to the eleventh, that is 144 to 233, and we obtained the sum of*

cuniculorum summam, uidelicet 377 ; et sic posses facere per ordinem de

* the above mentioned rabbits, that is 377; and you could have followed this rule to treat an*

infinitis numeris mensibus.

* infinite number of months.*

*-Tony PhillipsMarch, 2013*