Selected quad for the lemma: book_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
book_n	even_a	number_n	odd_a	1,722	5	15.7359	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A14226	The elements of arithmeticke most methodically deliuered. Written in Latine by C. Vrstitius professor of the mathematickes in the Vniuersitie of Basill. And translated by Thomas Hood, Doctor in Physicke, and well-willer of them which delight in the mathematicall sciences; Elementa arithmeticae. English	Wurstisen, Christian, 1544-1588.; Hood, Thomas, fl. 1582-1598.	1596 (1596)	STC 24540; ESTC S111477	81,241	217

if you shold seeke how often 2 were in 21 you can not take it tenne times but 9 times but 9 times at the most Moreouer the nature of the thing requireth that we find out alwayes such a quotient as being multiplied by the Diuisor maketh no greater a number then the diuidend is See the examples following An abridgement of diuision If the Diuisor end in cyphers the worke may be wrought by the signifying figures alone setting the cyphers in the meane time vnder the vtmost figures of the diuidend next to the right hand But if the last figure of the Diuisor be an vnitie and the rest cyphers then setting the Diuisor as before and taking the figures that haue no cyuphers vnderneath them for the quotient the diuision is dispatched the figures that remaine after the diuision is done must be set downe as the partes are with the diuisor vnderneath them for their denominator As for example diuide 165968 by 360. Item 6734 by 100 the example shall stand thus CHAP. VI. Of the double diuision of numbers Numbers by diuision are distinguished 2. manner of wayes First they are either Odde Or Euen which may be diuided either One way only and are either Euenly euen Or Oddely euen Many wayes and are both euenly and oddely euen Secondly as they be cōsidered either By thēselues alone and then they are Prime or Compound One with an other and then also they are Prime or Compound NVmbers are diuided two manner of wayes first into euen and odde numbers An euen number is that which may be diuided by 2. An odde number is that vvhich can not be diuided by 2. This is the 6 7 definition of the seuenth booke of Euclide whence this difference of numbers drawen out of their diuision is taken as that also which followeth whose vse in Arithmeticke is very great Euen numbers are as these following 2. 4. 6. 8. 10. 12. 14. and so forth after the same order alwaies omitting one Odde numbers are as 3. 5. 7. 9. 11. 13. 15. c. Of euen numbers some may be diuided but one way onely other some may be diuided many waies Those which may be diuided but one way onely are euenly euen or oddely euen A number euenly euen is that vvhich an euen number diuideth by an euen number This is the eight definition of the seuenth such are 4. 8. 16. 32. 64. c. that is to say all the numbers from 2 vpward doubled by 2. As appeareth by the 32 prop. of the 9 booke A number odly euen is that vvhich an odde number measureth by an euen number As it is in the 9 definition of the seuenth booke Euclide calleth it an euenly odde nūber as 6. 10. 14. 18. 22. For 3 an odde number diuideth 6 by 2 an euen nūber 5 an odde nūder diuideth 10. by 2 an euen nūber Such are all the numbers whose moytie or halfe is an odde number as appeareth by the 33 prop. of the seuenth booke The numbers vvhich may be diuided manie vvayes are euenly euen and odde which may be diuided both by an euen number and by an odde into an euen number This third kind of numbers is let passe of Euclide among the definitions of the seuenth booke but yet not neglected in the propositions of the ninth booke The examples therof are these 12. 20. 24. 28. 56. 144. As 2 an euen number diuideth 12 by 6 an euen number and 3 an odde number diuideth it by 4 an euen number Item 2 an euen number diuideth 20 into 10 an euen number and 5 an odde number diuideth it into 4 an euē number Such are all those numbers which are neither doubled by two from 2 vpward nor haue their halfe an odde number as it is in the 34. prop. of the 9 booke Againe numbers be distinguished otherwaies being considered both by themselues and one with another Being considered by themselues they are eyther prime vvhich may be diuided by an vnitie onely or compound vvhich may be diuided by some other number This is the 12 and 13 definition of the seuenth booke where Euclide diuideth numbers into prime compound numbers The matter of this diuision is taken out of the 34 prop of the seuenth booke which sayth That euery number is eyther a prime number or else diuided by a prime number that is a compound number as appeareth by the 33 prop. of the same booke A prime number is that which no other number diuideth besides an vnitie sauing that it measureth it selfe It may be called an vncompound number for that it is made of no number as 2. 3. 5. 7. 11. 13. c. A compound number is that which some other number maketh being taken certaine times as 4. 6. 10. 12. Of this sort are first of all all euen numbers then all those odde numbers which in the eleuenth definition of the seuenth booke are called oddely odde which may be diuided by an odde number into an odde number as 9. 15. 21. 25. 27. c. Numbers compared one with an other some are Prime in respect one of an other vvhich can not commonly be diuided by any other number but by an vnitie Other some are compound in respect one of an other vvhich may be commonly diuided by one or moe numbers This difference of numbers compared togeather is drawen out of the former and is set downe in the twelfth and eleuenth definition of the seuenth booke Numbers prime in respect one of another haue no common diuisor beside an vnitie which measureth all numbers As 3 and 8 6 and 7 5 and 12. Therefore when the numbers giuen are prime one to an other there can no lesse numbers be giuen in the same proportions So that prime numbers are the least and the least are prime numbers as appeareth in the twentie and twentie foure proposition of the seuenth booke And therefore when the numbers giuen are prime they are also the termes of the proportion giuen as we shall see afterward Compound numbers in respect one of an other may commonly be diuided by one or many numbers as 3 and 9 9 and 15 for 3 is the common Diuisor of them both Item 12 18 24 may be commonly diuided not onely by 6 but also by 3 and 2. If you vvould knowe vvhether the numbers giuen be prime or compounde one to an other you may doe it by the Theoreme following Two vnequall numbers being giuen if in subducting the lesse from the greater as often as may be the remainder diuideth not that which went before it vntill it come to an vnitie the numbers giuen are prime one to an other 1. prop. 7. As in 4 and 11 18 and 7 35 and 12 in subducting the one from the other continually you shall come to an vnitie wherefore I say that they be prime in respect one of an other And hereby we may easily conclude if after the continuall subducting of the one from the other we come not downe to an vnitie but meete with