Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	foot_n	half_a	inch_n	1,859	5	11.0254	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A07574	Mesolabium architectonicum that is, a most rare, and singular instrument, for the easie, speedy, and most certaine measuring of plaines and solids by the foote: necessary to be knowne of all men whatsoeuer, who would not in this case be notably defrauded: inuented long since by Mr. Thomas Bedwell Esquire: and now published, and the vse thereof declared by Wilhelm Bedwell, his nephew, Vicar of Tottenham.	Bedwell, William, ca. 1561-1632.	1631 (1631)	STC 1796; ESTC S101421	11,621	33

c. in nere the citys of London Westminster Be it enacted by the authority afor'said That a Mile shall be taken reckoned in this manner no otherwise That is to say a Mile to containe 8 Furlongs And euery Furlong to containe 40 lugges or poales And euery Lugge or Poale to containe 〈◊〉 foot and an halfe Although this same our Rule may bee fitted for sundry other sortes of measures Yet we haue here nothing to do But with the Foote and his partes which are Ynches Halfe-ynches Quarters Half-quarters and such other sensible partes of the same 2 Things to bee measured by this Rule are magnitudes 3 A magnitude is a continuall quantity Amagnitude or a bignesse is that which hath one or more dimensions Now dimensions are in number three to weet Length Breadth and Thicknesse 4 A magnitude is of one 〈◊〉 or many 5 The measure is of the same nature with the thing to be measured 6 A magnitude of one dimension is called a Line Aline is a magnitude of length onely Or Aline is a magnitude onely long Such are wayes or distances 〈◊〉 place and place Such a magnitude sayth Proclus out of Apollonius is conceiued in the measuring of iourneys And by the difference of a lightsome place from a darksome Such are Lenghts Heighths Depths and Breadths Therfore here 7 The measure vsed is a line Here therefore there is no further skill required in the measurer then a due application of the measure giuen And therefore here in this case there is not any vse of this our Instrument CHAP. II. Of the measuring of Plaines by the foot square 1 A magnitude of many dimensions is of two or three That is called a Surface This a Solid 2 If a dimension giuen be eyther greater or lesser then any of the numbers vpon the Rular you must take some lesser or greater which is proportionall vnto it 3 A surface is a magnitude long and broad That is a surface is a magnitude which hath two dimensions to weet Length and Breadth Such magnitudes sayth Apollonius are the shadowes vpon the ground which ouerspread the fields farre and wide but do not enter into or pierce the earth Neither haue they any thicknes at all The Greek woord Epiphania is here more significant For this worde intimateth no more but The outward appearance of any thing For of a magnitude nothing is to be seene but the surface Such are bourds esteemed to be by the Carpentars Wainscotte by the Ioyners Glasse by the Glasiers Cloth both linnen Woollen by the Drapers Land Medowe Wood by the Surueighers For in the measuring of these there is only Breadth Length considered with out any respect at all had to the Thicknesse Therfore 2 Here the measure is a Surface Surfaces according to their diuerse natures are measured with diuerse and sundry kindes of measures Wood Land Medowe are measured by the Rod or Perch Cloth Painting Pauing Wainscotte by the Yard Bourd and Stone by the Foote Although this our Instrument may be fitted to all these or any other like measure Yet wee at this time intend to meddle with no other but the last to weet With the Footesquare 4 A surface is either Plaine or Vneu'n 5 A Plaine surface is a surface which lyeth equally between his bounds A surface the learned knowe is geometrically made of Lines Therfore as lines are either straight or Crooked So from hence are all surfaces Straight or Crooked Or to speak more properly Eu'n or vneu'n Plaine or Rugged Yea by a straight line are surfaces tried whether they be Eu'n or vneu'n For if a rightline applyed to a surface euery way do touch it in all places it is Eu'n Otherwise it is vneu'n 9 Plaines as wee sayd are measured by the Foote square That is the quadrate of 12 ynches A 〈◊〉 of plaine or flatte measure is the quadrate of 12 ynches or that which is equall vnto it That is it 〈◊〉 44 〈◊〉 Ynches For 12 times 12 are 144. Hauing therefore a plaine giuen of 12 ynches broad there is no question but 12 ynches of that breadth shall make a Foote But if the breadth giuen be greater or lesse then 12 there is a question What length with the breadth giuen shall make a plaine 〈◊〉 to the square 144. Here 7 Of the two lines ' giuen the one is the breadth assigned the other is alwayes the beuelling line 12. Here againe it must bee remembred That onely those plaines are to be measured which are Rightangled parallelogramms Or to speake in their owne Language which are comprehended of a Base and Heigh which are rationall betweene 〈◊〉 Ramus 9 e IIII. Those plains therfore which are not such must bee reduced vnto these kinde of figures 1 An example or two shall make all plaine A bourd of 16 ynches broad and 18 ynches long And so a stocke of 13 bourds is to be measured Here I finde 16 the line answering to the Bredth to 〈◊〉 the beueller 12 at 9 ynches from the fore-end of the Rular Therefore I say euery 9 ynches of that length shall make a Foot of bourd Or which is all one shall be 〈◊〉 to 144 the square of 12 ynches Now 9 ynches I finde to bee contained in 18 foote the Length 24 times Therefore I say The bourd assigned doth containe 14 foote of bourd Lastly there being in the stocke 13 such bourds I say the whole stocke doth contayne 312 foot of bourd II A Table of 36 ynches broad and 28 foote long is to be measured Here 36 is greater then any of the parallels found vpon the Rular Therefore by the 2 e of this I take ●8 the halfe of it which I finde to meete with 22 the beuelling line 〈◊〉 8 ynches from the for'end of the Rular Therefore euery 8 ynches of length of the bredth 18 shall contayne a roote of bourd But the breadth giuen is 36 ynches That is twice 18 Therefore euery 8 ynches in length of that Table shall be 2 foote of bourd Now againe I finde 8 ynches in 28 foote 42 times Therefore the Table containeth twice so many foot That is 84 foote of bourd III A pane of Glasse 7 ynches broad is to bee measured Here 7 is lesser then any of the parallels Therefore by the 2 e of this I take 14 the double thereof Which I obserue to meete with 12 at 10 ynches and 2 seauenth parts of an ynch from the fore-fore-end Therefore euery 10 ynches and 2 seauenth partes of an ynch of 14 ynches breadth shall bee a foote of Glasse But the breadth giuen is but 7 ynches Therefore euery 10 ynches and 2 seauenth partes of an ynch shall be but halfe a foote of glasse Of the measuring of Triangles and all other Rightlined plaines 8 A triangle is nothing else but the halfe of a quadrangle or parallelogramme And if it haue one right angle it is the halfe of a rightangled parallelgramme Therefore 9

solid measure III A rightangled Prisma both whose sids 〈◊〉 I meane conteyning the rightangle are 18 ynches 〈◊〉 the whole being in length 16 foot is to be 〈◊〉 〈◊〉 vnderstand that as before was shewed as a Triangle was but the halfe of a quadrangle So a Prisma is nought but the halfe of a Parallelepipedum sawne longways from 〈◊〉 to corner though the midd'st And hence in 〈◊〉 it hath the name This knowne I enter with the numbers giu'n and I finde 18 to meet with 18 at 5 ynches and one third parte of an ynche from the oft named end of the Rular Therefore I say That 〈◊〉 5 ynches and 〈◊〉 third parte of an ynche in length of that sticke shall be but halfe a foote of solid measure Nowe because 5 ynches and 1 third of an ynche is conteined in 16 foote 67 tymes and 14 sixteen partes that is almost 68 times The fore I say The 〈◊〉 giu'n doth conteine 〈◊〉 68 halfe foot 's or 34 foote of 〈◊〉 measure IIII A sispaned solid all whole sides are 6 ynches broad a 〈◊〉 and 16 foote long is to bee measured Here the two lines giuen are as aboue was taught the Plumblin from the center vnto the middest of any one of the sides And the halfe of the compasse That as before was taught is 5 ynches and 2 〈◊〉 partes of an ynche This is as you see 18. Now 5 and 2 eleu'nths doth meet with 18 at 19 ynches and 〈◊〉 fifth parte of an inche from the fore-fore-end Therfore I say That euery 19 〈◊〉 and one 〈◊〉 parte of an ynch shall be a 〈◊〉 of solid measure Lastly because 16 ynches and 1 fifth parte is 〈◊〉 in 16 foot 10 times and 2 fifteene pates I say that the tymber sticke giu'n doth containe 10 foot of solid measure and some small quantity more Lastly a Round columne or Cylinder of 44 ynches about 12 foote long is to be measured Here according to that aboue taught the two lines giu'n are The half diameter the halfe circumference This is 22 That 7. Now these two do meete vpon the Rular at 11 ynches and 17 seauenty two partes of an ynch from the fore-fore-end there of Therefore the sticke containeth about 13 foot of tymber or solid measure FINIS AN APPENDIX TO THE MESOLABIVM TWo things for the further illustration of the Instrument wee haue thought good here to annex vnto the former The one is a collation of this manner of measuring with 〈◊〉 commonly taught and practised 〈◊〉 is of the Measuring of Land by the 〈◊〉 A foot of solid measure as all doe generally 〈◊〉 Cube of 12 ynches that is a square or 〈◊〉 〈◊〉 all whose dimensions to wit Thicknesse Breadth and Length are equall And the content in numbers is found by a continuall 〈◊〉 of 12 12 and 12 thus 12 〈◊〉 12 are 〈◊〉 and 12 times 〈◊〉 are 〈◊〉 Therefore a foot of solid measure doth conteine 1728 seuerall cubes of an 〈◊〉 thicknesse breadth and height This is 〈◊〉 it were the standard whereby this kinde of measuring is to be examined All artificers generally do measure by a Table of square numbers And therefore if the body giuen to be measured be square that is if the thicknesse and breadth bee 〈◊〉 they 〈◊〉 giue the iust content But where these two dimensions doe differ there by their rules they doe it not without some error For to bring it to the vse of their Table they must first make the thicknesse and breadth equall which they doe by taking the excesse from the greater and adding of it to the lesser or which is all one by girding of the body about and by taking of the quarter of the compasse An example or two will make all plaine Suppose a body giuen to bee measured were 10 ynches thick and 14 broad Here they take 2 from 14 and adde it vnto 10 and so doe make all the sides equall Or by girding of it they finde the compasse to be 48. And the quarter of 48 to be 12. And their table for the square of 12 ynches doth giue 12 ynches for the length required to make a foot of solid measure If this be 〈◊〉 then 10 14 and 12 continually multiplyed between themselues shall be equal to 12 12 12 continually multiplyed between themselues But 10 14 and 12 doe giue for the product 1680. And 12 12 and 12 as in former wee saw gaue 1728. 〈◊〉 the difference betweene 〈◊〉 and 1680 is 48. Therefore the losse in euery foot of 〈◊〉 body by their measure is 48 inches 〈◊〉 vpon our Rular you see 14 the parallell to meet 〈◊〉 〈◊〉 beuelling line at 12 inches and 12 35 of an inch 〈◊〉 end of the Rular And by multiplication you 〈◊〉 10 14 and 12 12 35 doe make 1728 Therefore our 〈◊〉 is true If the body giuen be 8 inches thicke and 16 broad they likewise take 4 from 16 and doe adde it vnto 8 and so as afore doe 〈◊〉 it to be equall to 12 inches square Which if it be true then the product of 8 16 and 12 shall bee equall to the product of 12 12 and 12. But the product by the continuall multiplication of 8 16 and 12 is but 1536 And the product of 12 12 and 12 is 1728 and the difference betweene 1728 and 1536 is 192 Therefore by that their measure there is lost in euery foot 192 inches Now vpon the 〈◊〉 we finde 8 and 16 to crosse one another at 13 ½ And 8 16 and 13 ½ continually multiplied one by another doe giue the product 1728 Therefore this kinde of measuring by the Rular is exact If it were 6 inches thick 18 inches broad by the same reason euery 12 inches in length should make a foot of solid measure For the summe of all the sides added together is 48 And the quarter of 48 is 12 And their Table for the square of 12 doth assigne 12 inches for the length 〈◊〉 6 18 and 12 multiplied continually doe make but 1296 which differeth from 1728 by 432. Therefore by this their measure in euery foot of solid measure there is lost 432 solid inches That is iust one quarter of a foot Vpon this our instrument 6 and 18 are obserued to meet at 16 inches from the said fore end and therefore it alloweth for a foot 16 in length And 6 18 and 16 continually multiplied doe make 〈◊〉 therefore our rule is true Of the measuring of Plaines or Land Meddows and Woods by the Aker ALthough this instrument as the title specifieth bee fitted only for the measuring of Plains and 〈◊〉 by the foot Yet as before is mentioned it may easily bee applyed to other like sort of measuring Now among others there being none of more frequent 〈◊〉 amongst vs then the Rod or Perch for the measuring of Land Meddow and Wood by the Aker And this being either not easie to be done by the vnlearned or not speedily to be performed by any I haue thought it not

It is to bee measured as the Rightangled-parallelogramme onely conceiue that the number found shall bee the double of that which is sought Here therefore it must bee conceiued That of the two sides encluding the Rightangle the one is to be vnderstood to be the Breadth the other the Length I Suppose a Rightangled-triangle whose sides including the Right-angle are 18 and 24 are to bee measured Here I take 18 for the Heighth or Breadth of the parallelogramme which also I finde to meete with the beuelling line 12 precisly at 6 ynches from the fore end of the Ruler Againe 6 the sayd line found I finde iust 4 times in 24 the Lenghth giuen Therfore I auerre the Triangle giuen to conteine the halfe of 4 foote that is 2 foote of bourd 20 If the triangle giuen bee not right-angled then is it by a perpendicular let fall within the triangle from one of the corners vnto the base to bee reduced vnto two rightangled triangles How this is to be done Euclide teacheth at the 11 12 propositions of his I booke And P. Ramus at the 9 10 elements of his V. booke of Geometry It is also to bee done by the squire Or by a triangled leuell and otherwise II An Obtuseangled triangle whose three sides are 25 40 and 42 is to bee measured Heere by one of those aboue named wayes I finde the perpendicular or plumbline falling from the greater corner vnto the opposite line to be ●8 And 24 I finde vpon the Ruler to meete with the line of 12 at 6 ynches from the fore-end of the same Againe 6 I find in 42 seauen times Therefore the Triangle giuen doth conteine halfe so many foote That is 3 foote and an halfe of bourd 11 From hence it is manifest how any Rhombus Rhomboides Trapezium or irregular rightlined multangles are to bee measured To weet that they are to be measured by parts or by the particular triangles which euery such figure doth contayne Examples you may haue in the XIIII booke of Ramus's Geometry or in any others which haue written of Geometry Of the measuring of any ordinate multangle figured 12 Ordinate multangled plaines are measured by their halfe Perimeter and the plumbline from the center vnto the middest of any one side These sortes of plaines may bee measured as the former were by diuiding them into their seuerall Triangles But this last is farre shorter And therefore to bee embraced rather to be vsed in practise Here the halfe of the perimeter or bout-line 〈◊〉 to the Length in a 〈◊〉 〈◊〉 And the plumbline here is in stead of the Heighth or Breadth there 1 An 〈◊〉 Pentangle whose sides are 24 ynches a piece And the 〈◊〉 from the center to the middest of any one of the sides 16 is to be measured Here 10 the Plumbline or Heighth doth vpon the Rular meet with the 〈◊〉 line 12 at 9 ynches from the oft named end And 9 is contayned in 60 the halfe of the perimeter 6 times and two thirds Therefore the Pentangle giuen conteineth 6 foot and two third partes of a foot of Bourd II A Sexangled ordinate figure whose sides are 12 ynches broad a piece is to bee measured Here the Plumbline from the center to the middest of any one side is 10 ynches and 8 one and twentyths of an ynch The double of 10 that is 20. and 〈◊〉 one twenty parts of one ynche I obserue to meete with the beueller 12 about 7 ynches one quarter of an ynch from the fore end of the Rular Which 7 and a quarter is contained in 44 six time and two twenty nineth partes Therfore I say the Sexangled figure giuen doth containe 6 foote of bourd and some small quantity more The Circle or Circular forme is in like manner measured For 13 The Circle is measured by the Ray and the halfe of the perimeter For savth the Geometrician Planus è radio peripheriae 〈◊〉 est area 〈◊〉 The plaine of the ray and halfe of the circumference is the content of the circle A Round table whose diameter is 4 foote and 8 ynches or 56 ynches is to be measured The halfe of 59 is 28 And the halfe of the circumference is 88. Now ●8 being geater then any of the 〈◊〉 I take 14 the half therof Wh ch I find to meet with the beuelling line 12 at 10 ynches and a quarter from the for'end of the Rular Therfore I say euery 10 ynches and a quarter of an ynche of that Table shall be 2 foot of bourd And because 88 doth containe 10 and 1 quarter 8 times and 20 fourty ones Therefore I say the whole doth containe 16 foot of of bourd and 144 ynches CHAP. III. Of the measuring of Bodies or Solids by the Foot 1 A Body is a magnitude of three dimensions A Body or Solid is a magnitude which hath Length Breadth and Thicknes 2 Here the measure is also a body to weet the Cube of 12 that is 1728. This is our opinion Yet if any shall thinke it a paradox or shall gaine say it or mainetaine the contrary wee will not contend And 3 Of the three dimensions two are giuen the third is sought 4 Bodies are of diverse sorts But we will at this time meddle only with such as are comprehended of parallelogrammes or with Cylinders True it is that this our instrument may bee fitted and applyed to the measuring of many other sorts of Solid bodies But because we see no great vse of it in the measuring of any other then of these two sorts Therefore wee will declare the vse of it in the measuring of these two onely Of these the first is the Parallelepipedum which is a plaine Solid whose opposite sides are parallelogramme I A rightangled parallelepipedum or a squared 〈◊〉 logge of 12 Ynches 〈◊〉 18 broad and 16 foote long is to be measured Here the 〈◊〉 and Breadth are giuen The Length is sought These I finde vpon the Rular to meet at 8 ynches from the 〈◊〉 named fore-fore-end Therfore I Say Euery 8 ynches of that Logge in 〈◊〉 shall make a 〈◊〉 〈◊〉 of tymber And because I finde 8 Ynches in 16 foote 24 times Therfore I say in the Tymbersticke giuen there is 24 foote of solid measure II A squared stone of 14 Ynches thicke fiue 〈◊〉 or 60 ynches broad and 10 foote long is to be measured Here 60 is greater then any of the parallels vpon the Rular Therfore I take 12 the 5 th part of it And I obserue 12 and 14 to meete at 10 ynches and 2 seaunth partes of an ynche from the fore-Fore-end of the Rular Therfore I say That euery 10 ynches and 2 seaunth partes of an ynch in length of that stone shall be 5 foote of solid measure And because that 10 foote conteineth 10 ynches and 2 seaunth parts of an 〈◊〉 11 times and 5 seau'nty twoos Therfore I say the whole stone conteineth 58 foote and one third parte of a Foote of

amisse for the further declaratiō of the vse excellency of this inuention and for the benefit of others to adde vnto the former something of this also An Aker of Land is as before we heard an oblong parallelogramme whose breadth is 4 Poles and length 40. Therefore an Aker conteineth 160 square Rods of what figure or forme soeuer it be For 4 times 40 are 160. This here in this case is as 144 was in Board and 1728 was in solid measure as it were the Standard whereby this kinde of measure is to be examined Land Meddow or Wood is to bee measured by this instrument in all respects as Board or Glasse was measured Only two things are here first to be knowne The first is That as there the beuelling line of 12 was alwayes giuen for the breadth as appropriate to that kinde of measure So here another peculiar to this manner of measure is in like sort to bee drawne ouerth wart the parallell lines from 6 〈◊〉 of an inch from the fore-fore-end of the Rular in the parallell 24 vnto 13 and ⅓ in the parallell 12. The second is That 〈◊〉 there lines and spaces did answer and were denominated of inches and parts of inches so here the same lines and spaces must bee supposed to signifie Rods and Perches and parts of the same An example or two will make all plaine and manifest 1 Suppose a right angled square field of 16 Pole broad and 30 in length were to be measured Here I finde 16 to meet with the line of Land measure at 10 inches from the fore end of the Rular Therefore I say that euery 10 rod in length of the breadth of 16 rods shall make an 〈◊〉 of Land And againe because the said 10 is found in 30 the length giuen 3 times Therefore I say the field assigned doth conteine 3 Akers 2 A square Meddow right-angled of 40 Poses in breadth and 60 in length 〈◊〉 to be measured Here 40 the lesser number of the two giuen is greater then any vpon the Rular Theresore I take 20 the halfe of 40 And I finde 20 to meet with the line of land measure at 8 inches from the said fore-end of the Rular Therefore 〈◊〉 I say That euery 7 Pole in length of the breadth of 40 Pole shall 〈◊〉 2 Akers of Meddow Againe because 8 is conteined in 60 seuen times and ½ therefore I auerre that the Meddow assigned to bee measured doth conteine 15 akers 3 Admit that a Wood to bee measured were 160 rods square that is that euery side of the same were 160 Poles in length Here 160 is farre greater then any number vpon the Rular Therefore I take 16 the tenth part of 160 which I 〈◊〉 to crosse the line of land measure at 10 inches from the fore end of the Rular wherefore first I affirme that euery 10 pole of the breadth of 160 pole shall conteine 10 Akers of Wood Againe because 160 doth 10 sixteene times I say that the Wood doth conteine 160 Akers Or which is all one that euery Pole in breadth of that length doth conteine an Aker But some man may obiect and say this is not a matter worth the learning or of so many words seeing that it is well knowne that there are many men wholly vnlearned yea and some of no extraordinary parts of capacity or vnderstanding which can measure Land Meddow or Woods so that they be square or of any ordinary forme I confesse I haue knowne diuers such And yet is not this our labour in 〈◊〉 or altogether vnprofitable For first what they doe with much study or contention of minde and are long in doing of it we teach to doe with great facility and speed For they although the field be a rightangled parallelogramme must first measure at the least two sides comprehending one or other of the rightangles And then multiply these two sides the one by the other And lastly the product found they must diuide by 160 And so by the quotient now found answer the question propounded We saue a great deale of this labour For we only measure the breadth of the field then wee seeke vpon the Rular how much in length of this breadth doth make an Aker Lastly we apply this last number found vnto the whole length and so witho ut either multiplication or diuision doe speedily answere the demand Another thing there is wherein this inuention doth goe farre beyond the reach of the vnlearned which is thus These 〈◊〉 can sooner measure and cast vp the whole content of the field then they can set you 〈◊〉 one two or three Akers of the same Here it is all one to giue the content of the whole or any part or parts of the same And that which to those is most hard here to vs is most easie I meane to set out any one or more Akers of the 〈◊〉 and that on which side or end of the field you shall thinke good