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
A64223	The semicircle on a sector in two books. Containing the description of a general and portable instrument; whereby most problems (reducible to instrumental practice) in astronomy, trigonometry, arithmetick, geometry, geography, topography, navigation, dyalling, &c. are speedily and exactly resolved. By J. T.	Taylor, John, 1666 or 7-1687.	1667 (1667)	Wing T533B; ESTC R221720	52,688	153

in length makes a Foot As the square in feet and inches on the right is to one foot on the left so is the point Sq. on the right to the number of feet and inches on the left for a foot square of Timber At 18 inches square 5 inches ¼ and almost half a quarter in length makes a foot When your Timber if it be proper to call such pieces by that name is under 3 inches square account the figured divisions on the right line from the letters Sq. to the end for inches and each sub-division twelve parts of an inch So that every three of them makes a quarter of an inch Then the proportion is as the inches and quarters square on the right is to 100 on the left so is the point 12 'twixt D and T D on the right to the number of feet in length on the left to make a foot of Timber As 2 inches ½ square you must have 23 foot 6 inches and somewhat better for the length of a foot of Timber PROBL. 3. The square and length of a plece of Timber given to finde the content As the point Sq. on the right is to the length in feet and inches on the left so is the square in feet and inches on the right to the content in feet on the left At 30 foot in length and 15 inches square you have 46 foot ½ of Timber At 20 foot in length and 11 inches square you have 16 foot and almost ¼ of Timber When you have a great piece of Timber exceeding 100 foot which you may easily see by the excursion upon the rule then take the true square and half the length sinde the content thereof by the former proportion and doubling that content you have the whole content PROBL. 4. The Circumference or girth of a round piece of Timber being given together with the length to finde the content As the point R. on the right is to the length in feet and inches on the left so is the circumference in feet and inches on the right to the content in feet on the left At 20 foot in length and 7 foot in girth you have 60 foot of Timber for the content This is after the common allowance for the waste in squaring and although some are pleased to quarrel with the allowancer as wronging the seller and giving the quantity less than in truth it is yet I presume when they buy it themselves they scarcely judge those Chips worth the hewing and have as low thoughts of the over-plus as others have of that their admonition If it be a Cylinder that you would take exact content of then say As the point T R on the right is to the length on the left so is the girt on the right to the exact content on the left At 15 foot in length and 7 foot in girt you have 59 foot of solid measure The Diameter of any Cylinder given you may by the same proportion finde the content placing the point D instead of R in the proportion for the usual allowance and the point T D for the exact compute PROBL. 5. To measure tapered Timber Take the square or girt at both ends and note the sum and difference of them Then for round Timber as the point R. on the right is to the length on the left so is half the sum of the girt at both ends on the right to a number of feet on the left Keep this number and say again As the point R. on the right is to the third part of the former length on the left so is half the difference of the girts on the right to a number of feet on the left which number added to the former gives the true content The same way you may use for square Timber only setting the feet and inches square instead of the girt and the point Sq. instead of the point R. At 30 foot in length 7 foot at one end and 5 at the other in girt half the sum of the girts is 6 foot or 72 inches the first number of feet found 67 half the difference of the girts is 1 foot or 12 inches the third part of the length 10 foot then the second number found will be 7 foot one quarter and half a quarter The sum of both or true content 74 foot one quarter and half a quarter For standing Timber take the girt about a yard from the bottom and at 5 foot from the bottom by Chap. 7 set down these two diameters without the bark and likewise the difference 'twixt them Again by Chap. 6. Probl. 4. finde the altitude of the tree so far as it bears Timber or as we commonly phrase it to the collar this done you may very near proportion the girt at the collar and content of the tree before it falls In case any make choice of the hollow contrivance mentioned Chap. 1. they need no compasses in the mensuration of any solid provided the lines for solid measure and gauging vessels be doubly impressed only in a reverted order one pair of lines proceeding from the head toward the end and the other pair from the end toward the head upon the sliding cover and its adjacent ledges This done the method of performing any of the Problems mentioned in this Chapter is easie For whereas you are before directed to extend the Compasses from the first term to the second and with that distance setting one point in the third term the other point gave the fourth or term sought So here observing the lines as before slide the cover until the first term stand directly against the second then looking for the third on its proper line it stands exactly against the fourth term or term sought on the other line Only note that when the second term is greater than the first it s performed by that pair of lines proceeding from the head toward the end But when the first term is greater than the second it is resolved by that pair of lines which is numbred from the end toward the head CHAP. X. The Gauge Vessels either for Wine or Ale Measure PROBL. 1 The Diameter at Head and Diameter at Boung given in Inches and tenth parts of an Inch to finde the mean Diameter in like measure TAke the difference in inches and tenth parts of an inch between the two diameters Then say by the line of numbers As 1 is to 7 so is the difference to a fourth number of inches and tenth parts of an inch This added to the Diameter at head gives the mean Diameter Ex. gr At 27 inches the boung and 19 inches two tenths at the head the difference is 7 inches 8 tenths The fourth number found by the proportion will be 5 inches 4 tenths and one half which added to the diameter at the head gives 24 inches 6 tenths and one half tenth of an inch for the mean diameter PROBL. 2. The length of the Vessel and the mean Diameter given in Inches and tenth parts of

runs thus As the co-tangent of the latitude is to the tangent of the Suns declination so is the radius to the sine of ascensional difference Then by the third variety you may make another Problem viz. As the radius is to the co-tangent of the latitude so is the sine of the Suns ascensional difference to the sine of his declination Again by the fourth variety you may make a third Problem thus As the sine of the Suns ascensional difference is to the tangent of the Suns declination so is the radius to the co-tangent of the latitude By this Artifice many have stuffed their Books with bundles of Problems CHAP. VII Some uses of the Lines of Circumference Diameter Square Equal and Square Inscribed ALL these are lines of equal parts bearing such proportion to each other as the things signified by their names Their use is this Any one of them given in inches or feet c. to finde how much any of the other three are in the same measure Suppose I have the circumference of a Circle Tree or Cylinder given in inches I take the same number of parts as the Circle is inches from the line of circumference and applying that distance to the respective lines I have immediately the square equal square inscribed and diameter in inches and the like if any of those were given to finde the circumference This needs no example The conveniency of this line any one may experiment in standing timber for taking the girth or circumference with a line finde the diameter from that diameter abate twice the thickness of the bark and you have the true diameter when it s barked and by Chap. 9. Probl. 5. you will guess very near at the quantity of timber in any standing Tree CHAP. VIII To measure any kinde of Superficies as Board Glass Pavement Walnscot Hangings Walling Slating or Tyling by the line of Numbers on the outward ledge THe way of accounting any number upon or working proportions by the line of numbers is sufficiently shewn already Chap. 6. which I shall not here repeat only propose the proportions for these Problems and refer you to those directions PROBL. 1. The breadth of a Board given in inches to finde how many inches in length make a foot at that breadth say As the breadth in inches is to 12 so is 12 to the length in inches for a foot at that breadth Ex. gr At 8 inches breadth you must have 18 inches in length for a foot PROBL. 2. The breadth and length of a Board given to finde the content As 12 is to the length in feet and inches so is the breadth in inches to the content in feet Ex. gr at 15 inches breadth and 20 foot length you have 25 foot of Board PROBL. 3. A speedy way to measure any quantity of Board The two former Problems are sufficient to measure small parcels of Board When you have occasion to measure greater quantities as 100 foot or more lay all the boards of one length together and when the length of the boards exceeds 12 foot use this proportion As the length in feet and inches is to 12 so is 100 to the breadth in inches for an 100 foot Ex. gr At 30 foot in length 40 inches in breadth make an 100 foot of board reckoning five score to the hundred This found with a rule or line measure 40 inches at both ends in breadth and you have 100 foot When one end is broader than another you may take the breadth of the over-plus of 100 foot at both ends and taking half that sum for the true breadth of the over-plus by Probl. 2. finde the content thereof When your boards are under 12 foot in length say As the length in feet and inches is to 12 so is 50 unto the breadth in inches for 50 foot of board and then you need only double that breadth to measure 100 foot as before In like manner you may measure two three four five a hundred c. foot of board speedily as your occasion requires PROBL. 4. To measure Wainscot Hangings Plaister c. These are usually computed by the yard and then the proportion is As nine to the length in feet and inches so is the breadth or depth in feet and inches to the content in yards Ex. gr At 18 foot in length and two foot in breadth you have four yards PROBL. 5. To measure Masons or Slaters Work as Walling Tyling c. The common account of these is by the rood which is eighteen foot square that is 324 square foot in one rood and then the proportion is As 324 to the length in feet so is the breadth in feet to the content in roods Ex. gr At 30 foot in length and 15 foot in breadth you have 1 rood 3 10 and better or one rood 126 124 parts of a rood CHAP. IX The mensuration of Solids as Timber Stone c. by the lines on the proportional side of the loose piece THese two lines meeting upon one line in the midst betwixt them for distinction sake I call one the right the other the left line which are known by the hand they stand toward when you hold up the piece in the right way to read the Figures The right line hath two figured partitions The first partition is from 3 at the beginning to the letters Sq. every figured division representing an inch and each subdivision quarters of an inch The next partition is from the letters Sq. unto 12 at the end every figured division signifying a foot and each sub-division the inches in a foot The letters T R and T D are for the circumference and Diameter in the next measuring of Cylinders The letters R and D. for the measuring of Timber according to the vulgar allowance when the fourth part of the girt is taken c. The letters A and W are the gauger points for Ale and Wine Measures Lastly the figures 12 'twixt D and T D. are for an use expressed Probl. 2. The left line also hath two figured partitions proceeding first from 1 at the beginning to one foot or 12 inches each whereof is sub-divided into quarters From thence again to 100 each whereof to 10 foot is sub-divided into inches c. and every foot is figured But from 10 foot to 100 only every tenth foot is figured the sub-divisions representing feet The method of working proportions by these lines only observing the sides is the same as by the line of Numbers viz. extending from the first to the second c. PROBL. 1. To reduce Timber of unequal breadth and depth to a true Square As the breadth on the left is to the breadth on the right so is the depth on the left to the square on the right line At 7 inches breadth and 18 inches depth you have 11 inches ¼ and better for the true square PROBL. 2. The square of a Piece of Timber given in Inches or Feet and Inches to finde how much