Selected quad for the lemma: land_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
land_n	acre_n	contain_v	perch_n	1,512	5	14.4869	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A64224	Thesaurarium mathematicae, or, The treasury of mathematicks containing variety of usefull practices in arithmetick, geometry, trigonometry, astronomy, geography, navigation and surveying ... to which is annexed a table of 10000 logarithms, log-sines, and log-tangents / by John Taylor.	Taylor, John, mathematician.	1687 (1687)	Wing T534; ESTC R23734	190,995	514

Observation taken according to the Doctrine of the last Proposition Upon your Paper draw a streight line as CD make it 5 Chains 97 100 take CB in your Compasses and strike an Obscure Arch then take BD and with that extent in D cross the former Arch in B and draw BC and BD. Then take in your Compasses BE and on B strike an Obscure Arch then take DE and also cross the former Arch in E and draw BE and ED. Lastly take the line CA and on C strike an Obscure Arch then take AB and on B intersect the former Arch in A then draw CA and AB so have you on your Paper the exact figure of the Field A B C D E as was required SECT III. Of finding the Area or superficial Content of any Field lying in any Regular or Irregular Form by reducing the Irregular Fields into Regular Forms HAving already shewed how to take the Plot of any Field divers ways by the Semicircle and Chain and also by the Protractor how to delineate the Draught thereof on Paper c. I now come to shew how the Area or superficial Content of a Field may be attained i. e. how many Acres Roods and Perches are therein contained To which end know That a Statute Pole or Perch contains 16½ Feet that 40 of those Perches in length and 4 in breadth makes an Acre So that an Acre contains 160 Perches and a Rood 40 Perches according to the Statute 33 of Edward the First Now the Original of the Mensuration of Land and all other Superficies depends on the Mensuration of certain Geometrical Figures as a Triangle Square c. which may be measured according to the directions of § 2. chap. 4 of Geometry It would therefore here be superfluous to make a repetition of things already handled I shall therefore omit it and come to shew how any Field lying in any Irregular Form may be measured by converting it into Regular Figures for it seldom happeneth but that the Plot of a Field is either a Trapezium or a many-sided Irregular Figure therefore I shall first shew how to find the Content of a Trapezium Secondly of any many sided Irregular Figure and thirdly how to reduce any number of Perches into Acres c. and on the contrary any number of Acres into Roods and Perches PROP. I. How to find the Area or superficial Content of a Trapezium Trapeziums are Quadrangles of sundry forms yet take this as a general Rule whereby their Content may be found Admit it be required to find the Area or superficial Content of the Trapezium ABCD to find which first by drawing the Diagonal AD you reduceth it into two Triangles ABD and ADC Then by prop. 3. § 1. of Chap. 4 let fall the two Perpendiculars on AD from B and C Then by prop 3. § 2 Ch. 4. find the superficial Content of the two Trianangles ABD and ADC which added together is the Content os the Trapezium by which Rule the Content of the Trapezium A B C D is found to be 630 Perches PROP. II. To find the Area or superficial Content of a many-sided Irregular Figure Admit A B C D E F G to be an Irregular many-sided Figure representing a Field whose Content is required now in regard the Field is Irregular therefore reduce it into Triangles viz. ABC ACG EDG DEG and DFG and then find the Content of all the said Triangles by prop. 3. § 2. Chap. 4 and add their Contents together so shall that Sum be the Content of the said Figure and so do for any other PROP. III. How to reduce any Number of Perches into Acres and on the contrary Acres into Perches To find how many Acres are contained in any Number of Perches given you must consider that 160 Perches do make a Statute Acre therefore if you divide the Number of Perches propounded by 160 the Quotient is the number of Acres contained therein and if there be a remainder which exceed 40 then divide it by 40 the Quotient shall be Roods and the remainder Perches But on the contrary if it were required to find how many Perches are contained in a certain Number of Acres propounded You must multiply the Number of Acres by 160 the product shall be the Perches contained therein It may be here expected that I should shew how to reduce customary Measure to statute Measure and also that I should treat of the Division and Separation of Land. But because Mr. Rathborne and of late Mr. Holwell hath sufficiently explained the same by many varieties I shall for brevity sake omit it and leave you to consult those Authors SECT IV. Of the Use of the Semicircle in taking Altitudes Distances c. PROP. I. How by the Semicircle to take an Accessible Altitude ADmit AB be the Height of a Tower which is required to be known First placing your Semicircle at D with the Arch downwards and the two sights fixed place it Horizontal and screw it fast Then move your Index till through the sights thereof you espy the top of the Tower at B and observe what degree the lower part of the Index cutteth and that will be equal unto the Angle at D 50 deg Then measure the distance DA which let be 299 Feet Now the heighth of the Tower AB is found according to prop. 1. § 2. Chap. 5. thus As Sc. V. at A 50° 00 ' To Log. cr DA 299 Feet So is S. V. at A 50 00 To Log. AB 356 3 10 Feet the height of the Tower AB required PROP. II. How by the Semicircle to take an Inaccessible Altitude at two Stations Let AB be a Tower whose height is required having placed your Instrument at E as before direct your sights unto the Top of the Tower at B and finding the Degree cut by the Index to be 23° 43 ' I say it is the Quantity of the Angle at E Now by reason of Water or such like Impediment you can approach no nearer the Base of the Tower than D Therefore measure ED which is found to be 512 Feet then at D make the like Observation and the Angle at D appeareth to be 50° 00 ' whose Complement is the Angle DBA 40° 00 ' and the Complement of the Angle E 23° 43 ' is the Angle EBA 66° 17 ' Now if the lesser Angle at B be taken out of the greater the remainder is 26° 17 ' the Angle EBD Now first to find the side BD of the Trangle EBD say according to prop. 1. § 3. chap. 5. thus As S. of V. EBD 26° 17 ' To Log. cr ED 512 Feet So is S. of V. at E 23° 43 ' To Log. cr BD 465 2 10 Feet required Now to find the Height of the Tower AB say according to prop. 2. § 2. chap. 5. thus As Radius or S. 90° To Log. cr DB 465 2 10 Feet found So is S. of V. BDA 50°