Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	limit_n	line_n	superficies_n	1,239	5	15.5004	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A48331	The compleat surveyor containing the whole art of surveying of land by the plain table, theodolite, circumferentor, and peractor ... : together with the taking of all manner of heights and distances, either by William Leybourn.	Leybourn, William, 1626-1716.	1653 (1653)	Wing L1907; ESTC R20856	115,157	173

To reduce Acres into Perches and the contrary 248. 19. The use of a Scale of Reduction necessary for finding the Fraction parts of an Acre 250 20. Divers compendious rules for the ready casting up of any plain Superficies with divers other Compendiums in Surveying by the line of Numbers 251. 21. Of Satute and Customary measure to reduce one to the other at pleasure 254. 22. Of the laying out of common fields into furlongs 255. 23. Of Hils and Mountains how to finde the lengths of the horizontall lines on which they stand severall wayes 257 24. Of mountanous and uneven grounds how to protract or lay the same down in plano after the best manner giving the area or content thereof 258. 25. How to take the Plot of a whole Manner by the Plain Table three severall ways 260. Circumferentor 266. or Peractor 266. With the keeping an account in your Field-book after the best and most certain manner 270. and to protract any observations so taken 271. 26. Of inlarging or diminishing of Plots according to any possible proportion by Two Semicircles Mr. Rathborns Ruler A Line into 100 parts The Parallelogram 273. 27 Of conveying of water 276. FOrasmuch as the whole Art of Surveying of Land is performed by Instruments of severall kindes and that the exact and carefull making and dividing of all such Instruments is chiefely to be aimed at I thought good to intimate to such as are desirous to practise this Art and do not readily know where to be furnished with necessary Instruments for the performance thereof that all or any of the Instruments used or mentioned in this Book or any Mathematicall Instrument whatsoever is exactly made by Mr. Anthony Thompson in Hosier lane neer Smithfield London THE COMPLEAT SURVEYOR The First Book THE ARGVMENT THis first Book consisteth of divers Definitions Problemes Geometricall extracted out of the Writings of divers ancient and modern Geometricians as Euclid Ramus Clavius c. and are here so methodically disposed that any man may gradually proceed from Probleme to Probleme without interruption or being referred to any other Author for the Practicall performance of any of them Onely the Demonstration is wholly omitted partly because those Books out of which they were extracted are very large in that particular and also for the avoiding of many other Propositions and Theoremes which had the ensuing Problemes been demonstrated must of necessity have been inserted Also the figures would have been so incumbred with multiplicity of lines that the intended Problemes would have been thereby much darkened And besides it was not my intent in this place to make an absolute or entire Treatise of Geometry and therefore I have onely made choice of such Problems as I conceived most usefull for my present purpose and come most in use in the practice of Surveying and ought of necessity to be known by every man that intendeth to exercise himselfe in the Practice thereof and those are chiefly such as concern the reducing of Plots from one forme to another and to inlarge or diminish them according to any assigned Proportion also divers of the Problemes in this Book will abundantly help the Surveyor in the division and seperation of Land and in the laying out of any assigned quantity whereby large parcels may be readily divided into divers severals and those again sub-divided if need be Also for the better satisfaction of the Reader I have performed divers of the following Problemes both Arithmetically and Geometrically GEOMETRICALL DEFINITIONS 1. A Point is that which cannot be divided A Point or Signe is that which is void of all Magnitude and is the least thing that by minde and understanding can be imagined and conceived than which there can be nothing lesse as the Point or Prick noted with the letter A which is neither quantity nor part of quantity but only the terms or ends of quantity and herein a Point in Geometry differeth from Unity in Number 2. A Line is a length without breadth or thicknesse A Line is created or made by the moving or drawing out of a Point from one place to another so the Line AB is made by moving of a Point from A to B and according as this motion is so is the Line thereby created whether streight or crooked And of the three kindes of Magnitudes in Geometry viz. Length Breadth and Thicknesse a Line is the first consisting of Length only and therefore the Line AB is capable of division in length only and may be divided equally in the point C or unequally in D and the like but will admit of no other dimension 3. The ends or bounds of a Line are Points This is to be understood of a finite Line only as is the line AB the ends or bounds whereof are the points A and B But in a Circular Line it is otherwise for there the Point in its motion returneth again to the place where it first began and so maketh the Line infinite and the ends or bounds thereof undeterminate 4. A Right line is that which lieth equally between his points As the Right line AB lyeth streight and equall between the points A and B which are the bounds thereof without bowing and is the shortest of all other lines that can be drawn between those two points 5. A Superficies is that which hath only length and breadth As the motion of a point produceth a Line the first kinde of Magnitude so the motion of a Line produceth a Superficies which is the second kinde of Magnitude and is capable of two dimensions namely length and breadth and so the Superficies ABCD may be divided in length from A to B and also in breadth from A to C. 6. The extreams of a Superficies are Lines As the extreams or ends of a Line are points so the extreams or bounds of a Superficies are Lines and so the extreams or ends of the Superficies ABCD are the lines AB BD DC and CA which are the terms or limits thereof 7. A plain Superficies is that which lieth equally between his lines So the Superficies ABCD lieth direct and equally between his lines and whatsoever is said of a right line the same is also to be understood of a plain Superficies 8. A plain Angle is the inclination or bowing of two lines the one to the other the one touching the other not being directly joyned together As the two lines AB and BC incline the one to the other and touch one another in the point B in which point by reason of the inclination of the said lines is made the Angle ABC But if the two lines which touch each other be without inclination and be drawn directly one to the other then they make no angle at all as the lines CD and DE touch each other in the point D and yet they make no angle but one continued right line ¶ And here note that an Angle commonly is signed by three Letters the middlemost whereof sheweth

the angular point As in this figure when we say the angle ABC you are to understand the very point at B And note also that the length of the sides containing any angle as the sides AB and BC do not make the angle ABC either greater or lesser but the angle still retaineth the same quantity be the containing sides thereof either longer or shorter 9. And if the lines which contain the angle be right lines then is it called a right lined angle So the angle ABC is a right lined angle because the lines AB and BC which contain the said angle are right lines And of right lined Angles there are three sorts whose Definitions follow 10. When a right line standing upon a right line maketh the angles on either side equall then either of those angles is a right angle and the right line which standeth erected is called a perpendicular line to that whereon it standeth As upon the right line CD suppose there do stand another right line AB in such sort that it maketh the angles on either side thereof equall namely the angle ABD on the one side equall to the angle ABC on the other side then are either of the two angles ABC and ABD right angles and the right line AB which standeth erected upon the right line CD without inclining to either part thereof is a perpendicular to the line CD 11. An Obtuse angle is that which is greater than a right angle So the angle CBE is an obtuse angle because it is greater than the angle ABC which is a right angle for it doth not only contain that right angle but the angle ABE also and therefore is obtuse 12. An Acute angle is lesse than a right angle So the angle EBD is an acute angle for it is lesse than the right angle ABD in which it is contained by the other acute angle ABE 13. A limit or term is the end of every thing As a point is the limit or term of a Line because it is the end thereof so a Line likewise is the limit and term of a Superficies and a Superficies is the limit and term of a Body 14. A Figure is that which is contained under one limit or term or many As the Figure A is contained under one limit or term which is the round line Also the Figure B is contained under three right lines which are the limits or terms thereof Likewise the Figure C is contained under four right lines the Figure E under five right lines and so of all other figures ¶ And here note that in the following work we call any plain Superficies whose sides are unequall as the Figure E a Plot as of a Field Wood Park Forrest and the like 15. A Circle is a plain Figure contained under one line which is called a Circumference unto which all lines drawn from one point within the Figure and falling upon the Circumference thereof are equall one to the other As the Figure ABCDE is a Circle contained under the crooked line BCDE which line is called the Circumference In the middle of this Figure is a point A from which point all lines drawn to the Circumference thereof are equall as the lines AB AC AF AD and this point A is called the center of the Circle 16. A Diameter of a Circle is a right line drawn by the Center thereof and ending at the Circumference on either side dividing the Circle into two equall parts So the line BAD in the former Figure is the Diameter thereof because it passeth from the point B on the one side of the Circumference to the point D on the other side of the Circumference and passeth also by the point A which is the center of the Circle And moreover it divideth the Circle into two equall parts namely BCD being on one side of the Diameter equall to BED on the other side of the Diameter And this observation was first made by Thales Miletius for saith he If a line drawn by the center of any Circle do not divide it equally all the lines drawn from the center of that Circle to the Circumference cannot be equall 17. A Semicircle is a figure contained under the Diameter and that part of the Circumference cut off by the Diameter As in the former Circle the figure BED is a Semicircle because it is contained of the right line BAD which is the Diameter and of the crooked line BED being that part of the circumference which is cut off by the Diameter also the part BCD is a Semicircle 18. A Section or portion of a Circle is a Figure contained under a right line and a part of the circumference greater or lesse then a semicircle So the Figure ABC which consisteth of the part of the Circumference ABC and the right line AC is a Section or portion of a Circle greater than a Semicircle Also the other figure ACD which is contained under the right line AC and the part of the circumference ADC is a Section of a Circle lesse than a Semicircle ¶ And here note that by a Section Segment Portion or Part of a Circle is meant the same thing and signifieth such a part as is either greater or lesser then a Semicircle so that a Semicircle cannot properly be called a Section Segment or part of a Circle 19. Right lined figures are such as are contained under right lines   20. Three sided figures are such as are contained under three right lines   21. Four sided figures are such as are contained under four right lines   22. Many sided figures are such as have more sides than four   23. All three sided figures are called Triangles And such are the Triangles BCD 24. Of four sided Figures a Quadrat or Square is that whose sides are equal and his angles right As the Figure A. 25. A Long square is that which hath right angles but unequal sides As the Figure B 26. A Rhombus is a Figure having four equall sides but not right angles As the Figure C. 27. A Rhomboides is a Figure whose opposite sides are equall and whose opposite angles are also equall but it hath neither equall sides nor equal angles As the Figure D. 28. All other Figures of four sides besides these are called Trapezias Such are all Figures of four sides in which is observed no equality of sides or angles as the figures A and B which have neither equall sides nor equall angles but are described by all adventures without the observation of any order 29. Parallel or equidistant right lines are such which being in one and the same Superficies and produced infinitely on both sides do never in any part concur As the right lines AB and CD are parallel one to the other and if they were infinitely extended on either side would never meet or concur together but still retain the same distance Geometricall Theoremes 1. ANy two right lines crossing one another make the contrary or verticall angles