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
A52264	Institutio mathematica, or, A mathematical institution shewing the construction and use of the naturall and artificiall sines, tangents, and secants in decimal numbers, and also of the table of logarithms in the general solution of any triangle, whether plain or spherical, with their more particular application in astronomie, dialling, and navigation / by John Newton.	Newton, John, 1622-1678.	1654 (1654)	Wing N1061; ESTC R20441	128,229	417

understanding of that which follows presuming that the reader hereof hath already gotten some competent knowledge in Arithmetick Concerning then this Science of Magnitude two things are to be considered First the severall heads to which all Magnitudes may be referred And then secondly the terms and limits of those Magnitudes All Magnitudes are either Lines Plains or Solids and do participate of Length Breadth or Thicknesse 1. A Line is a supposed length or a thing extending it self in length without breadth or thickness whether it be a right line or a crooked and may be divided into parts in respect of his length but admitteth no other division as the line AB 2. The ends or limits of a line are points as having his beginning from a point and ending in a point and therefore a Point hath neither part nor quantity it is only the term or end of quantity as the points A and B are the ends of the aforesaid line AB and no parts thereof 3. A Plain or Superficies is the second kind of magnitude to which belongeth two dimensions length and breadth but not thickness 4. As the ends limits or bounds of a line are points confining the line so are lines the limits bounds and ends inclosing a Superficies as in the figure you may see the plain or Superficies here inclosed with four lines which are the extreams or limits thereof 5. A Body or Solid is the third kinde of magnitude and hath three dimensions belonging to it length breadth and thickness And as a point is the limit or term of a line and a line the limit or term of a Superficies so likewise a Superficies is the end or limit of a Body or Solid and representeth to the eye the shape or figure thereof 6. A Figure is that which is contained under one or many limits Under one bound or limit is comprehended a Circle and all other figures under many 7. A Circle is a plain figure contained under one round line which is called a circumference as in the Figure following the Ring CBDE is called the circumference of that Circle 8. The Center of a Circle is that point which is in the midst thereof from which point all right lines drawn to the circumference are equal the one to the other as in the following figure the lines AB AC AD and AE are equal 9. The Diameter of a Circle is a right line drawn through the center thereof and ending at the circumference on either side dividing the Circle into two equal parts as the lines CAD and BAE are either of them the diameter of the Circle BCDE because that either of them doth passe through the center A and divideth the whole Circle into two equal parts 10. The Semidiameter of a Circle is half the Diameter and is contained betwixt the center and one side of the Circle as the lines AB AC AD and AE are either of them the Semidiameters of the Circle CBDE 11. A Semicircle is the one halfe of a Circle drawn upon his Diameter and is contained by the half circumference and the Diameter as the Semicircle CBD is halfe the Circle CBDE and contained above the Diameter CAD 12. A Quadrant is the fourth part of a Circle and is contained betwixt the Semidiameter of the Circle and a line drawn perpendicular unto the Diameter of the same Circle from the center thereof dividing the Semicircle into two equal parts of the which parts the one is the Quadrant or fourth part of the same Circle Thus the Diameter of the Circle BDEC is the line CAD dividing the Circle into two equal parts then from the center A raise the perpendicular AB dividing the Semicircle likewise into two equal parts so is ABD or ABC the Quadrant or fourth part of the Circle 13. A Segment or portion of a Circle is a figure contained under a right line and a part of the circumference of a Circle either greater or lesser than the Semicircle as in the former figure FBGH is a segment or part of the Circle CBDE contained under the right line FHG lesse than the Diameter CAD 14. By the application of several lines ●terms of a Superficies one to another are made Parallels Angles and many sided Figures 15. A Parallel line is a line drawn by the side of another line in such sort that they may be equidistant in all places and of such there are two sorts the right lined parallel and the circular parallel Right lined Parallels are two right lines equidistant in all places one from the other which being drawn to an infinite length would never meet or concur as may be seen by these two lines AB and CD A Circular Parallel is a Circle drawn within or without another Circle upon the same center as you may plainly see by the two Circles BCDE and FGHI these Circles are both of them drawn upon the same center A and therefore are parallel one to the other 16. An Angle is the meeting of two lines in any sort so as they both make not one line as the two lines AB and AC incline the one to the other and touch one another in the point A in which point is made the angle BAC And if the lines which contain the angle be right lines then it is called a right lined angle as the angle BAC A crooked lined angle is that which is contained of crooked lines as the angle DEF and a mixt angle is that which is contained both of a right and crooked line as the angle GHI where note that an angle is for the most part described by three letters of which the second or middle letter representeth the angular point as in the angle BAC A representeth the angular point 17. All Angles are either Right Acute or Obtuse 18. When a right line standeth upon a right line making the angles on either side equal either of those angles is a right angle and the right line which standeth erected is a perpendicular line to that upon which it standeth As the line AB in the following figure falling upon the line CBD perpendicularly doth make the angles on both sides equal that is the angle ABC is equal to the angle ABD and either of those angles is therefore a right angle 19. An acute angle is that which is lesse than a right angle as the angle ABE is an acute angle because it is less than the right angle ABD in the former figure 20. An Obtuse Angle is that which is greater than a right angle CBE in the former figure is greater than the angle ABC by the angle ABE and therefore it is an obtuse angle 21. The measure of every angle is the arch of a Circle described on the angular point as in the following figure the arch CD is the measure of the right angle CED The arch BC is the measure of the acute angle BEC And the arch BCD is the measure of the obtuse angle BED But of their