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A52257 Cosmographia, or, A view of the terrestrial and cœlestial globes in a brief explanation of the principles of plain and solid geometry applied to surveying and gauging of cask : the doctrine of primum mobile : with an account of the Juilan & Gregorian calendars, and the computation of the places of the sun, moon, and fixed stars ... : to which is added an introduction unto geography / by John Newton ... Newton, John, 1622-1678. 1679 (1679) Wing N1055; ESTC R17177 190,483 519

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Solid as hath its Vertex in the Center and the several Sides exposed to view and of this sort there are only three the Octohedron the Icosahedron of both which the Base is a Triangle and the Dodecahedron whose Base is a Quincangle 26. An Octohedron is a Solid Figure which is contained by eight equal and equilateral Triangles as in Fig. 18. 27. An Icosahedron is a Solid which is contained by twenty equal and equilateral Triangles as Fig. 19. 28. A Dodecahedron is a Solid which is contained by twelve equal Pentagons equilateral and equiangled as in Fig. 20. 29. A regular compound Solid is such a Solid as is Comprehended both by plain and circular Superficies and this is either a Cone or a Cylinder 30. A Cone is a Pyramidical Body whose Base is a Circle or it may be called a round Pyramis as Fig. 21. 31. A Cylinder is a round Column every where comprehended by equal Circles as Fig. 22. 32. Irregular Solids are such which come not within these defined varieties as Ovals Frustums of Cones Pyramids and such like And thus much concerning the description of the several sorts of continued Quantity Lines Plains and Solids we will in the next place consider the wayes and means by which the Dimentions of them may be taken and determined and first we will shew the measuring of Lines CHAP. VI. Of the Measuring of Lines both Right and Circular EVery Magnitude must be measured by some known kind of Measure as Lines by Lines Superficies by Superficies and Solids by Solids as if I were to measure the breadth of a River or height of a Turret this must be done by a Right Line which being applied to the breadth or height desired to be measured shall shew the Perches Feet or Inches or by some other known measure the breadth or height desired but if the quantity of some Field or Meadow or any other Plain be desired the number of square Perches must be enquired and lastly in measuring of Solids we must use the Cube of the measure used that we discover the number of those Cubes that are contained in the Body or Solid to be measured First therefore we will speak of the several kinds of measure and the making of such Instruments by which the quantity of any Magnitude may be known 2. Now for the measuring of Lines and Superficies the Measures in use with us are Inches Feet Yards Ells and Perches 3. An Inch is three Barley Corns in length and is either divided into halves and quarters which is amongst Artificers most usual or into ten equal Parts which is in measuring the most useful way of Division 4. A Foot containeth twelve Inches in length and is commonly so divided but as for such things as are to be measured by the Foot it is far better for use when divided into ten equal Parts and each tenth into ten more 5. A Yard containeth three Foot and is commonly divided into halves and quarters the which for the measuring of such things as are usually sold in Shops doth well enough but in the measuring of any Superficies it were much better to be divided into 10 or 100 equal Parts 6. An Ell containeth three Foot nine Inches aud is usually divided into halves and quarters and needs not be otherwise divided because we have no use for this Measure but in Shop Commodities 7. A Pole or Perch cotaineth five Yards and an half and hath been commonly divided into Feet and half Feet Forty Poles in length do make one Furlong and eight Furlongs in length do make an English Mile and for these kinds of of lengths a Chain containing four Pole divided by Links of a Foot long or a Chain of fifty Foot or what other length you please is well enough but in the measuring of Land in which the number of square Perches is required the Chain called Mr. Gunters being four Pole in length divided into 100 Links is not without just reason reputed the most useful 8. The making of these several Measures is not difficult a Foot may be made by repeating an Inch upon a Ruler twelve times a Yard is eight Foot and so of the rest the Subdivision of a Foot or Inch into halves and quarters may be performed by the seventeenth of the first and into ten or any other Parts by the first Proposition of the first Chapter and all Scales of equal Parts of what scantling you do desire And this I think is as much as needs to be said concerning the dividing of such Instruments as are useful in the measuring Right Lines 9. The next thing to be considered is the measuring of Circular Lines or Perfect Circles 10. And every Circle is supposed to be divided into 360 Parts called Degrees every Degree into 60 Minutes every Minute into 60 Seconds and so forward this division of the Circle into 360 Parts is generally retained but the Subdivision of those Parts some would have be thus and 100 but as to our present purpose either may be used most Instruments not exceeding the fourth part of a Degree 11. Now then a Circle may be divided into 360 Parts in this manner Having drawn a Diameter through the Center of the Circle dividing the Circle into two equal Parts cross that Diameter with another at Right Angles through the Center of the Circle also so shall the Circle be divided into four equal Parts or Quadrants each Quadrant containing 90 Degrees as in Fig. 7. GE. ED. DL and LG are each of them 90 Degrees and the Radius of a Circle being equal to the Chord of the sixth Part thereof that is to the Chord of 60 Degrees as in Fig. 14. if you set the Radius GB from L towards G and also from G towards L the Quadrant GL will be subdivided into three equal Parts each Part containing 30 Degrees GM 30. MH 30 and HL 30 the like may be done in the other Quadrants also so will the whole Circle be divided into twelve Parts each Part containing 30 Degrees And because the side of a Pentagon inscribed in a Circle is equal to the Chord of 72 Degrees or the first Part of 360 as in Fig. 13. therefore if you set the Chord of the first Part of the Circle given from G to L or L to G in Fig. 7. you will have the Chord of 72 Degrees and the difference between GP 72 and GH 60 is HP 12 which being bisected will give the Arch of 6 Degrees and the half of six will give three and so the Circle will be divided into 120 Parts each Part containing three Degrees to which the Chord Line being divided into three Parts the Arch by those equal Divisions may be also divided and so the whole Circle will be divided into 360 as was desired 12. A Circle being thus divided into 360 Parts the Lines of Chords Sines Tangents and Secants are so easily made if what hath been said of them in the Second Chapter be but considered