Selected quad for the lemma: doctrine_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
doctrine_n	america_n	asia_n	europe_n	2,462	5	15.3336	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

Fig. 23. Fig. 24. Fig. 25. Fig. 26. Fig. 27. Fig. 28. Fig. 29. Fig. 30. Fig. 31. Fig. 32. Fig. 33. ☞ Note that every Sphere is equal unto two Cones whose Height and Diameter of the Base is the same with the Axis of the Sphere And a Sphere is two thirds of a Cylinder whose Height and Diameter of the Base is the same with the Axis of the Sphere according unto the 9th Manifestation of the first Book of Archimedes of the Sphere and Cylinder Fig. 34. Fig. 36. Fig. 35. Fig. 34. Observe this for a general Rule in Trigonometry Fig. 34 Fig. 34. Fig. 34. Fig. 35. 〈…〉 Fig. 35. Fig. 35. Fig. 36. ☞ The Rule to find the Complement Arithmetical of any Logarithm Number 9. 962398. 0. 037602. Fig. 36. Fig. 36. Fig. 36. Fig. 37. Fig. 37. * That is equal unto the two Angles B 40° and B. 53° as afore in the former Proposition Fig. 37. Fig. 37. Fig. 37. Fig. 37. Fig. 38. Fig. 38. Fig. 38. Fig. 38. Fig. 38. Fig. 38. Fig. 38. Fig. 38. Fig. 38. Fig. 38. Fig. 38 Fig. 38. Fig. 38. Fig. 38. Fig. 38. Fig. 38. Fig. 39. Note that in thes● Operations for the more facility of the learner I omit Seconds which doth belong unto the Angles c. Fig. 39. Fig. 39. ☞ And here observe that if the Sum of the two contained Sides exceed a Semicircle then substract each side severally from 180° and proceed with those Complements as with the sides given the Operation produceth the Complements of the Angles sought unto a Semicircle or 180 Degrees Fig. 39. ☞ And here observe that if the Sum of the two given Angles excede a Semicircle or 180° substract them from a Semicircle and proceed with the Residues the Operation will produce each side 's Complement to a Semicircle or 180 Degrees Fig. 39. Fig. 39. Fig. 39. Fig. 39. Fig. 39. Fig. 39. Fig. 40. ☞ Note that if the Angles at the Base be both of one kind that then the Perpendicular falls within the Triangle if of diverse kinds without the Triangle Fig. 41. Fig. 40. Fig. 40. Fig. 40. Fig. 40. Fig. 40. Defin. Defin. Fig. 42. Fig. 42. Fig. 42. Fig. 42. Fig. 42. * Which is by the Greeks called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 i e. bring Life because the life of all Creatures depend on the cause of that Circle for the Sun ascending in it and moving towards us brings the Generation of things and in descending the Corruption of all things sensible and insensible which are below the concavity of the Moon c. Fig. 42. Fig. 42. Fig. 42. Fig. 42 Fig. 42. Fig. 42. Fig. 42. Fig. 42. Fig. 43. Fig. 43. * If the Sun's Declination be North and increasing this Proportion finds the Sun's distance from ♈ but if decreasing from ♎ in the northern Sines But if the Sun's Declination be South and increasing from ♎ if decreasing from ♈ among the Southern Sines † From the next Equinoctial point either ♈ or ♎ * As in Case 11 of Oblique Spherical Triangles * Watched the Time after Sun-setting when the Twilight in the West was shut in so that no more Twilight than in any other part of the Skie near the Horizon appeared there then by one of the known fixed Stars having found the true Hour of the Night he found the length of the Twilight to be as in the rule is mentioned * Or ½ Diurnal Arch. To find the length of the least Crepusculum or Twilight Defin. Defin. Europe * Which Pliny hath adorned in these words saith he Italia terrarum omnium alumna eadem parens numine Deûm electa qua Coelum ipsum clariùs faceret sparsa congregaret imperia ritus molliret tot populorum discordes linguas sermonis commercio ad Colloquia distraheret humanitati hominem daret i. e. Italy saith Pliny is the Nurse and the Parent of all Religion was elected by the Providence of the Gods to make if possible the Heavens more famous to gather the scattered Empires of the World into one Body to temper the Barbarous rites of the Nations to unite so many disagreeing Languages of Men by the benefit of one common Tongue and in a word to restore Man to his Humanity Europe Europe Europe Europe Europe Europe Europe Europe Europe Europe Europe Europe Europe Europe Europe Europe Europe Europe Europe Europe Europe Europe Europe Asia Asia Asia Asia Asia Asia Asia Asia Asia Asia Asia Asia Africa Africa Africa Africa Africa Africa Africa Africa America America America America America America America America America America America America The Doctrine of Rightlined Triangles both Right and Oblique-Angled applied to Propositions of Plain Sailing Fig. 44. Fig. 44. Fig. 44. Fig. 44. Fig. 45. Fig. 45. Fig. 46. Fig. 46. Fig. 47. Fig. 47. Fig. 48. Fig. 49 ' * But is indeed the Invention of our Learned Countryman Mr. Edw. Wright although this Stranger hath almost got the Name and Praise thereof Fig. 50. Fig. 50. Fig. 51. Fig. 51. Fig. 51. Fig. 51. Fig. 51. Fig. 51. * Which Instrument and the Plain Table I esteem as the two aptest Instruments for Surveying of Land i. e. the Plain Table for small Enclosures and the Semicircle for Champain Plains Woods and Mountains Fig. 52. Fig. 52. Fig. 53. Fig. 53. Fig. 54. Fig. 54. Fig. 55. Fig. 55. Fig. 55. Fig. 55. Fig. 55. Fig. 55. Fig. 56. Fig. 56. Fig. 56. Fig. 56. Fig. 57. Fig. 57. Fig. 58. Fig. 58. Fig. 58. Fig. 58. * Is a Quadrangle whose sides are not Parallel nor equal Euclides postulat hant fabricam'Trapezium tanquam mensulam vocari sanè nominis ejus ratio Geometrica nulla est P. Rami lib. 14 pag. 94. Fig. 59. Fig. 60. Fig. 61. * Which to do is no more than thus with a Thread and Plummet fastened at the Center of the Semicircle so that it hath liberty to play move the Semicircle until the Thread playeth against 90 deg then screw it fast and it is Horizontal Fig. 61. Fig. 61. Fig. 62. Fig. 63 Fig. 63. * Whose Surface is bounded by a Line called by Proclus a Helicoides but it may also be called a Helix a Twist or Wreath c. * See Procl lib. 2. cap. 3. Viturvius lib. 9. cap 3. * See Mr. Oughthred in his Book of the Circles of Proportion page the 57. and Mr. Edm. Gunter in his Book of the Cross-staff part 21. chap. the 4. * Which doth appear to have been in use above this 2400 Years for King Achaz had a Dial This Art requireth good skill in Geometry and Astronomy Now Cresibius that famous Philosopher measured the Hours and Times by the orderly running of Water Then by Sand was the Hours measured After that by Trochilike with Weights and of late with Trochilike with Springs Fig. 64. Fig. 64. Fig. 65. Fig. 65. * Which may be either a Pin of the length of Q S placed on Q and Perpendicular unto the Plane or it may be a piece of brass or elsewhat of the breadth of 12 to 3 or 9. Fig. 66. Fig. 66. Fig. 66. Fig. 67. Fig. 68. Fig. 70. Fig. 70. Fig. 70. Fig. 70. Fig. 71. Fig. 71. Fig. 71. Fig. 71. Fig. 71. Fig. 71. Fig. 71. Fig. 71. Fig. 72. Defin. Fig. 73. Fig. 73. Fig. 73. Fig. 73. * Because the length of the part of a Musket doth not much exceed that Mèasure Fig. 73. Fig. 73. Fig. 73. * Because the Defence ought to be easie quick certain and of little charge all which qualities the Musket hath and the Cannon hath not therefore the Defence of Fortification ought to be measured by the Port of a Musket and not by that of a Cannon Fig. 74. Fig. 74. Fig. 74. Fig. 74. Fig. 74. Fig. 74. Fig. 74. Fig. 74. Fig. 74. Fig. 74. Fig. 74. Fig. 74. Observe this for a general Rule in Regular Fortification Fig. 76. Case 1. Fig. 76. Case 2. Fig. 77. Fig. 78. Fig. 78. Fig. 78. Fig. 78. Fig. 78. Fig. 79. Fig. 79. Fig. 79. Fig. 80. Fig. 81. Fig. 83. Fig. 84. * Built to bridle the Town or the Place left the Burghers should be rebellious and to be the last refuge or place of retreat * The Inginier must first form a Map of the Town or Place with all the Ways Passages Old Walls Rivers Pools Enclosures and all other matters fit to be known in the draught and then he is to design what Works he findeth most agreeing to the place to be Fortified Fig. 84. Fig. 85. Fig. 86. Fig. 87. Fig. 88. Fig. 89. Fig. 90. Defin. This Military Engine Bombarda Gun Cannon c. So called from Bombo a resounding Noise Cannone or Cannon from the likeness it holds with his Canna Bore or Concavity Artigleria from Artiglio the Talons or Claws of Ravenous Fowls because its shot flying afar off tears and defaces all that it doth meet from whence some Natures of this Machine are called Smeriglii long winged Hawks Falconi Falconets Passa volanti swift flying Arrows c. Fig. 91. Fig. 91. Fig. 91. * In his Mathematical Manual page 165. Fig. 91. * See Mr. Diggs in his Pantometria page 179. General Rules to be observed in the battering down of a Place or making of Breaches * According to learned D'Chales on the 4th Prop. of the first Book of Euclid Fig. 93.