1: PLAIN SAILING; Or Sailing by the Plain Sea- Chart : And therein, (1) By laying down upon a Blank Chart, Places according to their Longitudes and Latitudes : (2) To find their Distances, Difference in Longitude, Latitude, Rumb and Distance upon the Rumb. (3) To Work a Travers, consisting of many Courses. With variety of Problems, useful in that Art.-- All being performed Geometrically by Scale and Compasses; and by Trigonometrical Calculation 2. Sailing by Mercators, or the True Sea-Chart SECT. VII. Of ASTRONOMr Theorical. And therein of 2. The Theory of the Sun, and other Primary Planets 335 to 336 3. Of the Motions of the Planets in their Elliptical Orbs 4. Finding the true Place of a Planet in its Orb 5. To Calculate the Place of a Planet Trigonometrically 340 to 346 6. Of the Magnitude of the Sun, Earth, Moon, and other Planets Geometrical Astronomy 349 to 366 CLA- Practical Geometry. HIS First Part consists only of such DEFINITIONS, Eticed, before farther Progress be made in any other Geometrical Definitions. I. A Point is that which hath no Part. That is, it hath no Parts into which it may be divided ; It being the least thing that by Mind and Understanding can be imagined or conceived; than which there can be nothing A iefs : As the point in the Margin, noted with the Letter A over it: It being neither Quantity, nor any part of QuanTity; but only the Term or End of Quantity. CD, II. A Line is a Lengıh without Breadth; as the Line A B. A -B E F 1 ID For a Line hath its beginning from a Point, and likewise Or, it is the Shorteft Distance that can be drawn between Point and Point so the Right Line G H, is the shortest Distance between the Points G and H. ܪ V. Parallel (or Equidistant) Right Lines are such, təbich being draton upon the same Plain, and infinitely produced, would ne ver meet. And such are these two. A -B Fig. I. VI. A Plain Angle is the Inclination for Bowing) of Two Right Lines, one to the other, and the one touching ihe other; and not being direilly joined together. So the Two Lines A B and B C incline one to the other, and touch each other in the Point B; in which Point (by reason of the Inclination of the said Two Lines) is made the Angle A BC; But if the Two Lines which incline one to the other, do (when they meet) make one Streight Line, then do they make no Angle at all: As the Lines D E and EF incline one to the other, and meet each other in the Point E, and yet they make no Angle. And, a And here Note, That an Angle (generally) is noted with Three Letters, of which, the middlemoft Letter represents the Kinds; viz. Right, Acute and Obtufe. Angles on either Side thereof Equal, then either of those Angles So upon the Right Line C D, suppose there do fand another Fig. II. Right Line A B, in such fort, that it maketh the Angles ABC and A BD (on either side of the Line A B) equal; then are either of those Angles, A BC and A B D, Right Angles; and the Line A B, which standeth ere£ted upon the Line CD, (without inclining on either side) is a Perpendicular to the Line CD. VIII. An Obtuse Angle is that which is Greater than a Right Angle: So the Angle E B D is an Acute Angle, it being Less than the X. A Limit or Term is the End of any thing. Forasmuch as there is no Quantity (or Magnitude) of which Geometry treateth, but it hath Bounds or Limits : And as Points are the Bounds or Limits of Lines, fo Lines are the Bounds or Li. mits of Plains or Superficies; and Plains (or Superficies) of Solids' (or Bodies.) XI. A Figure is that which is contained under One Term, or Limit; or Many. So A is a Figure contained under one Line or Limit: B is a Fig. III. Figure under Three Lines or Limits: C under Four : D under Five, &c. which are their respe&tive Bounds or Limits. A 2 XII. A Fig. IV. XII. A Circle is a Plain Figure contained under One Line, which is called a Circumference or Periferie; unto which all Right So the Figure BCD contained under One crooked Line, is a Fig. V. XIII. The Diameter of a Circle is any Right Line drawn through the Centre, and ending at the Circumference on either Side, So the Line E K F is á Diameter, because it passeth from the contained under one Right Line, and a Part of the Circumfe- So the Right Line L M divideth the Circle EGFMHL in- of that Circle. |