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SECT.VI. Of NAVIG ATION.

And therein of

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, confifting of

many Courses. With variety of Problems, useful in that Art.---

All being performed Geometrically by Scale and Compaffes;

and by Trigonometrical Calculation

2. Sailing by Mercators, or the True Sea-Chart

3. Sailing by the Middle Latitude

4. The several Ways compared

304 to 324

324 to 329

329 to 331

331 to 332

SECT. VII. Of ASTRONOMY Theorical.

1. The Planetary System

And therein of

2. The Theory of the Sun, and other Primary Planets

3. Of the Motions of the Planets in their Elliptical

4. Finding the true Place of a Planet in its Orb

5. To Calculate the Place of a Planet Trigonometrically

6. Of the Magnitude of the Sun, Earth, Moon, and

Geometrical Aftronomy

333 to 335

335 to 336

Orbs

336 to 339

339 to 340

340 to 346

other Planets

346 to 349

349 to 366

CLA-

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T

PARTI.

OF

Practical Geometry.

HIS First Part confifts only of fuch DEFINITIONS, PROBLEMS and THEOREMS, GEOMETRICAL, which of Neceffity ought to be understood and praEticed, before farther Progress be made in any other Mathematical Science: And so I will begin It with these following

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 less: 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.

B

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II. A

II. A Line is a Length without Breadth; as the Line A B.
AB

Unto Quantity there appertain Three Dimensions; viz. Length,
Breadth and Depth (or Thickness;) of which, a Line is the first,
and hath Length only, without Breadth of Thickness; as the Line
C D,

E

F

I-ID

which may be divided into Parts; either Equally, in the Point E or Unequally, in the Point F.

III. The Ends, or Limits, of a Line, are Points GH.

For a Line hath its beginning from a Point, and likewise endeth in a Point: So the Points Gand H are the Ends of the Line GH, and are no Parts of it.

IV. A Right Line is that which lyeth Equally between its Points.

Or, it is the Shortest Distance that can be drawn between Point and Point; so the Right Line GH, is the Shortest Distance between the Points G and H.

V. Parallel (or Equidiftant) Right Lines are such, which being drawn upon the Same Plain, and infinitely produced, would ne

VI. A Plain Angle is the Inclination (or Bowing) of Two Right Lines, one to the other, and the one touching the other; and not being directly joined together.

Fig. I.

So the Two Lines AB 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 DE and EF incline one to the other, and. meet each other in the Point E, and yet they make no Angle.

And,

And here Note, That an Angle (generally) is noted with Three
Letters, of which, the middlemoft Letter represents the
Angular Point; so, in this Angle ABC, the Letter B de-
notes the Angular Point. -And of Angles there are Three
Kinds; viz. Right, Acute and Obtufe.

VII. When a Right Line standing upon a Right Line maketh the
Angles on either Side thereof Equal, then either of those Angles
is a Right Angle; and the Right Line which standeth erected is
called a Perpendicular Line to that Line upon which it ftandeth.

So upon the Right Line CD, suppose there do stand another Fig. II. Right Line A B, in such fort, that it maketh the Angles ABC and ABD (on either fide of the Line A B) equal; then are either of those Angles, ABC and ABD, Right Angles; and the Line AB, which standeth erected upon the Line CD, (without inclining on either fide) is a Perpendicular to the Line C D.

VIII. An Obtuse Angle is that which is Greater than a
Right Angle:

So the Angle CBE is an Obtufe Angle, it being greater than the Right Angle ABC, by the Quantity of the Angle A B E.

IX. An Acute Angle is that which is Less than a Right Angle.
So the Angle EBD is an Acute Angle, it being Less than the
Right Angle ABD, by the Quantity of the Angle A В Е..

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, so Lines are the Bounds or Limits 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: Cunder Four: Dunder
Five, &c. which are their respective 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
Lines drawn from one certain Point within the Figure unto the
Circumference, are equal one to the other.

So the Figure BCD contained under One crooked Line, is a
Circle, whose Circumference of Periferie is BCD. In the mid-
dle whereof there is a Point A, from which all the Right Lines,
A B, AC, AD, being drawn to the Circumference BCD, are
Equal. And that Point A is called the Centre of the Circle
BC D.

XIII. The Diameter of a Circle is any Right Line drawn through the Centre, and ending at the Circumference on either Side, dividing the Circle into Two Equal Parts.

Fig. V.

So the Line EKF is à Diameter, because it paffeth from the Point E of the Circumference on the one Side, to the Point F on the other Side; and passeth alfo by the Point K, which is the Centre of the Circle: And moreover, it divideth the Circle into Two equal Parts, viz. into the Part EGF above, and EHF below, the Diameter; which Two Parts are termed Semicircles.

XIV. A Section, Segment or Portion, of a Circle, is a Figure contained under one Right Line, and a Part of the Circumference; Greater or Leffer than a Semicircle.

So the Right Line LM divideth the Circle EGFMHL into Two unequal Sections; namely, into the Section L GM above, Greater, and the Selfion LHM below, Leffer, than a Semicircle.

XV. The Semidiameter of a Circle, is half of the Diameter of that Circle.

So KE or KF are Semidiameters of the Circle EGFH: And so is any Right Line drawn from K the Center to the Circumference; which Lines are frequently called the Radius of the Circle.

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XVI, Right

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