Sum of all the Antecedents. And P- * will be the Sum of all the Confequents ; therefore it will be u: :: P: P-tē which AN CH A P. I. Sect. 1. Of Lines and Angles. 1. . . B. Such a Place may be conceived so infinitely small, as to be void of Length, Breadth, and Thickness; and therefore a Point may be said to have no Parts. 2. A LINE is called a Quantity of one Dimension, because it .. may have any supposed Length, but no Breadth nor Thickness, being made or represented to the Eye, by the Motion of a Point. That is, if the Point at A, be moved (upon the same Plane) to the Point at B, it will describe a Line either right or circular (viz. trooked) according to its Motion. Therefore the Ends or Limits of a Line are Points. 3. A RIGAT Line, is that Line which lieth even or freight betwixt those Points that limit its Length, being the shortest Line that can be drawn between any Two I A . Points, B. As the Line A B.. Therefore, between any two Points, there can lie or be drawn but one right Line, 4. A CIRCULAR, crooked or OBLIQUE Line, is that which lies bending between those Points which limit its Length, as the Lines CD or FG, &c. Of these kinds of Lines there are various Sorts; but those of the Circle, Parabola, Ellipsis, and Hyperbola are of most general Use in Geometry; of which a particular Account Jhall be given further on. 5. PARALLEL LINES, are those that lie equally diftant from one another in all their Parts, viz. such Lines as being infinitely extended (upon the fame Plane) will never meet : As the Lines A B and a b: or C D and c d. 6. Lines not PARALLEL, but INCLINING (viz. leaning) one towards another, whether they are Right Lines, or Circular Lines, will 4 (if they are extended) meet, and make an Angle; the point where they meet is called the Angular Point, as at A. And according as fuch Lines stand, nearer or further off each other, the Angle is said to be lefser or greater, whether the Lines that include the Angle be long or short. That is, the Lines Ad, and Af include the fame Angle as A B, and AC doth; notwithstanding that A B is longer than Ad, &c. 7. All ANGLEs included between Right Lines are called Rightlind Angles; and those included between Circular Lines are called Spherical Angles. But all Angles, whether Right-lin'd or Spherical, fall under one of these Three Denominations. A Right Angle. ( An acute Sngiz. 8. A RIGHT ANGLE is that which is included betwixt Two Lines, that meet one another Perpendicularly. That That is, when a Right Line, as That is, AC, and C B, are Perpendicular to DC, as well as D, C is to either or both of them. 9. An Obtuse Angle is that which is greater than a Right Angle. Such is the Angle included between the Lines AC and CB. 10. An Acute Angle is that A D which is less than a Right Angle: As the Angle included between the Lines CB and CD. These Two Angles are generally called Oblique Angles. Seet. 2. Of a Circle, &c. Before a Circle and its Parts are defined, it will be convenient to give a brief Account of Superficies in general. 1. A SUPERFICIES or SURFACE is the Upper, or very Out-side of any visible Thing. But by Superficies in GEOMETRY, is meant only so much of the Out-side of any Thing as is inclosed within a Line or Lines, according to the form or Figure of the Thing defigned; and it is produced or formed by the Motion of a Line, as a Line is described by the Motion of a Point ; thus : Suppose the Line A B were equally msved (upon the same Plane) to C D; then will the points at A and B describe the Two Lines AC and BD; and by so doing they will form (and inclose) the SUPERFI. CIES or Figure Å BCD, being a Quantity of Two Dimenfions, viz. it hath Length and Breadth, but not Thickness. Consequently the Bounds or Limits of a Superficies are Lines. Note, Note, The Superficies of any Figure, is usually called its AREA. 2. A CIRCLE is a plain regular Figure, whose Area is bounded or limited by one continued Line, called the CIRCUMFERENCE or PERIPHERY of the Circle, which may be thus described or drawn. Suppose a Right Line, as Ġ B, to have one of its Extream Points, as G, fo fix'd upon any Plane, as that the other Point at B may move about it ; then if the Point at B be moved round about (upon the same Plane) it will describe a Line equally difiant in all its Parts from the Point C, which will be the Circumference or Periphery of that Circle; the Point C, will be its CENTER, and the contained Space will be its Area, and the Right Line CB, by which the Circle is thus described, is called RADIUS. Confectary. From hence 'tis evident, that an infinite Number of Right Lines may be drawn from the Center of any Circle to touch its Periphery, which will be all equal to one another, because they are all Radius's. And with a little Consideration it will be ealy to conceive, that na more than two equal Right Lines can be drawn from any Point within a Circle to touch its Periphery, but from the Center only. (9.6.3.) 5. A Semicircle (viz. Half a Circle) is a Figure included between the Diameter, and Half the Periphery cut off by the Diameter; as AD B. |