Sides and Angles are all equal one to another: For your better understanding of which, obferve the Figures following. 19. Fig. 16. Now fuppofing the Sides and Angles to be all equal, (A) is a regular Pentagone, (B) a Hexagone, and C a Heptagone, &c. 20. Fig. 17. ACircle is a plain Figure, contained under one Line only, BDCGE, which is called the Perophery, in the Middle whereof there is a point A, which is called the Center; from whence all right Lines that are drawn to the Circumference are <qual; as AB, AC, AD. 21. The Diameter of a Circle is a right Line drawn through the Center, and terminated by the Circumference of the Cir-: cle; thereby dividing it into two equal. parts. 22. Fig.17.The Semi-diameter or Radius is+ the half of the whole Diameter; as AC or AB are Semi-diameters. 23. A Chord is a freight Line fubtending an Arch of a Circle, dividing into two parts. 24. Fig.17. A Semicircle is the half of aCircle, contained under the Diameter and half Periphery, as DBC or BEC. 25. Fig. 17. A Quadrant is one fourth part of a Circle; and is made by the interfecti-: on of two Diameters perpendicularly, as ADC or ABD. 26. Fig. 17. A Segment is aFigure comprehended under part of the Circumference of a Circle, and the Chord belonging to it, as ECG, by the Chord Line EC. 27. Fig 17.A Sector of a Circle is a Figure contained under two Right Lines, drawn from the Center A, and the Circumference lying between the fame Lines, as ABD. 23. All Circumferences,as alfo like Arches, Sines, Tangents, Chords and Secants, are proportional to their Radii; That is, if the Radius of one Circle be double, treble, &c. the Radius of another: TheCircumference as alfo like Arches(i.e. containing the fame number of degrees,) and their Sines, Tangents, Chords, &c. of the former will be double, treble, &c. the Circumference like Arches, their Sines, Tangents, &c. 29. Fig. 19. A Diagonal is a freight Line drawn from one Angle of any Figure, to the oppofite Angle, as CAB. MAXIM S. 1. Thofe Quantities that are equal to third, are equal betwixt themselves. 2. If equal Quantities be added to thofe that are equal, the Sums will also be equal. 3. If equal Quantities be taken away from thofe that are equal, the Remainders will be equal. 4. If you add equal Quantities to unequal, he whole will be unequal. 5. If from equal Quantities you take unqual, the Remainder will be unequal. 6. Quantities that are double, triple, quaIruble &c. to the fame Quantity, are equal mong themfelves. 7. Those things which mutally agree to each other, are equal. 8. Right Angles are equal to one another. 9. Parallel Lines have a common Perpendicular. ADVERTISEMENT. There are two forts of Propofitions, viz. Problems and Theorems. A Problem always propofes fomething to be done: But a Theorem is a fpeculative Propofition, in which are confidered the Affections and Propels ties of things already done. Of Proportion. Multiplied Magnitude, is that which cortains another Magnitude, a certain Number of times precifely. Ratio or Reason, is the Comparison of two Quantities one with another, whereby one is faid to be bigger or lefs than an other; in which Comparifon, that which proceeds, is called the Antecedent, and the other the Confequent. Thofe Quantities only admit of Reafon, which being multiplied may exceed each other. 10 TheHomologus Terms in any Proportion are the two Antecedents, or the two Confequents. Reciprocal Figures, are fuch as are when we compare the Sides of one Figure to the Sides of the other, and the Antecedents, and the Confequents of the Reafons are in both Figures. Of Solids, viz. Solid Bodies. A Solid Angle, is made by the meeting together of feveral plain Angles in one point, and of thefe there must be 3 at leaft. Like rectilineal folid Figures, are fuch as are contained under an equal Number of like Plains. A Pyramid is a folid Figure, contained under Plains collected from one Plain to another. A Sphere is a folid Figure, bounded with a Surface, to which Superficies all the ftreight Lines that can be drawn from the Center are equal. The Axis of a Sphere is a rightLine drawn through the Center to both parts of the Circumference, about which, if a Semi-circle be turn'd, it will beget a Sphere, A Cone is a folid Figure, arifing from a circular Bafe of freight Lines, ending in a Point called the Vertex, or top thereof; and the Axis of this Cone, is a right Line drawn from the Vertex to the Center of the Bafe, and is called a right Cone, if the Axis be perpendicular to. the Bafe, if not, a Scalene one. A Cylinder is a folid Figure, rifing from a circular Bafe as the Cone does; but the right Line end all in an equal Circle. A Cube is a Solid Figure contained under 6 equal Squares. A Tetrahedron, is a folid Figure comprehended under 4 equal and equilateral Triangles; fo that its Bafe is equal to each fide. An Octatredron is a folid Figure contain ed under 8 equal and Equilateral Triangles. The Dodecahedron, is a folid Figurecontained under 12 equal equiangular and Equilateral Pentagons. The Icofædron, is a folid Figure contained under 20 equal and equilateral Triangles. Befides thefe five regular Bodies, it's impoffible to find any others, i. e. to form any more regular Bodies than thefe laft, viz. three are made of Triangles, one of Squares, and one of Pentagons. |