CHAP. V. Of the Sextuplation, and Sextisection of an ARCH or ANGLE: And other following Multiplications and Sections.I. ACCORDING to the same methods may be had, the Sextupla∣tion, Septuplation, and other consequent Multiplications; as also the Sextisection, Septisection, and other consequent Sections, of an Arch or Angle. Of which I shall briefly touch at some.II. The Sextuplation, may be had, by Tripling the Double, or Doubling the Triple Arch. And, accordingly, the Sextisection, by Bisecting the Subtriple, or Trisecting the Subduple. (as is of it self manifest.) And the same holds, in like manner, for Multiplications and Sections which take their Denomination from a Compound number. For Multiplications and Sections successively made, according to the Components of such Compound number, amount to the same as one by such Compound number.III. But though Six were not a Compound number, or be not considered as such; yet may such Sextuplation and Sextisection be had in like manner as those before. Namely,IV. If in a Circle be inscribed a Quadrilater, whose opposite sides are B, B,Fig. XXXIII subtenses of the Duple; and B, G, subtenses of the Duple and Sextuple; and the Diagonals D, D, subtenses of the Quadruple. Then is, Dq−Bq = BG; and B) Dq−Bq (G.V. Or, Let the opposite sides be A, A, and D, G; and the Diagonals F, F.Fig. XXXIV. Then is, Fq−Aq = DG; and D) Fq−Aq (G.VI. Or, Let the opposite sides be A, B, and C, G; and the Diagonals D, F.Fig. XXXV. Then is, DF−AB = CG; and C) DF−AB (G.VII. Or, Let the opposite sides be A, C, and B, G; the Diagonals C, F.Fig. XXXVI. Then CF−AC = BG; and B) CF−AC (G.VIII. And therefore, Dq−Bq = CF−CA.IX. Or, Let the opposite sides be A, G, and A, D; the Diagonals B, F.Fig. XXXVII Then BF−AD = AG; and A) BF−AD (G.X. Or, Let the opposite sides be B, C, and A, G; the Diagonals C, D.Fig. XXXViii Then CD−BC−AG; and A) CD−BC (G.XI. And therefore, BF−AD = CD−BC.XII. It is manifest that from hence may be deduced a great number of Equations, and Analogies, and great variety of Theorems, in like manner, as is done in the Chapters foregoing. But I forbear here to pursue them in particular as is there done.0