dividing the circle into two equal parts. XVIII. A Semicircle is a figure which is contained under the diameter, and under that part of the circumference which is cut off by the diameter. In the circle EABCD, E is the center, AC the diameter, ABC the femicircle. XIX. Right-lined figures are fuch as are contained under right lines. XX. Three-fided or Trilateral figures are fuch as are contained under three right lines. XXI. Four-fided or Quadrilateral figures are fuch as are contained under four right lines. XXII. Many-fided figures are fuch as are contained under more right lines than four. A XXIII. Of Trilateral figures, that is an Equilateral Triangle, which hath three equal fides; as the Triangle A. 3 XXVI. Of these Trilateral figures, a right-angled Triangle is that which has one right angle; as the Triangle A. XXVII. An Amblygonium, or obtuse-angled Triangle, is that which has one angle obtufe; as B. A XXVIII. An Oxygonium, or acute-angled Triangle, is that which has three acute angles; as C. An Equiangular, or equal-angled figure is that whereof all the angles are equal. Two figures are e quiangular,if the feveral angles of the one figure be equal to the feveral angles of the other. The fame is to be underftood of Equilateral figures. A B D XXXIII. All other quadrilateral figures befides these are called Tra pezia, or Tables; as GNDH. XXXIV. Parallel, or equidiftant right lines are fuch, which being in the fame fuperficies, if infinitely produced, would never meet; as A and B. XXXV. A Parallelogram is a quadrilateral figure, whofe oppofite fides are parallel, or equidiftant; as GLHM. A XXXVI. In a Parallelogram ABCD, when a diameter AC, and two lines EF, HI parallel to the fides, cutting the diameter in one and the fame point G, are drawn, fo that the Parallelogram be divided by them into four parallelograms; thofe two DG, GB, through which the diameter paffeth not, are called Complements; and the other two HE, FI, through which the diameter paffeth, the Parallelograms standing about the diameter. A Problem is, when fomething is proposed to be done or effected. A Theoreme is, when fomething is, propofed to be demonftrated. A Corollary is a confectary, or fome confequent truth gained from a preceding demonftration A Lemma is the demonftration of fome premife, whereby the proof of the thing in hand becomes the Shorter. 1. Poftulates or Petitions. From any point to any point to draw a right 2. To produce a right line finite, ftrait forth continually. 3. Upon any center, and at any distance, to defcribe a circle. 1. Axioms. Hings equal to the fame third, are also As A B C. Therefore A-C. Or therefore all, A, B, C, are equal the one to the other. Note, When feveral quantities arejoined the one to the other continually with this mark, the firft quantity is by virtue of this axiome equal to the laft, and every one to every one: In which cafe we often ab 1 ftain from citing the axiome, for brevity's fake, al- 3. If from equal things you take away equal 5. If from unequal things you take away equal things, the remainders will be unequal. 6. Things which are double to the fame third, or to equal things, are equal one to the other. Understand the fame of triple, quadruple, &c. 7. Things which are half of one and the fame thing, or of things equal, are equal the one to the other. Conceive the fame of fubtriple, fubquadruple, &'c. 8. Things which agree together, are equal one to the other. The converfe of this axiome is true in right lines and angles, but not in figures, unless they be like. Moreover, magnitudes are faid to agree, when the parts of the one being applyed to the parts of the other, they fill up an equal or the fame place. 9. Every whole is greater than its part. 10. Two right lines cannot have one and the fame fegment (or part) common to them both. II. Two right lines meeting in the fame point, if they be both produced, they fhall neceffarily cut one the other in that point. 12. All right angles are equal the one to the other. 2 A 13. If a right line BA falling on two right lines A 4 AD, CB, |