An Equiangular, or Equal-angled Figure, is that whereof all the Angles are equal: And two Figures are equiangular, 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. all the Sides being not equal between themfelves, nor the Angles right ones; as CLMH. A B 34. Parallel, or Equidiftant right Lines, are fuch, which being in the fame plain Su perficies, if infinitely produced, would never meet; as A and B. diftant; asGLHM. 36. In a Parallelogram A B CD, when a Diameter A C, and two Lines F C EF, HI, parallel to the Sides, cutting the Dia D meter in one or the fame Point G, are drawn fo, that the Parallelogram be divided by them into four Parallelograms; then those two Parallelograms, DG and GB, thro' which the Diameter does not pafs, are called Complements; and the other two, HE, FI, which the Diameter paffeth thro', are called Parallelograms ftanding about the Diameter. A Definition is what determines the Idea of a Word, or which gives a clear Notion of the Thing that we would have fignified by that Word. An Axiom is that which is fo evident, that it has no need of a Proof; as that the Whole is greater than its Part, &c. A Theorem is fomething propofed, the Truth of which is to be made appear (which is called demonftrating it) fo evidently, that all fcruple con concerning the fame may vanifh; as that the Square of the Hypothenuse of a right-angled Triangle, is equal to the two Squares of the other Sides. A Problem is fomething propofed to be done as to make a Circle pass thro' three given Points. A Lemma is a Propofition laid down only for demonstrating fome following Propofition more eafily. A Corollary is a Confequence deduced from a foregoing Propofition. A Scholium is a Critical Expofition upon something faid before. Poftulates or Petitions. 1. Grant that a right Line may be drawn from any Point to any other Point. 2. That a finite right Line may be drawn out at pleasure. 3. That a Circle may be defcribed about any Centre with any Distance. Axioms. 1. Things equal to the fame third Thing, are alfo equal the one to the other. As, if ABC; then is A= C: or therefore all the Quantities A, B, C, are equal the one to the other. Note. When you find several Quantities connected together after this manner, the first Quantity, or any of the intermediate ones, by virtue of this Axiom, is equal to the laft: in which cafe, for brevity's fake, we usually omit citing this Axiom, notwithstanding the Force of the Confequence depends upon it. 2. If to equal things you add equal things, the wholes fhall be equal. As if AB, and C=D; then shall A+CB+D. 3. If 3. If from equal things you take away equa things, the things remaining will be equal. As if A+CBD, and AB; then fhall C=D.. 4. If to unequal things you add equal things, the wholes will be unequal. As if AB and C=D; then fhall A +CB+D. 5. If from unequal things you take away equal things, the remainders will be unequal. As if A+CB+ D, and C=D: then fhall A = D. 6. Things which are the double of the fame third thing, or of equal things, are equal one to the other. Understand the fame of things that are the triple, quadruple, &c. of the fame thing. As if A 2 B, and C 2 B: then fhall AC. = 7. Things which are the half of the one and the fame thing, or of equal things, are equal the one to the other; conceive the fame of things. that are the one third, one fourth of the fame thing. As if AB, and C = B: then fhall AC. 8. Things which agree together, or coincide, are equal the one to the other. The Converfe of this Axiom is true in right Lines and Angles, but not in Figures, unless they be fimilar. Moreover, Magnitudes are faid to agree, or coincide, when the parts of the one being apply'd to the parts of the other, they fill up an equal, or the fame Space. 9. Every Whole is greater than its Part. 10. Two right Lines cannot have one and the fame Segment (or Part) common to them both. 11. Two |