fingly, than to have many of them together in one Cut *, because the Learner's Attention to the Proposition he is reading, will be interrupted not only by constantly taking his Eye off from the place he is reading, to view the Scheme, which will always be too distant, let the Cuts fold out never fo advantageously; but likewise by the other circumjacent Figures of the fame Cut, not to mention the Trouble of finding a Figure Sometimes. Nay, even a Mathematician of a Languid Taste, will lay a Book aside, rather than take the trouble of seeking out the Figure of a Propofition among a number all together in one Cut. * As in Taquet's Euclid, and the English Edition of Keil's Commandine's Euclid. An Characters used in this Treatise. = Signifies Equality, as A = B, or AB = BC; or AB=BC=CD; implies that A is equal to B, or AB equal to BC, or AB equal to BC equal to CD. Signifies Majority, as A B, or ABEC; implies, that A is greater than B, or AB greater thán BC. Signifies Minority, as AB, or AB BC; fignifies, that A is less than B, or AB less than BC. + Signifies, that the Quantities between which it is, are added or to be added, as A+B=C+D, implies that A added to B, is equal to Cadded to D; and ABCD = EF + GH+IK, fignifies that AB added to CD is equal to EF added to GH added to IK. - Signifies Substraction, or that the latter of the two Quantities it is between, is substracted from the former, as A - B or AB-CD, implies, that Bis substracted from A, or CD from AB; that is, A-B or AB-CD is the Difference of A and B, or of AB and CD. x Is the Sign of Multiplication, as AX B, or AB x BC, or ABX BC x CD fignifies, that A is multiply'd or drawn into B, or AB multiply'd or drawn into BC, or AB multiply'd by BC, multiply'd by CD. The conjunction of the Letters fignifies the same thing, as A × B = AB, or ABX BC=ABC. - 2 or ✓ Signifies the Side of a Square, as AB is the Square Root, or the Side of the Square AB. And 3 over one or more Quantities, fignifies the Square or Cube of them, as A or or AB or AB+ AC fignifies the Square of A, or of AB, or of AB+ AC. Understand the fame of the Cubes. 2 SCHOLIU M. Tho' a Point, strictly ta ken, has no Parts, or is of no Bigness; yet in Practice, there is a Neceffity of taking it of some Bigness, and that various, according to the Figure it is in or near: as upon Paper a Point is represented by a Prick with the Point of the Compaffes, a Dott with the Pen, &c. but on the Ground by a Peg, Stake, &c. And when we have occafion to mention it, we usually call it by the name of some Letter of the Alphabet, as the Point A. B 2, 2. A Line is Length without Breadth; as AB. A Line is made by moving or drawing a Point from one place to another: it being the Mark or Trace that that Point leaves behind it. As if I move or draw the. Point of my Compasses, Pen, or Pencil, &c. upon Paper; or a Peg, Stake, &c. upon the Ground, from the place or point A to B : then the Mark or Trace made thereby; which I call A B, is a Line, which will have fome Breadth and Thickness in Practice, because the Point defcribing it is of some Bignefs. 3. The Bounds of a Line are Points, as the Points A, B. 4. A Right Line is that which lies evenly between its Points. 5. A Superficies is that which has only Length and Breadth. SCHOLIUM. As the Motion of a Point makes a Line, so the Motion of a Line makes a Superficies. A B C6. The Bound or Bounds of a Superficies are one or more D Ltnes; as AB, BC, 7. A Plane Superficies is that which lies evenly between its Lines. : SCHOLIUM. A plane Superficies is that to which a right Line may be apply'd all manner of ways, or which is made by the Motion of a streight Line. B A 8. A Plane Angle is the Inclination of two right Lines to one another, that are in the Same Plane, and touch one another; yet not so that both of them be in the Same Direction: as ABC. An Angle is faid to be so much the less, the nearer the Lines that make it are to one ano BO A C ther. Take two Lines AB, BC, touching one another in B: then if A you conceive these two Lines to open like the Legs of a Pair of Compasses, so as always to remain fasten'd to one another in B, as by the Rivet of the Compasses, whilst the Extremity A moves from the Extremity C; you will perceive, that the more these Extremities move from each other, the greater shall the Angle between the Lines AB, BC be; and on the contrary, the nearer you bring them to one another, the leffer will the Angle be. D Whence it must be observed, that the Bigness of Angles does not confist in the bigness of the two Lines that form them, (which are called the Sides of the Angle) but in the bigness of their Inclination, or bowing to one another: for example, the Angle DAF is greater than the Angle CAB; thơ' the Lines or Sides AD, AF of the one are less than the Sides AC, A F C B |