15. When a straight line HO, standing on anotherAB, makes the angle HOA eqnal to the angle HOB; each of these angles is called a right angle; and the line HO is said to be a perpendicular to AB. The measure of the angle HOA is 90 degrees, or the fourth part of 360 degrees. Hence a right angle is 90 degrees. 16, An acute angle is less than a right angle; as AOG, or GOH. 17. An obtuse angle is greater than a right angle; as GOB. 18. A plane Triangle is the space enclosed by three straight lines, and has three angles; as A. 19. A right angled Triangle is that which has one of its angles right; as ABC. The side BC, opposite the right angle is called the hypothenuse; the side AC is called the perpendicular; and the side AB is called the base, A B 20. An obtuse angled Triangle has one of its angles obtuse; as A. A 21. An acute angled Triangle has all its three angles acute, as in the figure A. 22. An equilateral Triangle has its three sides equal, and also its three angles; as C. C 23. An isosceles Triangle is that which has two of its sides equal, and the third side either greater or less than either of the equal sides; as D. 24. A scalene Triangle is that which has all its sides unequal; as E. E D 25. A quadrilateral figure is a space included by four straight lines. If its four angles be right, it is called a rectangular parallelogram. 26. A Parallelogram is a plane figure bounded by four straight lines, the opposite ones being parallel; that is, if produced ever so far, would never meet. 27. A Square is a four-sided figure, having all its sides equal, and all its angles right angles; as H. Η 28. An Oblong, or rectangle, is a right angled parallelogram, whose length exceeds its breadth; as I. I 29. A Rhombus is a parallelogram having all its sides equal, but its angles not right angles; as K. K 30. A Rhomboid is a parallelogram having its opposite sides equal, but its angles are not right angles, and its length exceeds its breadth; as M. 31. A Trapezium is a figure included by four straight lines, no two of which are parallel to each other; as N. M N A line connecting any two of its angles is called a diagonal. 32. A Trapezoid is a four-sided figure having two of its opposite sides parallel, but the remaining two not parallel; as F. F 33. Multilateral Figures, or Polygons, are those which have more than four sides. They receive particular names from the number of their sides. Thus, a Pentagon has five sides; a Hexagon, has six sides; a Heptagon, seven; an Octagon, eight; a Nonagon, nine; a Decagon, ten; an Undecagon, eleven; and a Duodecagon, has twelve sides. If all the sides of each figure be equal, it is called a regular polygon; but if unequal, an irregular polygon. B 34. The Diameter of a circle is a straight line passing through the centre, and terminated by the circumference; thus A B is the diameter of the circle. The diameter divides the circle into equal parts, each of which is called a semi-circle; the diameter also divides the circumerence into two equal parts, each A containing 180 degrees. Any line drawn from the centre to the circumference is called the radius, as A O, O B, or OS. If OS be drawn from the centre perpendicular to A B, it divides the semicircle into two equal parts, AOS and BOS, each of which is called a quadrant, or one-fourth of the circle; and the arcs AS and BS contain each 90 degrees, and they are said to be the measure of the angles A OS and BOS. S 35. A Sector of a circle is that part of the circle comprehended under two Radii, not forming one line, and the part of the circumference between them. From this definition it appears that a sector may be either greater or less than a semi-circle; thus AO B is a sector, and is less than a semi-circle ; and the remaining part of the circle is a sector also, but is greater than a semi-circle. Α. T B S 36. A Chord of an arc is a straight line joining its extremities, and is less than the diameter; TS is the chord of the arc T HS, or of the arc TABS. 37. A Segment of a circle is that part of the circle contained between the chord and the circumference, and may be either greater or less than a semi-circle; thus TSHT and TABST are segments, the latter being greater than a semicircle, and the former less. 38. Concentric circles are those having the same centre, and the space included between their circumferences is called a ring; as FE. F E PROBLEM I. To bisect a given straight line A B; that is, to divide it into two equal parts. From the centres A and B, with any radius, greater than half the given line A B, describe two arcs A intersecting each other at O and S, then the line joining O S will bisect A B. B PROBLEM II. Through a given point x to draw a straight line CD parallel to a given straight line A B. sy. Lay the extent or taken on the compasses from s to y; through a y draw C D, which will be parallel to A B. PROBLEM III. To draw a straight line CD parallel to A B, and at a given distance F, from it. touching these arcs at r and s, and it will be at the given distance from A B, and parallel to it. PROBLEM IV. To divide a straight line A B into any number of equal parts. H K G E F D B I Draw A K making any angle with A B; and through B draw BT parallel to A K; take any part A E and repeat it as often as there are parts to be in AB, and from the point B on the line BT, take BI, IS, SV, and V T equal to the parts taken on the line A K; then join AT, EV, GS, HI, and K B, will divide the line AB which V T into the number of equal parts required, as AC, CD, DF, FB. |