The Triangle DEO will be composed of three Right Lines equal to the three Right Lines given. AA, BB, CC. Obferve, that of three Right Lines given, two of them taken together must neceffarily be greater than the Third, otherwise they could not make a Triangle. PROPOSITION III. To draw a Square upon a Right Line given of Plate 3. Fig. a determined Length. 3. Let AB be the Right Line given, of a determined Length, apon which a Square is to be formed. ABCD will be the Square required, formed upon the Right Line given, AB. PROPOSITION IV. To draw a Regular Pentagon upon a Right Plate 3. Fig. Line given. 4. Let AB be the Line given, upon which a regular Pentagon is to be formed, PRAC PRACTICE. From the Extremity Describe the Arch Extending the Compaffes to the Extremity B B. 1. P. 2. Raife the Perpendicular BDF. AC Then divide the Circumference of this Circle into five Parts of an equal Length with the Line AB, and you will have the Regular Equiangular Equilinear Pentagon ABFGH. PROPOSITION V. . To draw a Regular Hexagon upon a Right Line given. Let AB be the Right Line upon which an Hexagon is to Divide this Circle into fix Parts of an equal Length with the Line AB, and you will have the Regular Hexagon, ABEFGD, formed upon the Right Line given AB. PROPOSITION VI. Upon a Right Line given, to defcribe whatever Polygon you have a mind, from the Hexagon to the Dodecagon. Let AB be the Line, upon which is to be formed an Hexagon, an Heptagon, or an Octagon, &c. PRA PRACTICE. Divide the Line AB equally in two at Raife the Perpendicular From the Point B defcribe the Arch 0 OI B. 1. P. 6. AC Divide AC into fix equal Parts MNPQR This you must do if your Defign is to make an Heptagon. From the Point C and the first Division CM Describe the Arch MD D will be the Center from whence to describe a Circle ca pable of containing seven times the Line AB. If you would make an Octagon, From the Point C, and the 2d Division CN NE E will be the Center from whence to describe a Circle capable of containing eight times the Line AB. If you would defcribe a Nonagon, you must take three Divifions CP, and fo of the others, always augmenting one Divifion. PROPOSITION VII. Upon a Right Line given, to draw whatever Polygon you pleafe, from 12, to one of 24 Sides. Let AB be the Line upon which a Polygon is to be formed. PRACTICE. Divide the Arch Into twelve equal Parts From the Point Take as many Divifions upon the Line AC C CA Di As will be neceffary, above twelve, to have as many vifions of its Circle as you require Sides. EXAMPLE. To make a Figure of fifteen Sides. From the Point And the third Divifion Describe the Arch с CE EO AC of 12, and EO of 3, will make together 15 Sides. From the Point Ŏ and the Space Describe the Arch From the Point And the Space OB BF F FA Defcribe a Circle, which will contain 15 times the given Line AB And fo of the other Sorts of Polygons. VOL. I. M PRO PROPOSITION VIII. Upon a Right Line given, to describe a Portion of a Circle capable of containing an Angle equal to an Angle given. Let AB be a Line of determined Length, upon which a Portion of a Circle is to be defcribed, capable of containing an Angle equal to the given Angle C. Raife the Perpendicular From the Section And the Space Defcribe the Portion of a Circle AEB The Angles which you shall make in this Portion of a Circle upon the Right Line given AB, will all be equal to the *Angle C. PROPOSITION IX. To find the Center of a given Circle. Let ABC be the given Circle whofe Center is to be found. B. 1. Prop. 6. Divide this Right Line In two, by the Line Alfo divide this Right Line Into two equal Parts at ABC AB DC CD F. The Point F will be the Center required of the Circle ABC. PRO |