Elements of geometry / from the Latin translation of Commandine. To which is added, a treatise of the nature of arithmetic of logarithms, likewise another of the elements of plain and spherical trigonometry; with a preface ... By Doctor John Keil ... The whole revised ... [with a] preface, by Samuel Cunn.

  • Euclid
Date:
1741
Catalogue details

Licence: Public Domain Mark

Credit: Elements of geometry / from the Latin translation of Commandine. To which is added, a treatise of the nature of arithmetic of logarithms, likewise another of the elements of plain and spherical trigonometry; with a preface ... By Doctor John Keil ... The whole revised ... [with a] preface, by Samuel Cunn. Source: Wellcome Collection.

    140/465 (page 107)
    PROPOSITION VIII, t * * \ Problem. %o defcribe a Circle in a given Square, TT E T the given Square be A B C D. It is required to defcribe a Circle within the fame. Bifed * the Sides A B, A D, in the Points F, E; * 10. t. and draw f E H thro’ E, parallel to A B, or DC- and f 3 x. u F K thro’' F, parallel f to B C, or A D. Then A K, K B, A FI, H D, AG,GC,BG,G D, are all Parallelo¬ grams, and their oppofite Sides are £ equal. ' And be- | 34« *• caufe DA is equal to AB, and AE is'half of AD,; and At half of AB, AE fhall be equal to AF; but the oppofite Sides are alfo equal. Therefore FG is equal to G E. In like manner we demonftrate, that G FI, or G K, is equal to either F G, or G E. There¬ fore GE, GF, GH, GK, are equal to each other: And fo a Circle being defcribed about the Centre G, with either of the Diftances GE, G F, GH, GK, will alfo pafs thro’ the other Points, and ilia'll touch the Sides AB, BC, CD, D A, becaufe the A ngles at E, F, H, K, are |Right Angles. For if the Circle fhould cut the Sides of the Square, a Right Line, drawn from the End of the Diameter of a Circle at Right Angles, will fall within the Circle; which is * abfurd. Wherefore a Circle defcribed about the * l6* 34 Centre G, with either of the Diftances GE, GF, GH, GK, will not cut AB, BC, CD, DA, the Sides of the Square. Wherefore it fliall neceffariiy toucn them, and will be defcribed in the Square A BCD; which was to he done. PROPOSITION IX. * ' , i ■ Problem. €To defcribe a Circle about a Square given, ' • t • \ • • \ ' T ET ABCDbea Square given. It is required to ; circumfcribe a Circle about the fame. Join AC, BD, mutually cutting one another in the Point E. , And