 Through a given point, to draw a straight line parallel to a given straight line. See Fig. 36; also 4 of Plate I. CONSTRUCTION. — Let P be the given point, and AB the given straight line 3|  Elementary geometrical drawing - Page 4by Samuel H. Winter - 1859 - 32 pagesFull view - About this book
 | Proclus - Mathematics - 1992 - 432 pages
...will both be parallel to the same line, and we come to the original theorem. XXXI. Through a given point to draw a straight line parallel to a given straight line. It was necessary for us not only to be taught in the Elements the essential properties of parallel... | |
 | Nick Huggett - Philosophy - 1999 - 292 pages
...[CN 1]; and they are alternate. Therefore AB is parallel to CD. QED PROPOSITION 31 Through a given point to draw a straight line parallel to a given straight line. [Fig. 2.4] Let A be the given point, and BC the given straight line; thus it is required to draw through... | |
 | Reinhard Laubenbacher, David Pengelley - Mathematics - 2000 - 292 pages
...parallel to the same straight line are also parallel to one another. PROPOSITION 31 . Through a given point to draw a straight line parallel to a given straight line. Lei A be the given point, and BC the given straight line; thus it is required to draw through the point... | |
 | Patrick Maynard - Art - 2005 - 300 pages
...of drawing operations. Thus, for example, Euclid's famous Proposition 31 of Book I, "Through a given point to draw a straight line parallel to a given straight line," includes in its proof the phrases "be constructed" and "has been drawn," and such is fairly typical.... | |
 | Euclid - 454 pages
...angle ABC; and hence the angle DEF is supplementary to the angle ABC. PROPOSITION 31. Through a given point to draw a straight line parallel to a given straight line. Let A be the given point, and BC the given straight line ; thus it is required to draw through the point... | |
 | Peter M. Engelfriet - Mathematics - 1998 - 516 pages
...original, for it only mentions two lines. 3 1 . - s; ± # if a » m ft is a » ¥ \ T Heath Through a given point to draw a straight line parallel to a given straight line. Note that the Chinese says "on a point". (Added: from this theorem is bom a practical method. Given... | |
 | Edinburgh Mathematical Society - Electronic journals - 1887 - 162 pages
...Join CE, and from C draw CF perpendicular toCE. OF is the perpendicular required. 6. Through a given point to draw a straight line parallel to a given straight line. Euclid I. 31. Let AB be the given straight line, C the given point. From B draw BD perpendicular to... | |
 | James McMahon - 2018 - 244 pages
...line joining their extremities is parallel to the given line . . 136 CONSTRUCTION. Through a given point to draw a straight line parallel to a given straight line .... 138 CONSTRUCTION. To draw a straight line parallel to a given straight line and at a given distance... | |
 | Edinburgh Mathematical Society - Electronic journals - 1894 - 168 pages
...to make an angle equal to a given angle. The construction may be effected by I. 31. Through a given point to draw a straight line parallel to a given straight line. The construction is frequently effected by The following method is due to Mr Gaston Tarry. FIGURE 3.... | |
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