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" 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 : it is required to draw through the point A a straight line parallel to BC. "
New Elementary Geometry: With Practical Applications : a Shorter Course Upon ... - Page 62
by Benjamin Greenleaf - 1874 - 176 pages
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Geometrical Drawing ; Mechanical Drawing ; Ship Drafting ; Sketching ...

Freehand technical sketching - 1918 - 1098 pages
...the arc PED in D. The line joining the points P and D will be perpendicular to A B. PROBLEM 4. — Through a given point, to draw a straight line parallel to a given straight line. See Fig. 6; also Problem 4 of Plate I. A CONSTRUCTION. — Let P be the given point and AB the given...
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Geometrical Drawing, Mechanical Drawing, Sketching, Practical Projection ...

Drawing - 1920 - 698 pages
...D. The line joining the points P and D will be perpendicular to A B. PROBLEM 4. — Through */ ' }C a given point, to draw a straight line parallel to a given straight line. See Fig. 6; also Problem 4 of Plate I. ACONSTRUCTION. — L 6 1 P FIG. 5 FIG. 6 an arc CD intersecting...
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The Teaching of Geometry in Schools: A Report Prepared for the Mathematical ...

Mathematical Association - Geometry - 1923 - 88 pages
...interior and opposite angle, and the interior angles on the same side equal to two right angles. I. 31 : Through a given point to draw a straight line parallel to a given straight line. I. 32 : In any triangle, if one of the sides be produced, the exterior angle is equal to the two interior...
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Manual of the Public Examinations Board

University of Adelaide. Public Examinations Board - Examinations - 1928 - 1280 pages
...line from a given point without it or upon it; (d) To con struct an angle equal to a given angle; (e) Through a given point to draw a straight line parallel to a given straight lino; (/) The con atruetion of a triangle from any of the following data: (i) Given the three sides;...
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A Source Book in Medieval Science

Edward Grant - History - 1974 - 890 pages
...Thus, the denial of the consequent implies the denial of the antecedent; therefore, 13. Which reads : "Through a given point to draw a straight line parallel to a given straight line." and so on. Indeed, one should even say in general that the whole of Book X of Euclid overthrows the...
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The Foundations of Geometry and the Non-Euclidean Plane

G.E. Martin - Mathematics - 1997 - 536 pages
...angles. 30. Straight lines parallel to the same straight line are also parallel to one another. 31. Through a given point to draw a straight line parallel to a given straight line. 32. In any triangle, if one of the sides be produced, the exterior angle is equal to the two interior...
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A Commentary on the First Book of Euclid's Elements

Proclus - Mathematics - 1992 - 432 pages
...the other parallel 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...
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The Poincaré Half-plane: A Gateway to Modern Geometry

Saul Stahl - Geometry, Non-Euclidean - 1993 - 320 pages
...his logical edifice. Proposition 2. To place at a given point (as an extremity) a straight line equal to a given straight line. Let A be the given point and BCthe given straight line (Fig. 1.2). Thus it is required to place at the point A (as an extremity)...
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Mathematical Expeditions: Chronicles by the Explorers

Reinhard Laubenbacher, David Pengelley - Mathematics - 2000 - 292 pages
...Straight lines 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...
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Space from Zeno to Einstein: Classic Readings with a Contemporary Commentary

Nick Huggett - Philosophy - 1999 - 292 pages
...to the angle, GKD [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...
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