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" If two straight lines be at right angles to the same plane, they shall be parallel to one another. Let the straight lines AB, CD be at right angles to the same plane : AB is parallel to CD. "
The Elements of Euclid for the Use of Schools and Colleges: Comprising the ... - Page 227
by Euclid, Isaac Todhunter - 1867 - 400 pages
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The Elements of Descriptive Geometry ...

Thomas Grainger Hall - Geometry, Descriptive - 1841 - 214 pages
...straight lines be perpendicular to a plane, they shall be parallel to each other. Let AB, ci>, be -L. to the same plane; AB shall be parallel to CD. Let them meet the plane in BD : join BD: draw DE -i- to BD, and in the same plane with it: make DE= AB: join BE, AE, AD. Then...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...BD, BE are in one and the same plane. Therefore, if three straight lines, &c. QED PEOP. VI. THEOR. IF two straight lines be at right angles to the same...lines AB, CD be at right angles to the same plane BDE : AB is parallel to CD. Let them meet the plane in the points B, D. Draw DE at right angles to...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...the same plane. PROP. VI. THEOR. Two straight lines which are at right angles to the same plane, are parallel to one another. Let the straight lines AB, CD be at right angles to the same plane BDE ; AB is parallel to CD. Let them meet the plane in the points B, D. Draw DE at right angles to...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...BC, BD, BE are in one and the same plane. Therefore, if three straight lines, &c. QED PROPOSITION VI. THEOREM. If two straight lines be at right angles...lines AB, CD be at right angles to the same plane. Then AB shall be parallel to CD. Let them meet the plane in the points B, D, and draw the straight...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...are in one and the same plane. Therefore, if three straight lines, &c. QED PROPOSITION VI. THEOR. — If two straight lines be at right angles to the same...lines AB, CD be at right angles to the same plane : AB is parallel to CD. Let them meet the plane, in the points B, D, and draw the straight line BD, to which...
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845 - 444 pages
...below it. Wherefore the three |« BC, BD, BE, are in one and the same plane. PROPOSITION LXXXIL — THEOREM. If two straight lines be at right angles to the same plane, they shall he parallel to one another. Let the \s AB, CD be at i* Ls to the same plane ; AB is || CD. Let them...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 382 pages
...BC, BD, BE are all in the sam« plane. Therefore, if three straight lines, eSzc. PROP. VI. THEOR. — If two straight lines be at right angles to the same plane, they are parallel to one another. Let the straight lines AB, CD be at right angles to the same plane BDE...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...straight lines, %c. QED PROP. VI. THEOR, If too straight lines be at right angles to the same plant, they shall be parallel to one another. Let the straight...AB shall be parallel to CD. Let them meet the plane in the points B, D, and join BD, to which draw DE at right angles, in the same plane ; make DE equal...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...the same plane. PROP. VI. THEOR. Two straight lines which are at right angles to the same plane, are parallel to one another. Let the straight lines AB, CD be at right angles to the same plane BDE ; AB is parallel to CD. Let them meet the plane in the points B, D. Draw DE at right angles to...
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An elementary course of mathematics, Volume 2

Samuel Hunter Christie - 1847 - 172 pages
...4). Wherefore, if from the foot of the perpendicular, &c.: which was to be proved. PROP. XVII. THEOR. If two straight lines, be at right angles to the same...parallel to one another. Let the straight lines AB, CD (fig. 24), meeting the plane MN in the points B and D, be at right angles to it: AB shall be parallel...
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