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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 Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 518 pages
...angles to the plane HGK. r~ Therefore AB, CD are each of CK n them at right angles to the plane HGK. But if two straight lines be at right angles to the same plane, they shall be parallel6 to one another. Therefore AB is c 6. 11. parallel to CD. Wherefore, two straight lines, &c....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 320 pages
...in one and the same plane. Therefore, if three straight lines, &c. QED j PROP. VI. THEOR. a 48. 1. f IF two straight lines be at right angles to the same plane they will be parallel to each other. Let the straight lines AB, CD be at right angles to the same plane...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1810 - 518 pages
...angles to the plane HGK. ~ Therefore AB, CD are each of ^ them at right angles to the plane HGK. But if two straight lines be at right angles to the same plane, they shall be parallelę to one another. Therefore AB isc6. 11. parallel to CD. Wherefore, two straight lines, &c. QED PROP. X. THEOR. IF two...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814 - 558 pages
...and the same plane. Therefore, if three straight PROP. VI. THEOR. if two straight lines be alright angles to the same plane, they shall be parallel to one another. Let them meet the plane in the points B, D, and draw the straight line BD, to which draw DE at right angles,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pages
...BD, BE arę in one and the same plane. Therefore, if three straight lines, 8cc. QED PROP. 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 dnlw the straight line BD, to which...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 pages
...lines, &c. Q, ED 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 ię parallel to CD-. Draw DE at right A B I) Let them meet the plane in the points B, D. angles...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Circle-squaring - 1819 - 348 pages
...lines, &c. Q,. ED PROP. VI. THEOR. Two straight lines which are at right angles to the same plane, arc parallel to one another. Let the straight lines AB, CD be at right angles to the snme plane BDE ; AB is parallel to CD. Let them meet the plane in the points B, D. Draw DE at angles...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1821 - 514 pages
...right angles to the plane HGK. Therefore AB, CD are each of them at right angles to the plane HGK. But if two straight lines be at right angles to the same plane, they shall be parallel ((?. H.) to one another. Therefore AB is parallel toCD. Wherefore, two straight lines, &c. QED i PROP....
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...is impossible : Therefore the straight line BC is not above the plane in which are BD and PROP. VI. THEOREM. If two straight lines be at right angles...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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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...BD, BE are in one and the same plane. Therefore, if three straight lines, &c. QED PROP. VI. THEOR. If two straight lines be at right angles to the same...AB shall be parallel to CD. Let them meet the plane in the points B, D, and draw the straight line BD, to t u. 1. which drawf DE at right angles, in the...
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