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" If a straight line stand at right angles to each of two straight lines at the point of their intersection, it shall also be at right angles to the plane which passes through them, that is, to the plane in which they are. "
Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... - Page 133
by Dennis M'Curdy - 1846 - 138 pages
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

Mathematics - 1835
...and perpendicular straight line. A straight line when said to be perpendicular to a plane , . 125 (a) If a straight line stand at right angles to each of two other straight lines at their point of intersection, it shall be at right angles to the plane in which...
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Solutions of the Cambridge Problems, from 1800 to 1820, Volume 2

John Martin Frederick Wright - Mathematics - 1836 - 776 pages
...perpendiculars from the angular points. EUCLID, BOOK XI. 1817. 1 . DEFINE the five regular solid figures. 2. If a straight line stand at right angles to each of two straight lines in the point of their intersection, it shall also be at right angles to the plane which passes through...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 472 pages
...are in one plane. III. If two planes cut one another, their common section is a straight line. IV. If a straight line stand at right angles to each of two straight lines in their point of intersection, it will also be at right angles to the plane in which these lines are....
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Solid and Spherical Geometry and Conic Sections: Being a Treatise on the ...

A. Bell - Conic sections - 1837 - 164 pages
...common to the planes AB and BC, or it is the common section of these planes. PROPOSITION IV. THEOREM. If a straight line stand at right angles to each of two straight lines in the point of their intersection, it will also be at right angles to the plane in which these lines...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - Geometry - 1837 - 410 pages
...straight line.* Therefore, if two planes, &c. PROP. IV. THEOR. IF a straight line be perpendicular to each of two straight lines at their point of intersection, it is also perpendicular to the plane in which they are. Let the straight line EF be perpendicular to...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 378 pages
...the planes AB, BC cannot but be a straight line. Wherefore, if two planes, &c. QED PROP. IV. THEOR. If a straight line stand at right angles to each of two straight lines in the point of their intersection, it shall also be at right angles to the plane which passes through...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...therefore common to the planes AB and BC, or it is the common section of these planes. PROP. IV. THEOR. If a straight line stand at right angles to each of two straight lines in the point of their intersection, it will also be at right angles to the plane in which these lines...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 320 pages
...planes AB and BC, or it is the common section of these planes. Therefore, &c. QED PROP. IV. THEOR. IF a straight line stand at right angles to each of two straight lines in the point of their intersection: it will also be at right angles to the plane in which these lines...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 544 pages
...AF is perpendicular to DE ; therefore AF is perpendicular to each of the straight lines GH, DE. But if a straight line stand at right angles to each of two straight lines in the point of their intersection, it is also at right angles to the plane passing through them :...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...AF is perpendicular to DE ; therefore AF is perpendicular to each of the straight lines GH, DE. But if a straight line stand at right angles to each of two straight lines in the point of their intersection, it shall * 4. 11. also be at right angles* to the plane passing...
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