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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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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - Geometry - 1860 - 453 pages
...— The truth of this proposition is implicitly assumed in the definitions of this Book. THEOREM III. If a straight line stand at right angles to each of two other straight lines at their point of intersection, it will be at right angles to the plane of those...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 520 pages
...planes AB, CD is a straight line. PROPOSITION IV. — THEOREM. 401. If a straight line is perpendicular to each of two straight lines, at their point of intersection, it is perpendicular to the plane in which the two lines lie. Let the straight line AB be perpendicular...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 514 pages
...planes AB, CD is a straight line. PROPOSITION IV. — THEOREM. 401. If a straight line is perpendicular to each of two straight lines, at their point of intersection, it is perpendicular to the plane in which the two lines lie. Let the straight line AB be perpendicular...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 320 pages
...AB, CD is a straight line. B 1> PROPOSITION IV. — THEOREM. 401. If a straight line is pcrpemlicular to each of two straight lines, at their point of intersection, it is perpendicular to the plane in which the two lines lie. Let the straight line AB be perpendicular...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 pages
...and AFis perpendicular to DE; therefore AFis 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's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...and AFis perpendicular to DE; therefore AFis 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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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...plane can he drawn through three points which are not on the same right line * . . . . . XI. 2. 3. 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 through them, that is,...
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A collection of elementary test questions in pure and mixed mathematics ...

James Robert Christie - Mathematics - 1866 - 404 pages
...internally, any straight line drawn through the point of contact will cut off similar segments. 4. If a straight line stand at right angles to each of...straight lines at their point of intersection, it shall also be at right angles to the plane which passes through them, that is, to the plane in which...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...AB and BC cannot but be a straight line. Wherefore, if t wo planes &c. QED PROPOSITION 4. THEOREM. 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...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...planes AB and EC cannot but be a straight line. Wherefore, if two planes &c. QED PROPOSITION 4. THEOREM. If a straight line stand at right angles to each of two straight lines at the -point of their intersection, it shall also lie at right angles to the plane which passes through...
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