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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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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...assumed the truth of this proposition, and it seems almost impossible to do otherwise. PROP. IV. THEOREM. If a straight line stand at right angles to each of two straight lines at the point of their intersection, it is at rigid angles to the plane in, which they arc. Let the straight...
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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855
...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 (d):...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 460 pages
...intersection of the two planes is in a straight line. THEOREM Iv. If a straight line is perpendicular to each of two straight lines at their point of intersection^ it is perpendicular to the plane of these lines. Let AP be perpendicular to the two lines PB, PC, at their...
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Report of Her Majesty's Civil Service Commissioners: Together with ..., Volume 3

1858
...between its points of contact is a mean proportional between the diameters. BOOK XI. 10. PROP. IV. — 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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Parliamentary Papers, Volume 25

Great Britain. Parliament. House of Commons - Bills, Legislative - 1858 - 690 pages
...between its points of contact is a mean proportional between the diameters. BOOK XI. 10. PROP. IV. — 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 and Conic Sections

Elias Loomis - Conic sections - 1858 - 234 pages
...common section. Hence, if two planes, &c. PROPOSITION IV. THEOREM. If a straight line be perpendicular to each of two straight lines at their point of intersection, it will be perpendicular to the plane in which these lines are. Let the straight line AB be perpendicular to...
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A complete practical guide to her majesty's Civil service, by a certificated ...

Civil service - 366 pages
...between its .points of contact is a mean proportional between the diameters. BOOE XI. PROP. IV.— 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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Government examinations, a companion to 'Under government' and a key to the ...

Joseph Charles Parkinson - 1860
...between its points of contact is a mean proportional between the diameters. BOOK XI. 10. PROP. IV. — 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 Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860 - 396 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 (d)...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 443 pages
...intersection of the two planes is in a straight line. THEOREM IV. If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of these lines. Let AP be perpendicular to the two* lines PB, PC, at...
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