| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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 :... | |
| 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 :... | |
| 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,... | |
| 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... | |
| 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... | |
| 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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