| Benjamin Greenleaf - Geometry - 1863 - 502 pages
...them. Therefore, the common section of the two planes AB, CD is a straight line. PROPOSITION IY. — **THEOREM. 401. If a straight line is perpendicular...intersection, it is perpendicular to the plane in** ivhich the two lines lie. Let the straight line AB be perpendicular to each of the straight lines CD,... | |
| Adrien Marie Legendre - Geometry - 1863 - 464 pages
...straight line ; which was to be proved. PROPOSITION IY. THEOREM. If a straight line is perpendicular to **two straight lines at their point of intersection, it is perpendicular to the plane** of those lines. AP be perpendicular to every line of the plane which pusses through P, and consequently,... | |
| Eli Todd Tappan - Geometry, Modern - 1864 - 292 pages
...points are all in one straight line (59). PERPENDICULAR LINES. 517. Theorem — A straight line which **is perpendicular to each of two straight lines at their point of intersection,** is perpendicular to every other straight line which lies in the plane of the two, and passes through... | |
| James Robert Christie - Mathematics - 1866 - 426 pages
...through the point of contact will cut off similar segments. 4. If a straight line stand at right angles **to each of two 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... | |
| Eli Todd Tappan - Geometry - 1868 - 432 pages
...are all in one straight line (59). PERPENDICULAR LINES. •»17. Theorem. — A straight line which **is perpendicular to each of two straight lines at their point of intersection,** is perpendicular to every other straight line which lies in the plane of the two, and passes through... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...these points; the straight line AP will be the required perpendicular. PROPOSITION V.— THEOREM. 13. **If a straight line is perpendicular to each of two...of intersection, it is perpendicular to the plane** of those lines. Let AP be perpendicular to PB and PC, at their intersection P; then, AP is perpendicular... | |
| Edinburgh univ - 1871 - 392 pages
...similar triangle whose area is threefourths of the former. 7. If a straight line be at right angles **to each of two straight lines at their point of intersection, it is** at right angles to their plane. 8. Prove the inequality — x* +y* + z*>xy + xz +yz. 9. Solve the equations... | |
| William Chauvenet - Geometry - 1872 - 382 pages
...these points; the straight line AP will be the required perpendicular. PROPOSITION V.— THEOREM. 13. **If a straight line is perpendicular to each of two...of intersection, it is perpendicular to the plane** of those lines. Let AP be perpendicular to PB and PC, at their intersection P; then, AP is perpen.... | |
| Manchester univ - 1872 - 380 pages
...circumscribing circle, one of these lines is equal to the sum of the other two. 6. 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. 7. Define parallel planes. Prove that two planes... | |
| Charles Davies - Geometry - 1872 - 464 pages
...line ; which, was to be proved. • PROPOSITION IV. THEOREM. If a straight line is perpendicular to **two straight lines at their point of intersection, it is perpendicular to the plane** of those lines. AP be perpendicular to every straight line of the plane which passes through P, and... | |
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