 | William Chauvenet - Geometry - 1871 - 380 pages
...unequal oblique lines, the greater meets the plane at the greater distance from the perpendicular. 12. Corollary II. Equal straight lines from a point...AP will be the required perpendicular. PROPOSITION V.— THEOREM. 13. If a straight line is perpendicular to each of two straight lines at their point... | |
 | Aaron Schuyler - Geometry - 1876 - 384 pages
...the plane. In this case, the plane is oblique to the line. 8. The projection of a point on a plane is the foot of the perpendicular from the point to the plane. 9. The projection of a line on a plane is the locus of the projections of all its points. 10. The angle... | |
 | George Albert Wentworth - Geometry - 1877 - 436 pages
...points of either be equally distant from the other. 435. DEF. The Projection of a point on a plane is the foot of the perpendicular from the point to the plane. 436. DEF. The projection of a line on a plane is the locus of the projections of all its points. 438.... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...when it is neither perpendicular nor parallel to the plane. 6. The Projection of a Point on a plane is the foot of the perpendicular from the point to the plane. E 7. The Projection of a Line on a plane is the straight line joining the projections of its extremities.... | |
 | Edward Olney - Geometry - 1883 - 352 pages
...sufficiently produced), but is not perpendicular to the plane. 464. The Projection of a Point on a plane is the foot' of the perpendicular from the point to the plane. PROPOSITION XI. 466. Theorem.—The projection of a straight line upon a plane is a straight line.... | |
 | George Bruce Halsted - Geometry - 1885 - 389 pages
...line.) THEOREM XV. 598. Equal obliques from a point to a plane meet the plane in a circle whose center is the foot of the perpendicular from the point to the plane. HYPOTHESIS. AB, AC, equal sects from A to the plane MN. AD _L plane MN. CONCLUSION. DB — DC. PROOF.... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...tu:o right diedml angles; and conversely. 252 482. DEFINITIONS. The projection of a point on a plane is the foot of the perpendicular from the point to the plane. The projection of a line on a plane is the locus (§ 39) of the projections of its points. 483. The... | |
 | George Albert Wentworth - 1886 - 322 pages
...=OPcos6=p cos 6. We readily obtain also tan 0 = - , tan </, = -. 220. The Projection of a point on a plane is the foot of the perpendicular from the point to the plane. The perpendicular itself is the Projector of the point. Thus, the point JV(Fig. 97) is the projection... | |
 | William Chauvenet - Geometry - 1888 - 826 pages
...meets the plane at the greater distance from the perpendicular. 12. Corollary II. Equal straight liu&s from a point to a plane meet ^/ the plane in the circumference...AP will be the required perpendicular. PROPOSITION V.— THEOREM. 13. If a straight line is perpendicular to each of two straight lines at' their point... | |
 | Seth Thayer Stewart - Geometry, Modern - 1891 - 422 pages
...the plane. Conclusion : AB being any line perpendicular, etc. 431. A projection of a point on a plane is the foot of the perpendicular from the point to the plane ; the projection of a line on a plane is the locus of the projections of its points. PROPOSITION III.... | |
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The projection of a point on a plane is the foot of the perpendicular from the point to the plane. The projection of a figure upon a plane is the locus of the projections of all the points of the figure upon the plane. Thus, A'B' represents the projection... 
