Elements of Geometry for the Use of Beginners
Elements of Geometry for the Use of Beginners
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II. The oblique lines AD and AC, meeting the plane at equal distances from the foot of the perpendi- cular, are equal.
Cor. III. From a given point to a given plane only one perpendicular can be drawn.
PEOPOSITIOK Y.
SQ. If from the foot of a perpendicular to a plame a line be drawn meeting at right angles a straight line of that plane, a line joining the point of their in- tersection with any poioit of the perpendicular will be perpendicular to the line of the plane.
Proof. Let AP be perpendic...ular to the plane JO^, and BC the given line at right ans^les with PQ. Talie QC=QB, and draw BP, CP, BA, CA, and AQ. The triangles PBQ and PCQ will be equal, for they have equal sides about a right angle ; hence PC = PB. The triangles APB and APC will also be equal, for they, too, have equal sides about a right 0EOMETRY.
75 angle ; hence AB = AC Consequently the triangle ABC is isosceles, and the line AQ which bisects its base BC is perpendicular to BC (ISTo. 14, Cor. ) Q. E. D.
Cor. The line BCis perpendicular to the plane of the triangle APQ ; for it is perpendicular to the two lines P^ and ^(g (No.
What to read after Elements of Geometry for the Use of Beginners?
You can find similar books in the "Read Also" column, or choose other free books by Joseph Bayma to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
II. The oblique lines AD and AC, meeting the plane at equal distances from the foot of the perpendi- cular, are equal.
Cor. III. From a given point to a given plane only one perpendicular can be drawn.
PEOPOSITIOK Y.
SQ. If from the foot of a perpendicular to a plame a line be drawn meeting at right angles a straight line of that plane, a line joining the point of their in- tersection with any poioit of the perpendicular will be perpendicular to the line of the plane.
Proof. Let AP be perpendic...ular to the plane JO^, and BC the given line at right ans^les with PQ. Talie QC=QB, and draw BP, CP, BA, CA, and AQ. The triangles PBQ and PCQ will be equal, for they have equal sides about a right angle ; hence PC = PB. The triangles APB and APC will also be equal, for they, too, have equal sides about a right 0EOMETRY.
75 angle ; hence AB = AC Consequently the triangle ABC is isosceles, and the line AQ which bisects its base BC is perpendicular to BC (ISTo. 14, Cor. ) Q. E. D.
Cor. The line BCis perpendicular to the plane of the triangle APQ ; for it is perpendicular to the two lines P^ and ^(g (No.
What to read after Elements of Geometry for the Use of Beginners?
You can find similar books in the "Read Also" column, or choose other free books by Joseph Bayma to read onlineMoreLess
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