Plane and solid geometry . pre-sent lines perpendicular to a plane, and strings to represent oblique lines,any figure may be actually made with a comparatively small expenditureof time and with practically no expense. Eor reproductions of modelsactually made by high school students, see group on p. 302 ; also §§ 622,633, 678, 756, 762, 770, 797. 606. Assumption 20. Revolution postulate. A plane mayrevolve about a line in it as an axis, and as it does so revolve, itcan contain any particular point in space in one and only oneposition. 607. From the revolution postulate it follows that:Through a
Plane and solid geometry . pre-sent lines perpendicular to a plane, and strings to represent oblique lines,any figure may be actually made with a comparatively small expenditureof time and with practically no expense. Eor reproductions of modelsactually made by high school students, see group on p. 302 ; also §§ 622,633, 678, 756, 762, 770, 797. 606. Assumption 20. Revolution postulate. A plane mayrevolve about a line in it as an axis, and as it does so revolve, itcan contain any particular point in space in one and only oneposition. 607. From the revolution postulate it follows that:Through a given straight line any nuinber of planes may he passed. For, as plane MN revolves about AB as an axis (§ 606) itmay occupy anunlimited num-ber of positionseach of whichwill represent adifferent planethrough AB. 608. Def. A plane is said to be determined by given condi-tions if that plane and no other plane fulfills those conditions. 609. From §§ 607 and 608 it is seen that:A straight line does not determine a Ex. 1153. IIow many planes may be passed through any two pointsin space ? why ? Ex. 1154. At a point P in a given straight line AB in space, con-struct a line perpendicular to AB. IIow many such lines can be drawn ? BOOK VI 301 LINES AND PLANESProposition I. Theorem 610. A plane is determined hy a straight line and apoint not in the line.
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
