Plane and solid geometry . §309. 4. § 54, §309. 6. § 54, 11. 7. §309. 8. §337. 9. Args. 5 and 7. 10. §341. III. A full discussion of this problem will be found Id theAppendix, § 598. CONSTANTS AND VAEIABLES. LIMITS 346. Consider an isosceles triangle ABC, whose base is ACand whose altitude is LB. Keeping the base AC the sam» (con-stant), suppose the altitude to change (vary). If LB increases, what will be theeffect upon the lengths of AB and CB ?what the effect upon the base angles?upon the vertex angle ? Will the baseangles always be equal to each other?What limiting value have they ? I
Plane and solid geometry . §309. 4. § 54, §309. 6. § 54, 11. 7. §309. 8. §337. 9. Args. 5 and 7. 10. §341. III. A full discussion of this problem will be found Id theAppendix, § 598. CONSTANTS AND VAEIABLES. LIMITS 346. Consider an isosceles triangle ABC, whose base is ACand whose altitude is LB. Keeping the base AC the sam» (con-stant), suppose the altitude to change (vary). If LB increases, what will be theeffect upon the lengths of AB and CB ?what the effect upon the base angles?upon the vertex angle ? Will the baseangles always be equal to each other?What limiting value have they ? Is thebase angle related to half the vertexangle or are the two independent ?What relation is there ? Is this relationconstant or does it change ? Imagine the altitude of the triangle to diminish. Repeat thequestions given above, considering the altitude as is now the limiting value for the altitude ? what for thelength of one of the equal sides ? for the base angles ? for theangle at the vertex ?. Ex. 474. Consider an isosceles triangle with a constant altitude anda variable base. Repeat the questions given above. 138 PLANE GEOMETRY Ex. 475. Consider an isosceles triangle with constant base angles,but variable base. Tell what other constants and what other variablesthere would be in this case. Ex. 476. If through any point in the base of an isosceles trianglelines are drawn parallel to the equal sides of the triangle, a parallelo-gram will be formed whose perimeter will be constant; the perimeterwill be independent of the position of the point. 347. Def. A magnitude is constant if it does not changethroughout a discussion. 348. Def. A magnitude is variable if it takes a series ofdifferent successive values during a discussion. 349. Def. If a variable approaches a constant in such a waythat the difference between the variable and the constant maybe made to become and remain smaller than any fixed numberpreviously assigned, however small, the constan
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