Plane and solid geometry . Given pyramid F— ABODE and plane MN \\ base AD cuttingthe lateral edges in F, G, H, I, and ^T and the altitude in P. VB_VC_ ^ ^ — VG~ Vh ~ VP To prove: I. i^ VG VHII. FGHIJ^ ABODE. I. Argument 1. Through V pass plane RS II plane KL. 2. Then plane RS II plane MN. VA __ VB VB __ VC 3. VAVF VGVB VG VHVO VO VO . — = —, etc. VH VF ^t% • • ?^? VOVP = . Reasons 1. § 652. 2. § 654. 3. § 650. 4. § 54, 1. VG VH11. The proof of II is left as an exercise for the student. 757. Cor I. Ally section of a pyramid ])arallel to thebase is to tJw base as the square of its d
Plane and solid geometry . Given pyramid F— ABODE and plane MN \\ base AD cuttingthe lateral edges in F, G, H, I, and ^T and the altitude in P. VB_VC_ ^ ^ — VG~ Vh ~ VP To prove: I. i^ VG VHII. FGHIJ^ ABODE. I. Argument 1. Through V pass plane RS II plane KL. 2. Then plane RS II plane MN. VA __ VB VB __ VC 3. VAVF VGVB VG VHVO VO VO . — = —, etc. VH VF ^t% • • ?^? VOVP = . Reasons 1. § 652. 2. § 654. 3. § 650. 4. § 54, 1. VG VH11. The proof of II is left as an exercise for the student. 757. Cor I. Ally section of a pyramid ])arallel to thebase is to tJw base as the square of its distance thevertex is to the square of the altitude of the pyramid. Hint. Prove FCf yCr yp Aii- VB VO BOOK VII 353 758. Cor. II. If two pyramids having equal altitudasare cut hy planes parallel to their bases, and at equal dis-tances froin their vertices,the sections have the sameratio as the bases. Hint. Apply § 757 to eachpyramid. 759. Cor. III. // twopyramids have equiva- ^lent bases and equal
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
