Plane and solid geometry . 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 VI
Plane and solid geometry . 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 al-titudes, sections made by planes parallel to the bases, and at equal distances fromthe vertices, are Ex. 1275. Is every truncated pyramid a frustum of a pyramid? Isevery frustum of a pyramid a truncated pyramid? What is the lowerbase of a frustum of a pyramid ? the upper base ? the altitude ? Ex. 1276. Classify the figures whose faces are as indicated below : (a) one quadrilateral and four triangles ; (6) one square and four equal isosceles triangles ; (c) one pentagon and five triangles ; (d) two pentagons and five trapezoids; (e) two squares and four equal isosceles trapezoids ;(/) two regular hexagons and six rectangles. Ex. 1277. In the figure of § 758, if FP= 12, PO = 8, YA = 28,and VB = 25, find VF and VG, Ex. 1278. The base of a pyramid, whose altitude is 2 decimeters,contains 200 square centimeters. Find the area of a section 6 centimetersfrom the vertex ; 10 centimeters from the vertex. Ex. 1279. The altitude of a pyramid with square base is 16 inches ;the area of a section parallel to the base and 10 inches from the vertex is56^ square inches. Find th
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
