Plane and Solid Geometry: Suggestive MethodTracy, Gibbs, 1894 - 395 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 26.
Σελίδα 309
... PYRAMIDS . 439. A pyramid is a polyhedron all but one of whose faces meet in the same point . A The point in which all the faces but one meet is called the vertex . The face which does not pass through the vertex is the base . F The ...
... PYRAMIDS . 439. A pyramid is a polyhedron all but one of whose faces meet in the same point . A The point in which all the faces but one meet is called the vertex . The face which does not pass through the vertex is the base . F The ...
Σελίδα 311
... pyramid are proportional to the squares of the distances of the cutting planes from the vertex . ( See Art . 268. ) 449. COROLLARY II . In pyramids whose bases are equal in area and whose altitudes are equal , sections at equal ...
... pyramid are proportional to the squares of the distances of the cutting planes from the vertex . ( See Art . 268. ) 449. COROLLARY II . In pyramids whose bases are equal in area and whose altitudes are equal , sections at equal ...
Σελίδα 312
... pyramids having equal alti tudes and bases equal in area , are equal in volume . R 이 N M S S ' D CAL B B ' Let S - A B C and S ' - A'B'C ... pyramid S'- A'B'C ' .. SUG . 2. Compare the areas of the sections D 312 SOLID GEOMETRY .
... pyramids having equal alti tudes and bases equal in area , are equal in volume . R 이 N M S S ' D CAL B B ' Let S - A B C and S ' - A'B'C ... pyramid S'- A'B'C ' .. SUG . 2. Compare the areas of the sections D 312 SOLID GEOMETRY .
Σελίδα 314
... pyramid is one third the volume of a triangular prism having the same base and altitude . E B Let A - BCD represent a triangular pyramid . To prove that the volume of A - BCD is one third the volume of a prism having BCD for a base and ...
... pyramid is one third the volume of a triangular prism having the same base and altitude . E B Let A - BCD represent a triangular pyramid . To prove that the volume of A - BCD is one third the volume of a prism having BCD for a base and ...
Σελίδα 315
... pyramid . To prove that the volume of O - A B C D E is equal to one third the area of the base A B C D E multiplied ... pyramid O - ABCDE ? Therefore 454. COROLLARY I. If two pyramids have bases which are POLYHEDRONS . 315.
... pyramid . To prove that the volume of O - A B C D E is equal to one third the area of the base A B C D E multiplied ... pyramid O - ABCDE ? Therefore 454. COROLLARY I. If two pyramids have bases which are POLYHEDRONS . 315.
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
A B and C D A B C and D E F A B sustain A C equals adjacent angles altitude angles are equal apothem arc A B bisects chord circumference circumscribed Compare the ratios Compare Zs construct COROLLARY cylinder diagonal diameter dihedral angles distance draw drawn equal circles equal in area equally distant equals the ratio frustum Give auth given line given point Hence hypotenuse inscribed angle intersect isosceles triangle lateral area lateral edges Let A B C represent line A B locus middle point number of sides parallel lines parallelogram parallelopiped perimeter perpendicular plane M N polyhedron prism Prop PROPOSITION XVIII pyramid radii radius rectangle regular polygon respectively right angles right triangle SCHOLIUM segment slant height sphere spherical polygon spherical triangle subtended tangent THEOREM triangles A B C trihedral unit of measure vertex vertices volume
Δημοφιλή αποσπάσματα
Σελίδα 137 - The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
Σελίδα 48 - If two triangles have two sides of one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.
Σελίδα 138 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Σελίδα 59 - If two triangles have two sides of one equal to two sides of the other but the third side of the first greater than the thin!
Σελίδα 292 - ADC ; the last two are therefore right angles ; hence the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base, is perpendicular to the base, and bisects the vertical angle.
Σελίδα 211 - The projection of a point on a plane is the foot of the perpendicular from the point to the plane. The projection of a figure upon a plane is the locus of the projections of all the points of the figure upon the plane. Thus, A'B' represents the projection of AB upon plane MN.
Σελίδα 119 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Σελίδα 96 - It is read the ratio of a to b equals the ratio of c to d, or briefly, a is to b as c is to d.
Σελίδα 254 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism and whose vertices are the three...
Σελίδα 263 - That is, the lateral areas, or the total areas, of similar cylinders of revolution are to each other as the squares of their altitudes, or as the squares of the radii of their bases.