Elements of Geometry and Trigonometry: With NotesOliver & Boyd, 1822 - 367 sider |
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Side 196
... cylinder's base ; H the altitude ; let surf . CA , repre- sent the area of the circle whose radius is CA : we are to shew that the solidity of the cylin- H der is surf . CA × H. For , if surf . CAXH is not the measure of the given cylinder ...
... cylinder's base ; H the altitude ; let surf . CA , repre- sent the area of the circle whose radius is CA : we are to shew that the solidity of the cylin- H der is surf . CA × H. For , if surf . CAXH is not the measure of the given cylinder ...
Side 197
... cylinder , being contain- ed in it ; hence the base of a cylinder , multiplied by its altitude , cannot be the measure of a greater cylinder . Hence finally , the solidity of a cylinder is equal to the pro- duct of its base by its ...
... cylinder , being contain- ed in it ; hence the base of a cylinder , multiplied by its altitude , cannot be the measure of a greater cylinder . Hence finally , the solidity of a cylinder is equal to the pro- duct of its base by its ...
Side 198
... cylinder and that of the prism may be considered as having the same length , since every section made in either ... cylinder might be shewn to be less than that of any circumscribed prism BCDKLKH . ( See the fig . of Def . 6 ...
... cylinder and that of the prism may be considered as having the same length , since every section made in either ... cylinder might be shewn to be less than that of any circumscribed prism BCDKLKH . ( See the fig . of Def . 6 ...
Side 199
... cylinder is inscrib- ed in the prism : hence the convex surface of the prism must be less than that of the inscribed cylinder . On the other hand ( 3. VIII . ) it is greater ; hence our hypothesis was false : hence , in the first place ...
... cylinder is inscrib- ed in the prism : hence the convex surface of the prism must be less than that of the inscribed cylinder . On the other hand ( 3. VIII . ) it is greater ; hence our hypothesis was false : hence , in the first place ...
Side 201
... cylinder having the same base and the same altitude ; whence it follows , 1. That cones of equal altitudes are to each other as their bases ; 2. That cones of equal bases are to each other as their alti- tudes ; 3. That similar cones ...
... cylinder having the same base and the same altitude ; whence it follows , 1. That cones of equal altitudes are to each other as their bases ; 2. That cones of equal bases are to each other as their alti- tudes ; 3. That similar cones ...
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Elements of Geometry and Trigonometry from the Works of A. M. Legendre A. M. Legendre Ingen forhåndsvisning tilgjengelig - 2017 |
ELEMENTS OF GEOMETRY & TRIGONO A. M. (Adrien Marie) 1752-183 Legendre Ingen forhåndsvisning tilgjengelig - 2016 |
ELEMENTS OF GEOMETRY & TRIGONO A. M. (Adrien Marie) 1752-183 Legendre Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
AC² adjacent adjacent angles altitude angle ACB angle BAC centre chord circ circle circular sector circumference circumscribed common cone consequently construction continued fraction convex surface cos² cosine cylinder demonstration determined diagonal diameter draw drawn equal angles equation equivalent faces figure formulas frustum greater homologous sides hypotenuse inclination inscribed intersection isosceles join less likewise manner measure multiplied number of sides opposite parallel parallelepipedon parallelogram perpendicular plane MN polyedron prism PROBLEM Prop PROPOSITION quadrilateral quantities radii radius ratio rectangle rectilineal triangle regular polygon right angles right-angled triangle SABC Scholium sector segment shew shewn side BC similar sin² sines solid angle sphere spherical polygon spherical triangle square straight line suppose tang tangent THEOREM third side three angles three plane angles triangle ABC triangular pyramids vertex vertices
Populære avsnitt
Side 152 - AMB be a section, made by a plane, in the sphere, whose centre is C. From the...
Side 24 - THEOREM. In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs.
Side 22 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Side 62 - Similar triangles are to each other as the squares of their homologous sides.
Side 211 - If two angles of one triangle are equal to two angles of another triangle, the third angles are equal, and the triangles are mutually equiangular.
Side 187 - Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases.
Side 140 - AT into equal parts .Ax, xy, yz, &c., each less than Aa, and let k be one of those parts : through the points of division pass planes parallel to the plane of the bases : the corresponding sections formed by these planes in the two pyramids will be respectively equivalent, namely, DEF to def, GHI to ghi, &c.
Side 150 - The radius of a sphere is a straight line, drawn from the centre to any point...
Side 168 - THEOREM. The surface of a spherical triangle is measured by the excess of the sum of its three angles above two right angles, multiplied by the tri-rectangular triangle.
Side 135 - XII.) ; in like manner, the two solids AQ, AK, having the same base, AOLE, are to each other as their altitudes AD, A M.