Elements of Plane and Solid GeometryGinn and Heath, 1877 - 398 σελίδες |
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Σελίδα viii
... . COMPARISON AND MEASUREMENT OF SPHERICAL SURFACES VOLUME OF THE SPHERE · 251 268 275 277 . 286 302 317 322 326 328 339 349 356 · 363 365 383 396 ELEMENTS OF GEOMETRY . BOOK I. RECTILINEAR FIGURES . INTRODUCTORY viii CONTENTS .
... . COMPARISON AND MEASUREMENT OF SPHERICAL SURFACES VOLUME OF THE SPHERE · 251 268 275 277 . 286 302 317 322 326 328 339 349 356 · 363 365 383 396 ELEMENTS OF GEOMETRY . BOOK I. RECTILINEAR FIGURES . INTRODUCTORY viii CONTENTS .
Σελίδα 286
... volume . 504. DEF . Equal polyhedrons are polyhedrons which have the same form and volume . ON PRISMS . 505. DEF . A Prism is a polyhedron two of whose faces are equal and parallel polygons , and the other faces are parallelo- grams ...
... volume . 504. DEF . Equal polyhedrons are polyhedrons which have the same form and volume . ON PRISMS . 505. DEF . A Prism is a polyhedron two of whose faces are equal and parallel polygons , and the other faces are parallelo- grams ...
Σελίδα 297
... in common are to each other as the products of their other two dimensions ) . Multiply these equalities together ; then P ахъхс P = a ' X U ' X c Q. E. D. PROPOSITION X. THEOREM . 538. The volume of a rectangular PRISMS . 297.
... in common are to each other as the products of their other two dimensions ) . Multiply these equalities together ; then P ахъхс P = a ' X U ' X c Q. E. D. PROPOSITION X. THEOREM . 538. The volume of a rectangular PRISMS . 297.
Σελίδα 298
... volume . We are to prove volume of P = axbx c . But P Ū P a x b x c = U IXIXI is the volume of P ; .. the volume of P = axbx c . $ 537 $ 500 Q. E. D. 539. COROLLARY I. Since a cube is a rectangular parallelo- piped having its three ...
... volume . We are to prove volume of P = axbx c . But P Ū P a x b x c = U IXIXI is the volume of P ; .. the volume of P = axbx c . $ 537 $ 500 Q. E. D. 539. COROLLARY I. Since a cube is a rectangular parallelo- piped having its three ...
Σελίδα 299
George Albert Wentworth. PROPOSITION XI . THEOREM . 542. The volume of any parallelopiped is equal to the product of its base by its altitude . G Ri N H E K B Let ABCD - F be a parallelopiped having all its faces oblique , and HR its ...
George Albert Wentworth. PROPOSITION XI . THEOREM . 542. The volume of any parallelopiped is equal to the product of its base by its altitude . G Ri N H E K B Let ABCD - F be a parallelopiped having all its faces oblique , and HR its ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
AABC ABCD altitude arc A B axis base and altitude bisect centre circle circumference circumscribed coincide conical surface COROLLARY cylinder denote diagonals diameter dihedral angle distance divided Draw equal respectively equally distant equilateral equivalent figure frustum Geometry given point greater Hence homologous sides hypotenuse intersection isosceles lateral area lateral edges lateral faces Let A B Let ABC limit line A B measured by arc middle point mutually equiangular number of sides opposite parallel parallelogram parallelopiped perimeter perpendicular plane MN prism prove pyramid Q. E. D. PROPOSITION radii radius equal ratio rectangles regular polygon right angles right triangle SCHOLIUM segment sides of equal similar polygons slant height sphere spherical angle spherical polygon spherical triangle square subtend surface symmetrical tangent tetrahedron THEOREM third side trihedral vertex vertices volume
Δημοφιλή αποσπάσματα
Σελίδα 132 - To describe an isosceles triangle having each of the angles at the base double of the third angle.
Σελίδα 140 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Σελίδα 206 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 40 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Σελίδα 353 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Σελίδα 179 - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 192 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Σελίδα 150 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.