Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement of the Quadrature of the Circle and the Geometry of SolidsF. Nichols, 1806 - 311 Seiten |
Im Buch
Ergebnisse 1-5 von 12
Seite 247
... pyramid is a solid figure contained by planes that are con- stituted between one plane and a point above it in which they meet . IV . A prism is a solid figure contained by plane figures , of which two that are opposite are equal ...
... pyramid is a solid figure contained by planes that are con- stituted between one plane and a point above it in which they meet . IV . A prism is a solid figure contained by plane figures , of which two that are opposite are equal ...
Seite 264
... pyramids , which have equal ba- ses and altitudes , be cut by planes that are paral- lel to the bases , and at equal distances from them , the sections are equal to eacl : other . Let ABCD , EFGH be two pyramids , having equal bases BDC ...
... pyramids , which have equal ba- ses and altitudes , be cut by planes that are paral- lel to the bases , and at equal distances from them , the sections are equal to eacl : other . Let ABCD , EFGH be two pyramids , having equal bases BDC ...
Seite 265
... pyramid parallel to the base is a triangle similar to the base . And in the same manner it may be shown that the sections parallel to the base of a polygonal pyramid are similar to the base . COR . 2. Hence also , in polygonal pyramids ...
... pyramid parallel to the base is a triangle similar to the base . And in the same manner it may be shown that the sections parallel to the base of a polygonal pyramid are similar to the base . COR . 2. Hence also , in polygonal pyramids ...
Seite 266
... pyramid , such that the sum of the prisms shall exceed the pyramid by a solid less than any given solid . Let ABID be a pyramid , and Z * a given solid ; a series of prisms having all the same altitude may be circumscribed about the ...
... pyramid , such that the sum of the prisms shall exceed the pyramid by a solid less than any given solid . Let ABID be a pyramid , and Z * a given solid ; a series of prisms having all the same altitude may be circumscribed about the ...
Seite 267
... pyramid ABCD , because ABCD is greater than the sum of the inscribed prisms . Much more , therefore , is the excess of the circumscribed prisms above the pyramid less than the solid Z. Therefore a series of prisms of the same altitude ...
... pyramid ABCD , because ABCD is greater than the sum of the inscribed prisms . Much more , therefore , is the excess of the circumscribed prisms above the pyramid less than the solid Z. Therefore a series of prisms of the same altitude ...
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle contained angle EDF arch base BC bisected Book centre circle ABC circumference coincide cylinder definition demonstrated diameter draw drawa equal angles equiangular equilateral polygon equimultiples Euclid exterior angle fore four right angles given circle given straight line greater inscribed interior and opposite join less Let ABC Let the straight meet multiple opposite angle parallelogram perpendicular point F polygon prism PROB produced proportional proposition pyramid Q. E. D. COR Q. E. D. PROP ratio rectangle contained rectilineal figure remaining angle segment solid angle solid parallelepipeds straight line AB straight line AC Suppl THEOR third touches the circle triangle ABC triangle DEF
Beliebte Passagen
Seite 121 - 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. either the sides adjacent to the equal...
Seite 42 - TO a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Seite 63 - Therefore, in obtuse-angled triangles, &c. QED PROP. XIII. THEOREM. In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.
Seite 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Seite 183 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF be equiangular parallelograms having the angle BCD equal to the angle ECG ; the ratio of the parallelogram AC to the parallelogram CF is the same with the ratio which is compounded •f the ratios of their sides.
Seite 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Seite 291 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 160 - ... extremities of the base shall have the same ratio which the other sides of the triangle have to one...
Seite 10 - ... shall be greater than the base of the other. Let ABC, DEF be two triangles, which have the two sides AB, AC, equal to the two DE, DF, each to each, viz.
Seite 14 - Therefore, upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extretnity equal to one another.