Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids : to which are Added, Elements of Plane and Spherical TrigonometryMarot & Walter, 1826 - 320 sider |
Inni boken
Side ix
... pyramid to the sphere . The com- parison of this last solid with the cylinder , concludes the last Book of the Supplement , and is a proposition that may not improperly be considered as terminating the ele- mentary part of Geometry ...
... pyramid to the sphere . The com- parison of this last solid with the cylinder , concludes the last Book of the Supplement , and is a proposition that may not improperly be considered as terminating the ele- mentary part of Geometry ...
Side 188
... pyramid is a solid figure contained by planes that are constituted betwixt 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 constituted betwixt 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 ...
Side 201
... pyramids , which have equal bases and altitudes , be cut by planes that are parallel to the bases , and at equal distances from them , the sections are equal to one another . Let ABCD and EFGH be two pyramids , having equal bases BDC ...
... pyramids , which have equal bases and altitudes , be cut by planes that are parallel to the bases , and at equal distances from them , the sections are equal to one another . Let ABCD and EFGH be two pyramids , having equal bases BDC ...
Side 202
... pyramid pa- rallel to the base , is a triangle similar to the base . And in the same manner it is shown , that the sections parallel to the base of a poly- gonal pyramid are similar to the base . COR . 2. Hence also , in polygonal pyramids ...
... pyramid pa- rallel to the base , is a triangle similar to the base . And in the same manner it is shown , that the sections parallel to the base of a poly- gonal pyramid are similar to the base . COR . 2. Hence also , in polygonal pyramids ...
Side 203
... pyramid , such that the sum of the prisms shall exceed the pyramid by a solid less than any given solid . N W V T H M Let ABCD be a pyramid and Z * a given solid ; a series of prisms having all the same altitude , may be circumscribed ...
... pyramid , such that the sum of the prisms shall exceed the pyramid by a solid less than any given solid . N W V T H M Let ABCD be a pyramid and Z * a given solid ; a series of prisms having all the same altitude , may be circumscribed ...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ... Euclid,John Playfair Uten tilgangsbegrensning - 1826 |
Elements of Geometry: Containing the First Six Books of Euclid; With Two ... Formerly Chairman Department of Immunology John Playfair Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC meet multiple opposite angle parallel parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle side BC sine solid angle solid parallelopipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Populære avsnitt
Side 125 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 39 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel. Let AB, CD be equal and parallel straight lines, and joined towards the same parts by the straight lines AC, BD ; AC, BD are also equal and parallel.
Side 41 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Side 19 - BG; and things that are equal to the same are equal to one another; therefore the straight line AL is equal to BC. Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC.
Side 145 - If two triangles which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another ; the remaining sides shall be in a straight line. Let ABC, DCE be two triangles which have the two sides BA, AC proportional to the two CD, DE, viz.
Side 30 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle.
Side 136 - FGL, have an angle in one equal to an angle in the other, and their sides about these equal angles proportionals ; the triangle ABE is equiangular (6.
Side 51 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Side 20 - DEF, and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other and be equal to them, viz. the angle ABC to the angle DEF, and the angle ACB to DFE.
Side 55 - If a straight line be divided into two equal, and also into two unequal parts ; the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section.