The Elements of geometry; or, The first six books, with the eleventh and twelfth, of Euclid, with corrections, annotations, and exercises, by R. Wallace. Cassell's ed |
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Seite 156
A cone is a solid figure described by the revolution of a rightangled triangle about one of the sides containing the right angle , that side remaining fixed . If the fixed side be equal to the other side containing the right angle ...
A cone is a solid figure described by the revolution of a rightangled triangle about one of the sides containing the right angle , that side remaining fixed . If the fixed side be equal to the other side containing the right angle ...
Seite 189
I. A PYRAMID is said to be inscribed in a cone , when its base is inscribed in the base of the cone , and both solids have a common vertex ; and , a cone is said to be described about a pyramid , when its base is described about the ...
I. A PYRAMID is said to be inscribed in a cone , when its base is inscribed in the base of the cone , and both solids have a common vertex ; and , a cone is said to be described about a pyramid , when its base is described about the ...
Seite 199
X. THEOREM A cone is the third part of a cylinder , having the same base and altitude . Let a cone and a cylinder have the same base , viz . , the circle ABCD , and the same altitude . The cone is the third part of the cylinder ...
X. THEOREM A cone is the third part of a cylinder , having the same base and altitude . Let a cone and a cylinder have the same base , viz . , the circle ABCD , and the same altitude . The cone is the third part of the cylinder ...
Seite 200
Lem . i ) than the excess of the cylinder above the triple of the cone . Let these cylindric segments be those upon the circular segments A E , E B , B F , FC , CG , GD , DH , and H A. Therefore the rest of the cylinder , that is ...
Lem . i ) than the excess of the cylinder above the triple of the cone . Let these cylindric segments be those upon the circular segments A E , E B , B F , FC , CG , GD , DH , and H A. Therefore the rest of the cylinder , that is ...
Seite 201
cone . each of these triangles erect pyramids having the same vertex with the Each of these pyramids is greater than the half of the segment of the cone which contains it , as was before demonstrated of the prisms and segments of the ...
cone . each of these triangles erect pyramids having the same vertex with the Each of these pyramids is greater than the half of the segment of the cone which contains it , as was before demonstrated of the prisms and segments of the ...
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The Elements of Geometry: Or, the First Six Books, with the Eleventh and ... Euclides Keine Leseprobe verfügbar - 2016 |
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ABCD altitude angle BAC base bisected Book centre circle circle ABC circumference common compounded cone Const contained Corollary cylinder definition demonstration described diagonal diameter divided double draw equal angles equiangular equimultiples Exercise exterior angle extremities fore four fourth given straight line greater half homologous inscribed interior join less magnitudes manner meet multiple parallel parallelogram parallelopiped pass perpendicular plane polygon prism PROBLEM produced PROP proportionals proposition proved pyramid ratio reason rectangle rectangle contained rectilineal figure remaining angle right angles segment shown sides similar similarly solid solid angle sphere square straight line A B Take taken THEOREM third touch triangle A B C twice vertex Wherefore whole
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Seite 23 - 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.
Seite 34 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Seite 2 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Seite 122 - 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.
Seite 5 - LET it be granted that a straight line may be drawn from any one point to any other point.
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 135 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar.
Seite 20 - PROBLEM. At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle.
Seite 147 - Similar solid figures are such as have all their solid angles equal, each to each, and are contained by the same number of similar planes.
Seite 37 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...
Bibliografische Informationen
| Titel | The Elements of geometry; or, The first six books, with the eleventh and twelfth, of Euclid, with corrections, annotations, and exercises, by R. Wallace. Cassell's ed |
| Autor/in | Euclides |
| Herausgeber | Robert Wallace |
| Veröffentlicht | 1855 |
| Original von | Oxford University |
| Digitalisiert | 8. Sept. 2006 |
| Zitat exportieren | BiBTeX EndNote RefMan |