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 97
A greater magnitude is said to be a multiple of a less , when the greater is measured by the less ; that is , when the greater contains the Jess a certain number of times exactly . The meaning of this definition , taken in connexion ...
A greater magnitude is said to be a multiple of a less , when the greater is measured by the less ; that is , when the greater contains the Jess a certain number of times exactly . The meaning of this definition , taken in connexion ...
Seite 98
if the multiple of the first be greater than that of the second , the multiple of the third is also greater than that of the fourth . This is the most important definition of the Fifth Book . Upon it , as a hinge or centre , turns the ...
if the multiple of the first be greater than that of the second , the multiple of the third is also greater than that of the fourth . This is the most important definition of the Fifth Book . Upon it , as a hinge or centre , turns the ...
Seite 101
A multiple of a greater magnitude is greater than the same multiple of a less . IV . Of two magnitudes , that one of which a multiple is greater than the same multiple of the other , is the greater . V. A part or submultiple of a ...
A multiple of a greater magnitude is greater than the same multiple of a less . IV . Of two magnitudes , that one of which a multiple is greater than the same multiple of the other , is the greater . V. A part or submultiple of a ...
Seite 102
Therefore , whatsoever multiple AB is of E , the same multiple is AB and CD together , of E and F together . The same demonstration holds in any number of magnitudes , which is here applied to two . Therefore , if any number of ...
Therefore , whatsoever multiple AB is of E , the same multiple is AB and CD together , of E and F together . The same demonstration holds in any number of magnitudes , which is here applied to two . Therefore , if any number of ...
Seite 103
EF is the same multiple of B , that GH is of D. Divide EF into the magnitudes EK and KF , each equal to A ; K F G L and G H into GL and LH , each equal to C. A Because the number of the magnitudes EK and K F is equal B Dto the number of ...
EF is the same multiple of B , that GH is of D. Divide EF into the magnitudes EK and KF , each equal to A ; K F G L and G H into GL and LH , each equal to C. A Because the number of the magnitudes EK and K F is equal B Dto the number of ...
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The Elements of Geometry: Or, the First Six Books, with the Eleventh and ... Euclides Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
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 |