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 6
If a straight line meets two straight lines , so as to make the two interior angles on the same side of it , taken together , less than two right angles , these straight lines , being continually produced , shall at length meet upon ...
If a straight line meets two straight lines , so as to make the two interior angles on the same side of it , taken together , less than two right angles , these straight lines , being continually produced , shall at length meet upon ...
Seite 16
... the vertical angles be bisected , the bisecting lines are in one and the same straight line . PROP . XVI . THEOREM . If one side of a triangle be produced , the exterior angle is greater than either of the interior opposite angles .
... the vertical angles be bisected , the bisecting lines are in one and the same straight line . PROP . XVI . THEOREM . If one side of a triangle be produced , the exterior angle is greater than either of the interior opposite angles .
Seite 17
The three interior angles of any triangle are less than three right angles . Exercise 2. ... Because A D B is the exterior angle of the triangle BDC , it is greater ( I. 16 ) than the interior and opposite angle DCB .
The three interior angles of any triangle are less than three right angles . Exercise 2. ... Because A D B is the exterior angle of the triangle BDC , it is greater ( I. 16 ) than the interior and opposite angle DCB .
Seite 19
But it has been shown that B A , AC are greater than BE , EC . Much more then are BA , A C , greater than BD , D C. Again , the exterior angle B D C of the triangle CDE is greater than its interior and opposite angle CED ...
But it has been shown that B A , AC are greater than BE , EC . Much more then are BA , A C , greater than BD , D C. Again , the exterior angle B D C of the triangle CDE is greater than its interior and opposite angle CED ...
Seite 23
Therefore also the angle B H A is equal ( Ax . 1 ) to the angle BCA ; that is , the exterior angle B HA of the triangle A H C is equal to its interior and opposite angle B CA ; which is impossible ( I. 16 ) .
Therefore also the angle B H A is equal ( Ax . 1 ) to the angle BCA ; that is , the exterior angle B HA of the triangle A H C is equal to its interior and opposite angle B CA ; which is impossible ( I. 16 ) .
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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 |