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 4
Of four - sided figures , a square is that which has all its sides equal , and all its angles right angles . This definition is redundant . If the general definition annexed to the 34th Prop . of this book be considered , the square is ...
Of four - sided figures , a square is that which has all its sides equal , and all its angles right angles . This definition is redundant . If the general definition annexed to the 34th Prop . of this book be considered , the square is ...
Seite 14
To describe a square upon a given straight line . H B D PROP . XII . PROBLEM . To draw a straight line perpendicular to a given straight line of unlimited length , from a given point without it . Let AB be the given straight line ...
To describe a square upon a given straight line . H B D PROP . XII . PROBLEM . To draw a straight line perpendicular to a given straight line of unlimited length , from a given point without it . Let AB be the given straight line ...
Seite 37
The figure A E is a square . Because AE is a parallelogram ( Def . 36 ) AB is equal ( I. 34 ) to D Е , and AĎ to BĚ . But BA is equal to AD . Therefore the four lines BA , AD , DE , EB are all equal to one another , and the ...
The figure A E is a square . Because AE is a parallelogram ( Def . 36 ) AB is equal ( I. 34 ) to D Е , and AĎ to BĚ . But BA is equal to AD . Therefore the four lines BA , AD , DE , EB are all equal to one another , and the ...
Seite 38
The construction of this problem may be effected , in accordance with Euclid's definition of a square , by Prop . XI . of this book . Euclid's corollary has also been anticipated . Corollary 2. - If two squares be equal , their sides ...
The construction of this problem may be effected , in accordance with Euclid's definition of a square , by Prop . XI . of this book . Euclid's corollary has also been anticipated . Corollary 2. - If two squares be equal , their sides ...
Seite 39
To describe a square equal to two given squares ; and , consequently , to any given number of squares . ... any two given squares ; and , consequently , to the difference between a given square , and any number of given squares .
To describe a square equal to two given squares ; and , consequently , to any given number of squares . ... any two given squares ; and , consequently , to the difference between a given square , and any number of given squares .
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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 |