The Contents of the Fifth and Sixth Books of Euclid |
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Seite xv
... sides of a triangle are divided proportionally , so that the segments terminating at the vertex common to the two sides correspond to each other , then the straight line joining the points of division is parallel to the other side .
... sides of a triangle are divided proportionally , so that the segments terminating at the vertex common to the two sides correspond to each other , then the straight line joining the points of division is parallel to the other side .
Seite 8
On AB produced take any number of lengths BD , DE , EF each equal to AB , and join CD , CE , CF. Then the triangles CAB , CBD , CDE , CEF all stand on equal bases , and have the same altitude . Therefore they are equal in area .
On AB produced take any number of lengths BD , DE , EF each equal to AB , and join CD , CE , CF. Then the triangles CAB , CBD , CDE , CEF all stand on equal bases , and have the same altitude . Therefore they are equal in area .
Seite 30
Join GK . Draw HL parallel to GK cutting OY in L. Then KL is the fourth line required . A C. E. H O B G K F Since GK is parallel to HL , X .. [ OG , GH ] = [ OK , KL ] . [ Prop . 13 . .. [ AB , CD ] ~ [ EF , KL ] .
Join GK . Draw HL parallel to GK cutting OY in L. Then KL is the fourth line required . A C. E. H O B G K F Since GK is parallel to HL , X .. [ OG , GH ] = [ OK , KL ] . [ Prop . 13 . .. [ AB , CD ] ~ [ EF , KL ] .
Seite 31
... the given straight line AB in the same way as the line CF is divided at D and E. Through A draw any straight line AX ( not in the same straight line as AB ) , and on it measure off AG = CD , GH = DE , HK = EF . Join BK , and draw GL ...
... the given straight line AB in the same way as the line CF is divided at D and E. Through A draw any straight line AX ( not in the same straight line as AB ) , and on it measure off AG = CD , GH = DE , HK = EF . Join BK , and draw GL ...
Seite 32
Join BH . Draw CG parallel to BH cutting AB at G. Then [ AH , AC ] = [ AB , AG ] . Suppose that AH = n = n ( AC ) . [ Prop . 13 . X Fig . 45 . Then the scale of AH , AC will contain the fact shown by the following figure .
Join BH . Draw CG parallel to BH cutting AB at G. Then [ AH , AC ] = [ AB , AG ] . Suppose that AH = n = n ( AC ) . [ Prop . 13 . X Fig . 45 . Then the scale of AH , AC will contain the fact shown by the following figure .
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The Contents of the Fifth and Sixth Books of Euclid (with a Note on ... Euclid,Micaiah John Muller Hill Keine Leseprobe verfügbar - 2015 |
The Contents of the Fifth and Sixth Books of Euclid Euclid,Micaiah John Muller Hill Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
ABCD alternatives angle base called centre circle column compartments consequent construction corresponding sides Definition described determine difference divided draw drawn duplicate ratio ENUNCIATION equal equal angles equimultiples Euclid's EXAMPLE exist externally extremities fact Fifth figures follows four fourth given greater harmonic Hence idea integers internally Join kind length magnitudes manner mean proportional measure necessary NOTE opposite parallel parallel to BC parallelogram perpendicular possible produced proof Prop proportional PROPOSITION prove rA rB reciprocally rect rectangle contained rectilineal figure relative multiple scale respectively result right angle segments similar similar figures similarly square stage standing straight line Take taken term third triangle ABC triangles are similar vertex whole
Beliebte Passagen
Seite 99 - IF two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals : the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides.
Seite xviii - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Seite 102 - If two similar parallelograms have a common angle, and be similarly situated ; they are about the same diameter.
Seite 99 - Prove that similar triangles are to one another in the duplicate ratio of their homologous sides.
Seite xvi - If the vertical angle of a triangle be bisected by a straight line which also cuts the base, the segments of the base shall have the same ratio which the other sides of the triangle have to one another...
Seite 80 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means.
Seite 99 - ABC, DEF have one angle in the one equal to one angle in the other, viz. the angle BAC to the angle EDF, and the sides about...
Seite 73 - P moves in a plane so that the ratio of its distances from two fixed points A, B in that plane is always the same.
Seite 35 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth: or, if the multiple of the first be equal to that of the second, the multiple of the third is also equal to that of the fourth : or, if...
Seite 84 - If they do not intersect, show that the radical axis is perpendicular to the line joining the centres of the circles...
Bibliografische Informationen
| Titel | The Contents of the Fifth and Sixth Books of Euclid |
| Autoren | Euclid, Micaiah John Muller Hill |
| Herausgeber | Micaiah John Muller Hill |
| Verlag | The University Press, 1900 |
| Original von | Harvard University |
| Digitalisiert | 29. Sept. 2005 |
| Länge | 143 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |