The Contents of the Fifth and Sixth Books of Euclid |
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Seite xiii
If X , Y , Z be magnitudes of the same kind , and if I be less than Y , then integers n , s exist such that nX < sZ < n Y. 8. The scale of A , B is the same as that of C , D. I If when rA > sB , then rC > sD ; if when rA = sB , then rC ...
If X , Y , Z be magnitudes of the same kind , and if I be less than Y , then integers n , s exist such that nX < sZ < n Y. 8. The scale of A , B is the same as that of C , D. I If when rA > sB , then rC > sD ; if when rA = sB , then rC ...
Seite 4
( ab ) is a positive integer which may be called c . .. a = b + c . : . aR = ( b + c ) R = bR + cR . : . cRaR − bR - .. ( a - b ) R = aR − bR . Art . 11 . - EXAMPLE 4 . [ Prop . 2 . If A and B are multiples of G , then the difference ...
( ab ) is a positive integer which may be called c . .. a = b + c . : . aR = ( b + c ) R = bR + cR . : . cRaR − bR - .. ( a - b ) R = aR − bR . Art . 11 . - EXAMPLE 4 . [ Prop . 2 . If A and B are multiples of G , then the difference ...
Seite 7
If rA > sB , and rC < 8D , prove that no integers r ' , s ' can exist such that and r'A < s ' B , r'C > s'D . Art . 17. Def . 2 . EQUIMULTIPLES . If the same multiples be taken of each of two magnitudes , they are called equimultiples ...
If rA > sB , and rC < 8D , prove that no integers r ' , s ' can exist such that and r'A < s ' B , r'C > s'D . Art . 17. Def . 2 . EQUIMULTIPLES . If the same multiples be taken of each of two magnitudes , they are called equimultiples ...
Seite 10
Let Y be greater than X. It is to be proved that integers n and s exist , such that or more briefly , nX < sZ , and sZ < nY ; nX < sZ < nY . Since YX , therefore Y - X is a magnitude of the same kind as Z. Hence an integer n exists ...
Let Y be greater than X. It is to be proved that integers n and s exist , such that or more briefly , nX < sZ , and sZ < nY ; nX < sZ < nY . Since YX , therefore Y - X is a magnitude of the same kind as Z. Hence an integer n exists ...
Seite 11
Replacing ( t + 1 ) by s , it follows that integers n and s exist , such that nX < sZ < nY . Art . 25. An illustration of Prop . 7 is given in Fig . 7 in the case where X , Y , Z are segments of straight lines .
Replacing ( t + 1 ) by s , it follows that integers n and s exist , such that nX < sZ < nY . Art . 25. An illustration of Prop . 7 is given in Fig . 7 in the case where X , Y , Z are segments of straight lines .
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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 |