The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With Notes and Illus., and an Appendix in Five Books |
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Seite 7
But ( axiom 9. ) GFK or its equal KFH , is greater than GFE or its equal EFH , which is impossible , since ( ax . 9. ) EFH is greater than KFH : therefore BA cannot have the position FK ; and in the same manner it might be shown ...
But ( axiom 9. ) GFK or its equal KFH , is greater than GFE or its equal EFH , which is impossible , since ( ax . 9. ) EFH is greater than KFH : therefore BA cannot have the position FK ; and in the same manner it might be shown ...
Seite 8
It will be shown in the 10th proposition of the 3d book , that two circles can cut each other in only two points ; and hence there can be only two equilateral triangles on a straight line . In the practical construction it is sufficient ...
It will be shown in the 10th proposition of the 3d book , that two circles can cut each other in only two points ; and hence there can be only two equilateral triangles on a straight line . In the practical construction it is sufficient ...
Seite 9
But it has been shown , that BC is equal to BE ; wherefore AF and BC are each of them equal to BE ; and things that are equal to the same are equal ( I. ax . 1. ) to one another ; therefore the straight line AF is equal to BC .
But it has been shown , that BC is equal to BE ; wherefore AF and BC are each of them equal to BE ; and things that are equal to the same are equal ( I. ax . 1. ) to one another ; therefore the straight line AF is equal to BC .
Seite 11
AC and the point C are then shown to coincide with DF and the point F , in the same manner in which AB and the point B were shown to coincide with DE and the point E. Now , B and C coinciding with E and F , the lines between them must ...
AC and the point C are then shown to coincide with DF and the point F , in the same manner in which AB and the point B were shown to coincide with DE and the point E. Now , B and C coinciding with E and F , the lines between them must ...
Seite 12
This is shown by taking , first , one side as base , and then another . G D B * In this proposition , the hypothesis is , that the triangle under consideration has two of its sides equal ; and on this hypothesis it is to be proved that ...
This is shown by taking , first , one side as base , and then another . G D B * In this proposition , the hypothesis is , that the triangle under consideration has two of its sides equal ; and on this hypothesis it is to be proved that ...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... Euclid Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
ABCD altitude base bisected called centre chord circle circumference coincide common cone consequently const construction contained continual cylinder demonstrated describe diagonal diameter difference divided double draw equal equal angles extremities figure fore four fourth given given circle given point given straight line greater half Hence inscribed join less magnitudes manner means meet method multiple opposite parallel parallelogram pass perpendicular plane polygon prism PROB produced proof PROP proportional proposition proved pyramid radius ratio reason rectangle remaining respectively right angles Schol segments semicircle shown sides similar square straight line taken THEOR third touching triangle triangle ABC twice vertical wherefore whole
Beliebte Passagen
Seite 94 - 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 53 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Seite 143 - 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 4 - A rhombus is that which has all its sides equal, but its angles are not right angles.
Seite 57 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.
Seite 138 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
Seite 43 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Seite 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 40 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Seite 36 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...
Bibliografische Informationen
| Titel | The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With Notes and Illus., and an Appendix in Five Books |
| Autor/in | Euclid |
| Herausgeber | James Thomson |
| Ausgabe | 2 |
| Verlag | Adam and Charles Black, 1837 |
| Original von | University of Michigan |
| Digitalisiert | 15. Mai 2008 |
| Länge | 390 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |