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 8
the circle ACE ; and from the point c , in which the circles cut one another , draw ( 1 . post . 1. ) the straight lines CA , CB to the points A , B : ABC is the equilateral triangle required . Because the point A is the centre of the ...
the circle ACE ; and from the point c , in which the circles cut one another , draw ( 1 . post . 1. ) the straight lines CA , CB to the points A , B : ABC is the equilateral triangle required . Because the point A is the centre of the ...
Seite 17
To draw a straight line at right angles to a given straight line , from a given point in the same . Let AB be a given straight line , and C a point given in it ; and E as centres with any radius greater than the half of DE , and the ...
To draw a straight line at right angles to a given straight line , from a given point in the same . Let AB be a given straight line , and C a point given in it ; and E as centres with any radius greater than the half of DE , and the ...
Seite 18
A D се в it is required to draw a straight line from C at right angles to AB . Take any point D in AC , and make ( I. 3. ) CE equal to CD ; upon DE describe ( I. 1. ) the equilateral triangle DFE , and ( I. post . 1. ) ...
A D се в it is required to draw a straight line from C at right angles to AB . Take any point D in AC , and make ( I. 3. ) CE equal to CD ; upon DE describe ( I. 1. ) the equilateral triangle DFE , and ( I. post . 1. ) ...
Seite 31
to LKD , the interior and remote angle on the same side of LH : therefore AB is parallel ( 1. 28. part 1. ) to CD . Wherefore two straight lines , & c . 6 A B К. C D E F : PROP . XXXI . PROB . To draw a straight line parallel to a given ...
to LKD , the interior and remote angle on the same side of LH : therefore AB is parallel ( 1. 28. part 1. ) to CD . Wherefore two straight lines , & c . 6 A B К. C D E F : PROP . XXXI . PROB . To draw a straight line parallel to a given ...
Seite 35
To do this , draw AC making any angle with AB , and draw ( I. 31. ) ... In the same manner , BO may be proved to be equal to ON : and by drawing NQ parallel to AC , MN may proved in a similar manner to be equal to NO . * Cor . 3.
To do this , draw AC making any angle with AB , and draw ( I. 31. ) ... In the same manner , BO may be proved to be equal to ON : and by drawing NQ parallel to AC , MN may proved in a similar manner to be equal to NO . * Cor . 3.
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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 |