Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books and the First Twenty-one Propositions of the Eleventh Book ...T. Stevenson, 1845 - 199 Seiten |
Im Buch
Ergebnisse 1-5 von 51
Seite 5
... Parallel straight lines , are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . I. Let it be granted that a straight line may be drawn from any one point to any other point ...
... Parallel straight lines , are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . I. Let it be granted that a straight line may be drawn from any one point to any other point ...
Seite 25
... parallel . Let the straight line EF , which falls upon the two straight lines AB , CD , make the alternate angles AEF , EFD equal to one another ; AB is parallel to CD . For , if it be not parallel , AB and CD being produced shall meet ...
... parallel . Let the straight line EF , which falls upon the two straight lines AB , CD , make the alternate angles AEF , EFD equal to one another ; AB is parallel to CD . For , if it be not parallel , AB and CD being produced shall meet ...
Seite 26
... parallel to CD . * D H Because the angle EGB is equal to the angle GHD , and the angle EGB equal † to the angle AGH , the angle AGH is equal to the angle GHD ; and they are the alter- nate angles ; therefore AB is parallel || to CD ...
... parallel to CD . * D H Because the angle EGB is equal to the angle GHD , and the angle EGB equal † to the angle AGH , the angle AGH is equal to the angle GHD ; and they are the alter- nate angles ; therefore AB is parallel || to CD ...
Seite 27
... parallel by the hypothesis ; therefore the angle AGH is not unequal to the angle GHD , that is , it is equal to it ... parallel to the same straight line are parallel to each other . Let AB , CD be each of them parallel to EF ; AB is ...
... parallel by the hypothesis ; therefore the angle AGH is not unequal to the angle GHD , that is , it is equal to it ... parallel to the same straight line are parallel to each other . Let AB , CD be each of them parallel to EF ; AB is ...
Seite 28
... parallel to the given straight line BC . Which was to be done . PROPOSITION XXXII . THEOR . - lf a side of any ... parallel to the straight line AB ; and because AB is parallel to CE , and AC meets them , the alternate angles BAC , ACE ...
... parallel to the given straight line BC . Which was to be done . PROPOSITION XXXII . THEOR . - lf a side of any ... parallel to the straight line AB ; and because AB is parallel to CE , and AC meets them , the alternate angles BAC , ACE ...
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
ABCD adjacent angles angle ABC angle ACB angle BAC angle BCD angle DEF angle EDF angles equal base BC BC is equal bisected centre circle ABC Constr describe diameter double draw equal angles equal to F equiangular equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given straight line gnomon greater ratio join less Let ABC Let the straight likewise meet multiple opposite angle parallel to BC parallelogram perpendicular plane polygon proportionals Q. E. D. PROPOSITION rectangle contained remaining angle right angles segment semicircle sides square of AC straight line AB straight line AC THEOR THEOR.-If three straight lines tiple touches the circle triangle ABC triangle DEF twice the rectangle wherefore
Beliebte Passagen
Seite 12 - If two triangles have two sides of the one equal to two sides of the...
Seite 29 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.
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 69 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Seite 20 - If from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle. Let the two straight lines BD.
Seite 102 - A LESS magnitude is said to be a part of a greater magnitude, when the less measures the greater; that is, ' when the less is contained a certain number of times
Seite 44 - 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 71 - The opposite angles of any quadrilateral figure described in a circle, are toe/ether equal to two right angles. Let ABCD be a quadrilateral figure in the circle ABCD : any two of its opposite angles are together equal to two right angles.
Seite 66 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Seite 83 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.