The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth Books : with Notes, an Appendix, and ExercisesMacmillan, 1883 - 400 Seiten |
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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 . [ Note . The terms oblong and rhomboid are not often used . Practically the following definitions are used . Any ...
... Parallel straight lines are such as are in the same plane , and which being produced ever so far both ways do not meet . [ Note . The terms oblong and rhomboid are not often used . Practically the following definitions are used . Any ...
Seite 31
... parallel . Therefore AB is parallel to CD . Wherefore , if a straight line & c . Q.E.D. PROPOSITION 28 . THEOREM . [ Definition 35 . If a straight line falling on two other straight lines , make the exterior angle equal to the interior ...
... parallel . Therefore AB is parallel to CD . Wherefore , if a straight line & c . Q.E.D. PROPOSITION 28 . THEOREM . [ Definition 35 . If a straight line falling on two other straight lines , make the exterior angle equal to the interior ...
Seite 32
... parallel to CD . Because the angle EGB is equal to the angle GHD , [ Hyp . and the angle EGB is also equal A to the angle AGH , [ I. 15 . therefore the angle AGH is equal to the angle GHD ; [ Ax.1 . and they are alternate angles ...
... parallel to CD . Because the angle EGB is equal to the angle GHD , [ Hyp . and the angle EGB is also equal A to the angle AGH , [ I. 15 . therefore the angle AGH is equal to the angle GHD ; [ Ax.1 . and they are alternate angles ...
Seite 33
... parallel by hypothesis . Therefore the angle AGH is not unequal to the angle GHD ; that is , it is equal to it . But ... parallel to 3 BOOK I. 29 . 33.
... parallel by hypothesis . Therefore the angle AGH is not unequal to the angle GHD ; that is , it is equal to it . But ... parallel to 3 BOOK I. 29 . 33.
Seite 34
... parallel to the same straight line are parallel to each other . Let AB , CD be each of them parallel to EF : AB shall be parallel to CD . Let the straight line GHK cut AB , EF , CD . Then , because GHK cuts the parallel straight lines ...
... parallel to the same straight line are parallel to each other . Let AB , CD be each of them parallel to EF : AB shall be parallel to CD . Let the straight line GHK cut AB , EF , CD . Then , because GHK cuts the parallel straight lines ...
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Häufige Begriffe und Wortgruppen
ABCD AC is equal angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC bisects the angle centre chord circle ABC circle described circumference Construction Corollary describe a circle diameter double draw a straight equal angles equal to F equiangular equilateral equimultiples Euclid Euclid's Elements exterior angle given circle given point given straight line gnomon Hypothesis inscribed intersect isosceles triangle less Let ABC magnitudes middle point multiple opposite angles opposite sides parallelogram perpendicular plane polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION quadrilateral radius rectangle contained rectilineal figure remaining angle rhombus right angles right-angled triangle segment shew shewn side BC square on AC straight line &c straight line drawn tangent THEOREM touches the circle triangle ABC triangle DEF twice the rectangle vertex Wherefore
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Seite 262 - 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 71 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a Right Angle; and the straight line which stands on the other is called a Perpendicular to it.
Seite 262 - To draw a straight line at right angles to a given straight line, from a given point in the same. Let AB be...
Seite 182 - 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 8 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Seite 298 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Seite 58 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Seite 60 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts in the point D ; The squares on AD and DB shall be together double of AD»+DB
Seite 242 - Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken more than its half, and from the remainder more than its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied, so at length to become greater than AB.
Seite 4 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.