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 Exercises |
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Seite 14
[ Axiom 8 . Wherefore , if two triangles & c . Q.E.D. i PROPOSITION 9. PROBLEM . To bisect a given rectilineal angle , that is to divide it into two equal angles . Let BAC be the given rectilineal angle : it is 14 EUCLID'S ELEMENTS .
[ Axiom 8 . Wherefore , if two triangles & c . Q.E.D. i PROPOSITION 9. PROBLEM . To bisect a given rectilineal angle , that is to divide it into two equal angles . Let BAC be the given rectilineal angle : it is 14 EUCLID'S ELEMENTS .
Seite 15
Let BAC be the given rectilineal angle : it is required to bisect it . Take any point D in AB , and from AC cut off AE ... Wherefore the given rectilineal angle BAC is bisected by the straight line AF . Q.E.F. PROPOSITION 10. PROBLEM .
Let BAC be the given rectilineal angle : it is required to bisect it . Take any point D in AB , and from AC cut off AE ... Wherefore the given rectilineal angle BAC is bisected by the straight line AF . Q.E.F. PROPOSITION 10. PROBLEM .
Seite 17
Take any point D the other side of AB , and from the centre C , at the distance CD , describe the E circle EGF , meeting AB at F and G. [ Postulate 3 . G B Bisect FG at H , [ I. 10 . and join CH . The straight line CH drawn from the ...
Take any point D the other side of AB , and from the centre C , at the distance CD , describe the E circle EGF , meeting AB at F and G. [ Postulate 3 . G B Bisect FG at H , [ I. 10 . and join CH . The straight line CH drawn from the ...
Seite 20
Bisect AC at E , [ I. 10 . join BE and produce it to F , making EF equal to EB , [ I . 3 . and join FC . Because AE is equal to EC , and BE to EF ; [ Constr . the two sides AE , EB are equal to the two sides CE , EF , each to each ...
Bisect AC at E , [ I. 10 . join BE and produce it to F , making EF equal to EB , [ I . 3 . and join FC . Because AE is equal to EC , and BE to EF ; [ Constr . the two sides AE , EB are equal to the two sides CE , EF , each to each ...
Seite 21
In the same manner if BC be bisected , and the side AC be produced to G , it may be shewn that the angle BCG , that is the angle ACD , is greater than the angle ABC . [ I. 15 . Wherefore , if one side & c . Q.E.D. PROPOSITION 17.
In the same manner if BC be bisected , and the side AC be produced to G , it may be shewn that the angle BCG , that is the angle ACD , is greater than the angle ABC . [ I. 15 . Wherefore , if one side & c . Q.E.D. PROPOSITION 17.
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ABCD AC is equal angle ABC angle BAC Axiom base bisected Book centre chord circle ABC circumference common Construction Corollary Definition demonstration describe a circle described diameter divided double drawn equal equal angles equiangular equilateral equimultiples Euclid extremities fall figure fixed formed four fourth given circle given point given straight line greater half Hypothesis inscribed intersect join less magnitudes manner meet multiple namely opposite sides parallel parallelogram pass perpendicular plane polygon PROBLEM produced proportionals PROPOSITION Q.E.D. PROPOSITION quadrilateral radius ratio reason rectangle contained rectilineal figure remaining respectively right angles segment shew shewn sides similar square straight line &c straight line drawn suppose Take taken tangent THEOREM third triangle ABC twice Wherefore whole
Beliebte Passagen
Seite 286 - 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 30 - 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. either the sides adjacent to the equal...
Seite 34 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles...
Seite 37 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.
Seite 12 - 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 302 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Seite 220 - 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 354 - Prove that the square on any straight line drawn from the vertex of an isosceles triangle to the base, is less than the square on a side of the triangle by the rectangle contained by the segments of the base : and conversely.
Seite 104 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Seite 96 - The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles.
Bibliografische Informationen
| Titel | 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 Exercises |
| Autoren | Euclid, Isaac Todhunter |
| Herausgeber | Isaac Todhunter |
| Verlag | Macmillan, 1867 |
| Original von | University of Michigan |
| Digitalisiert | 11. Juni 2007 |
| Länge | 400 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |