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 5
That a terminated straight line may be produced to any length in a straight line : 3. And that a circle may be described from any centre , at any distance from that centre . AXIOMS . 1. Things which are equal to the same DEFINITIONS .
That a terminated straight line may be produced to any length in a straight line : 3. And that a circle may be described from any centre , at any distance from that centre . AXIOMS . 1. Things which are equal to the same DEFINITIONS .
Seite 7
Therefore CA , AB , BC are equal to one another . Wherefore the triangle ABC is equilateral , [ Def . 24 . and it is described on the given straight line AB . Q.E.F. [ I. 1 . A G PROPOSITION 2. PROBLEM .
Therefore CA , AB , BC are equal to one another . Wherefore the triangle ABC is equilateral , [ Def . 24 . and it is described on the given straight line AB . Q.E.F. [ I. 1 . A G PROPOSITION 2. PROBLEM .
Seite 44
Wherefore a parallelogram FECG has been described equal to the given triangle ABC , and having one of its angles CEF equal to the given angle D. Q.E.F. PROPOSITION 43. THEOREM . a E The complements of the 44 EUCLID'S ELEMENTS.
Wherefore a parallelogram FECG has been described equal to the given triangle ABC , and having one of its angles CEF equal to the given angle D. Q.E.F. PROPOSITION 43. THEOREM . a E The complements of the 44 EUCLID'S ELEMENTS.
Seite 49
[ Definition 30 And it is described on the given straight line AB . Q.E.F. COROLLARY . From the demonstration it is manifest that every parallelogram which has one right angle has all its angles right angles . F CE ; B PROPOSITION 47.
[ Definition 30 And it is described on the given straight line AB . Q.E.F. COROLLARY . From the demonstration it is manifest that every parallelogram which has one right angle has all its angles right angles . F CE ; B PROPOSITION 47.
Seite 50
THEOREM , In any right - angled triangle , the square which is described on the side subtending the right angle is equal to the squares described on the sides which contain the right angle . Let ABC be a right - angled triangle , having ...
THEOREM , In any right - angled triangle , the square which is described on the side subtending the right angle is equal to the squares described on the sides which contain the right angle . Let ABC be a right - angled triangle , having ...
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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 difference 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 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 |