A Text-book of Euclid's Elements for the Use of Schools, Bücher 1Macmillan, 1904 - 456 Seiten |
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Seite 7
... circle may be described from any centre , at any distance from that centre ... circles . In the Postulates , or requests , Euclid claims the use of these ... describe is used in Geometry in the sense of to draw . ON THE AXIOMS . The ...
... circle may be described from any centre , at any distance from that centre ... circles . In the Postulates , or requests , Euclid claims the use of these ... describe is used in Geometry in the sense of to draw . ON THE AXIOMS . The ...
Seite 12
... describe the circle BCD . Post . 3 . With centre B , and radius BA , describe the circle ACE . Post . 3 . From the point C at which the circles cut one another , draw the straight lines CA and CB to the points A and B. Then shall the ...
... describe the circle BCD . Post . 3 . With centre B , and radius BA , describe the circle ACE . Post . 3 . From the point C at which the circles cut one another , draw the straight lines CA and CB to the points A and B. Then shall the ...
Seite 13
... describe the circle CGH . Produce DB to meet the circle CGH at G. With centre D , and radius DG , describe the circle Produce DA to meet the circle GKF at F. Then AF shall be equal to BC . Post . 3 . Post . 2 . GKF . Post . 2 . Proof ...
... describe the circle CGH . Produce DB to meet the circle CGH at G. With centre D , and radius DG , describe the circle Produce DA to meet the circle GKF at F. Then AF shall be equal to BC . Post . 3 . Post . 2 . GKF . Post . 2 . Proof ...
Seite 14
... describe the circle DEF , cutting AB at E. Then AЕ shall be equal to C. Proof . Because A is the centre of the circle DEF , therefore AE is equal to AD . But C is equal to AD . Therefore AE and C are each equal to AD . Therefore AE is ...
... describe the circle DEF , cutting AB at E. Then AЕ shall be equal to C. Proof . Because A is the centre of the circle DEF , therefore AE is equal to AD . But C is equal to AD . Therefore AE and C are each equal to AD . Therefore AE is ...
Seite 15
... circle CGH . 7. In Proposition 2 the point A may be joined to either ex- tremity of BC . Draw the figure , and prove the proposition in the case when A is joined to C. 8. On a given straight line AB describe an isosceles triangle having ...
... circle CGH . 7. In Proposition 2 the point A may be joined to either ex- tremity of BC . Draw the figure , and prove the proposition in the case when A is joined to C. 8. On a given straight line AB describe an isosceles triangle having ...
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Häufige Begriffe und Wortgruppen
ABCD AC is equal adjacent angles Algebra angle BAC angle equal base BC bisected bisectors centre chord circumference circumscribed circle concyclic Constr Describe a circle diagonal diameter divided equal angles equiangular Euclid Euclid's exterior angle find the locus given circle given point given straight line given triangle greater Hence hypotenuse inscribed circle isosceles triangle Let ABC line which joins magnitudes meet middle point nine-points circle opposite sides orthocentre par¹ parallelogram parm pass pedal triangle perp perpendiculars drawn plane XY polygon produced Proof proportional PROPOSITION PROPOSITION 13 prove quadrilateral radical axis radius rectangle contained rectilineal figure regular polygon right angles segment shew shewn side BC Similarly square straight line drawn tangent THEOREM triangle ABC twice the rect vertex vertical angle
Beliebte Passagen
Seite 353 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
Seite 340 - 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 65 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Seite 162 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.
Seite 326 - From this it is manifest that prisms upon triangular bases, of the same altitude, are to one another as their bases. Let the...
Seite 162 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together •with the square...
Seite 291 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Seite 79 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.
Seite 18 - 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 242 - We may here notice that the perpendiculars from the vertices of a triangle to the opposite sides are concurrent ; their meet is called the orthocentre, and the triangle obtained by joining the feet of the perpendiculars is called the pedal triangle.