A Text-book of Euclid's Elements for the Use of Schools, Bok 1Macmillan, 1904 - 456 sider |
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Side 170
Euclid. PROPOSITION 4. THEOREM . If in a circle two chords cut one another , which do not both pass through the centre , they cannot both be bisected at their point of intersection . A Let ABCD be a circle , and AC , BD two chords which ...
Euclid. PROPOSITION 4. THEOREM . If in a circle two chords cut one another , which do not both pass through the centre , they cannot both be bisected at their point of intersection . A Let ABCD be a circle , and AC , BD two chords which ...
Side 174
... given point to the circumference , one on each side of the diameter . K Let ABCD be a circle , and from F , any point within it which is not the centre , let FA , FB , FC , FG , and FD be drawn to the Oce , of which FA passes through E ...
... given point to the circumference , one on each side of the diameter . K Let ABCD be a circle , and from F , any point within it which is not the centre , let FA , FB , FC , FG , and FD be drawn to the Oce , of which FA passes through E ...
Side 186
Euclid. PROPOSITION 14 . THEOREM . Equal chords in a circle are equidistant from the centre . Conversely , chords which are equidistant from the centre are equal . B Let ABC be a circle , and let AB and CD be chords , of which the perp ...
Euclid. PROPOSITION 14 . THEOREM . Equal chords in a circle are equidistant from the centre . Conversely , chords which are equidistant from the centre are equal . B Let ABC be a circle , and let AB and CD be chords , of which the perp ...
Side 188
... Let ABCD be a circle of which AD is a diameter , and E the centre ; and let BC and FG be any two chords , whose perp . distances from the centre are EH and EK . Then ( i ) AD shall be greater than BC ; ( ii ) if EH is less than EK , BC ...
... Let ABCD be a circle of which AD is a diameter , and E the centre ; and let BC and FG be any two chords , whose perp . distances from the centre are EH and EK . Then ( i ) AD shall be greater than BC ; ( ii ) if EH is less than EK , BC ...
Side 199
... needs no proof beyond that given under Case I. NOTE 2. If the arc BFC , on ... circle are equal . Let ABCD be a circle , and let BAD , BED be angles in the ... semicircle . Join BF , DF . Proof . Because the BFD is at the centre , and the ...
... needs no proof beyond that given under Case I. NOTE 2. If the arc BFC , on ... circle are equal . Let ABCD be a circle , and let BAD , BED be angles in the ... semicircle . Join BF , DF . Proof . Because the BFD is at the centre , and the ...
Andre utgaver - Vis alle
A Text-book of Euclid's Elements: For the Use of Schools : Parts ..., Bøker 1-6 Euclid,Henry Sinclair Hall,Frederick Haller Stevens Uten tilgangsbegrensning - 1889 |
A Text-book of Euclid's Elements for the Use of Schools. Books I ..., Bøker 1-6 Euclid,Henry Sinclair Hall,Frederick Haller Stevens Uten tilgangsbegrensning - 1898 |
A Text-book of Euclid's Elements: For the Use of Schools : Books I-VI and XI Euclid,Henry Sinclair Hall Uten tilgangsbegrensning - 1891 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 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.
Side 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.
Side 326 - From this it is manifest that prisms upon triangular bases, of the same altitude, are to one another as their bases. Let the...
Side 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...
Side 291 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Side 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.
Side 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.
Side 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.