## The Contents of the Fifth and Sixth Books of Euclid |

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The Contents of the Fifth and Sixth Books of Euclid (with a Note on ... Euclid Uten tilgangsbegrensning - 1908 |

The Contents of the Fifth and Sixth Books of Euclid Euclid,Micaiah John Muller Hill Uten tilgangsbegrensning - 1900 |

### Vanlige uttrykk og setninger

ABCD alternatives angle base Book called centre circle Comparing consequent construction corresponding sides definition described determine divided draw drawn duplicate ratio ENUNCIATION equal equal angles Euclid's EXAMPLE exist externally fact Fifth figures follows given greater Hence idea integer internally inversion Join kind known length magnitudes manner mean proportional measure meet necessary NOTE opposite pair parallel to BC parallelogram perpendicular possible produced proof Prop PROPOSITION prove ratio compounded ratio of equality rect rectangle contained rectilineal figure relative multiple scale required to prove respectively result right angle scale segments similar similar figures similarly square stage standing straight line Take taken term third triangle ABC vertex

### Populære avsnitt

Side 99 - IF two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals : the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides.

Side xviii - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM 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.

Side 99 - Prove that similar triangles are to one another in the duplicate ratio of their homologous sides.

Side xvi - If the vertical angle of a triangle be bisected by a straight line which also cuts the base, the segments of the base shall have the same ratio which the other sides of the triangle have to one another...

Side 99 - ABC, DEF have one angle in the one equal to one angle in the other, viz. the angle BAC to the angle EDF, and the sides about...

Side xvi - In a right triangle, if a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.

Side 35 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth: or, if the multiple of the first be equal to that of the second, the multiple of the third is also equal to that of the fourth : or, if...

Side 84 - If they do not intersect, show that the radical axis is perpendicular to the line joining the centres of the circles...

Side 100 - If an 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 of the straight line bisecting the angle.

Side 80 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means.