## The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored ; Also the Book of Euclid's Data, in Like Manner Corrected |

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Resultat 1-5 av 7

Side 69

If in a circle two straight lines cut one another which do not both

centre , they do not bisect each other . Let ABCD be a circle , and AC , BD two

straight lines in it which cut one another in the point E , and do not both

If in a circle two straight lines cut one another which do not both

**pass**through thecentre , they do not bisect each other . Let ABCD be a circle , and AC , BD two

straight lines in it which cut one another in the point E , and do not both

**pass**... Side 75

If two circles touch each other internally , the straight line which joins their centres

being produced shall

A straight line which joins the centres F , G , being produced ,

If two circles touch each other internally , the straight line which joins their centres

being produced shall

**pass**through the ... and G the centre of the circle ADE : theA straight line which joins the centres F , G , being produced ,

**passes**through ... Side 95

If AC , BD

is evident , that AE , EC , BE , ED , being all equal , the rectangle AE , EC is

likewise equal to the B rectangle BE , ED . But let one of them BD

the ...

If AC , BD

**pass**each of them through the A E D centre , so that E is the centre ; itis evident , that AE , EC , BE , ED , being all equal , the rectangle AE , EC is

likewise equal to the B rectangle BE , ED . But let one of them BD

**pass**throughthe ...

Side 97

Either DCA

centre E , and join EB ; therefore the angle EBD is a right ( 18. 3. ) angle : and D

because the straight line AC is bisected in E , and produced to the point D , the ...

Either DCA

**passes**through the centre , or it does not ; first , let it**pass**through thecentre E , and join EB ; therefore the angle EBD is a right ( 18. 3. ) angle : and D

because the straight line AC is bisected in E , and produced to the point D , the ...

Side 197

If it be possible , let AB , part of the straight line ABC , be in the plane , and the

part BC above it : and since the straight line AB is in the plane , it can be proс

duced in that plane : let it be produced to D : and let any plane

If it be possible , let AB , part of the straight line ABC , be in the plane , and the

part BC above it : and since the straight line AB is in the plane , it can be proс

duced in that plane : let it be produced to D : and let any plane

**pass**through the ...### Hva folk mener - Skriv en omtale

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### Andre utgaver - Vis alle

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1825 |

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Euclid,Robert Simson Uten tilgangsbegrensning - 1838 |

### Vanlige uttrykk og setninger

added altitude angle ABC angle BAC base centre circle circle ABCD circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples Euclid excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid Q. E. D. PROP radius reason rectangle rectangle contained rectilineal figure remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole

### Populære avsnitt

Side 9 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 81 - The angles in the same segment of a circle are equal to one another.

Side 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Side 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.

Side 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

Side 155 - 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 22 - ANY two angles of a triangle are together less than two right angles.

Side 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.

Side 24 - Any two sides of a triangle are together greater than the third side.