## 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 12

Side 26

not ; therefore the side AC is not less than AB ; and it has been shown that it is not

equal to AB ; therefore AC is

Q. E. D. PROP . XX . THEOR . Any two sides of a triangle are together

not ; therefore the side AC is not less than AB ; and it has been shown that it is not

equal to AB ; therefore AC is

**greater**than AB . Wherefore the**greater**angle , & c .Q. E. D. PROP . XX . THEOR . Any two sides of a triangle are together

**greater**... Side 29

AB equal to DE , and AC to DF ; but the angle BAC

the base BC is also

be the side which is not

...

AB equal to DE , and AC to DF ; but the angle BAC

**greater**than the angle EDF ;the base BC is also

**greater**than the base EF . Of the two sides DE , DF , let DEbe the side which is not

**greater**than the other , and at the point D , in the straight...

Side 136

and of A and C , M and G are equimultiples : and of B and D , N and K are

equimultiples : if M be

and if less , less ( 5. def . 5. ) : but G is

N : but ...

and of A and C , M and G are equimultiples : and of B and D , N and K are

equimultiples : if M be

**greater**than N , G is**greater**than K , and if equal , equal ;and if less , less ( 5. def . 5. ) : but G is

**greater**than K , therefore M is**greater**thanN : but ...

Side 273

Nor can the circle ABCD be to the circle EFGH , as the cone AL to any solid

circle ...

Nor can the circle ABCD be to the circle EFGH , as the cone AL to any solid

**greater**than the cone EN : for , if it be possible , let it be so to the solid I , which is**greater**than the cone EN : therefore , by inversion , as the circle EFGH to thecircle ...

Side 289

the circle BCDE : let this be the circumference KB ; therefore the straight line KB

is less than GU ; and because the angle BZK is obtuse , as was proved in the

preceding , therefore BK is

more ...

the circle BCDE : let this be the circumference KB ; therefore the straight line KB

is less than GU ; and because the angle BZK is obtuse , as was proved in the

preceding , therefore BK is

**greater**than BZ : but GU is**greater**than BK ; muchmore ...

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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.