## 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 8

Side 90

K , L , the centres of the circles , and join BK , KC , EL , LF : and because the

angle BKC is equal ( 27. 3. ) to the angle ELF : and because the circles ABC ,

DEF are ...

K , L , the centres of the circles , and join BK , KC , EL , LF : and because the

**circumference**BGC is equal to А D K L B с Е F G H the**circumference**EHF , theangle BKC is equal ( 27. 3. ) to the angle ELF : and because the circles ABC ,

DEF are ...

Side 189

In equal circles , angles , whether at the centres or

same ratio which the

...

In equal circles , angles , whether at the centres or

**circumferences**, have thesame ratio which the

**circumferences**on ... EDF at their**circumferences**: as the**circumference**BC to the**circumference**EF , so is the angle BGC to the angle EHF...

Side 190

to the angle EHN ; and if the

angle BGL is greater than EHN ; and if less , less : there being then four

magnitudes , the two

the ...

to the angle EHN ; and if the

**circumference**BL be greater than EN , likewise theangle BGL is greater than EHN ; and if less , less : there being then four

magnitudes , the two

**circumferences**BC , EF , and the two angles BGC , EHF ; ofthe ...

Side 191

Therefore ( 5. def . 5 ) , as the

the sector BGC to the sector EHF . Wherefore , in equal circles , & c . Q. E. D.

PROP . B. THEOR . If an angle of a BOOK VI .. 191 THE ELEMENTS OF EUCLID .

Therefore ( 5. def . 5 ) , as the

**circumference**BC is to the**circumference**EF , so isthe sector BGC to the sector EHF . Wherefore , in equal circles , & c . Q. E. D.

PROP . B. THEOR . If an angle of a BOOK VI .. 191 THE ELEMENTS OF EUCLID .

Side 289

the circle BCDE : let this be the

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 ; much

more ...

the circle BCDE : let this be the

**circumference**KB ; therefore the straight line KBis 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 ; much

more ...

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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.