## 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 |

### Inni boken

Resultat 1-5 av 13

Side 111

to the other sides , and the third angle to the third angle : therefore the straight

line KC is equal to CL , and the angle FKC to the angle FLC : and because KC is

equal to CL , KL is double of KC : in the same manner , it may be

is ...

to the other sides , and the third angle to the third angle : therefore the straight

line KC is equal to CL , and the angle FKC to the angle FLC : and because KC is

equal to CL , KL is double of KC : in the same manner , it may be

**shown**that HKis ...

Side 140

NM ; and because GH , HK are equimultiples of AB , BE , and that AB Kis greater

than BE , therefore GH N is greater ( 3. Ax . 5. ) than KH : but KO is not greater

than KH , wherefore GH is greater than Ko . In like manner it may be

...

NM ; and because GH , HK are equimultiples of AB , BE , and that AB Kis greater

than BE , therefore GH N is greater ( 3. Ax . 5. ) than KH : but KO is not greater

than KH , wherefore GH is greater than Ko . In like manner it may be

**shown**, that...

Side 141

which was likewise

greater than KO , taking KH from both , GK is greater than 0 ; wherefore K. also

LN is greater than MP ; and , consequently , adding NM to both , B LM is greater

than ...

which was likewise

**shown**in the preН. P ceding case . If therefore GH be Mgreater than KO , taking KH from both , GK is greater than 0 ; wherefore K. also

LN is greater than MP ; and , consequently , adding NM to both , B LM is greater

than ...

Side 273

than the pyramid in the cone EN ; but it is less , as was

therefore the circle ABCD is not to the circle EFGH , as the cone AL to any solid

which is less than the cone EN . In the same manner it may be denionstrated that

...

than the pyramid in the cone EN ; but it is less , as was

**shown**, which is absurd :therefore the circle ABCD is not to the circle EFGH , as the cone AL to any solid

which is less than the cone EN . In the same manner it may be denionstrated that

...

Side 296

... which is the boundary of the superficies KBCL , does nevertheless remain :

therefore the line BC has no breadth : and because the line BC is a superficies ,

and that a superficies has no thickness , as was

neither ...

... which is the boundary of the superficies KBCL , does nevertheless remain :

therefore the line BC has no breadth : and because the line BC is a superficies ,

and that a superficies has no thickness , as was

**shown**; therefore a line hasneither ...

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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.