## 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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Side 269

Therefore the rest of the cylinder , that is , the prism of which the base is the

polygon AEBFCGDH , and of which the altitude is the same with that of the

cylinder , is greater than the triple of the

12. ) of the ...

Therefore the rest of the cylinder , that is , the prism of which the base is the

polygon AEBFCGDH , and of which the altitude is the same with that of the

cylinder , is greater than the triple of the

**cone**: but this prism is triple ( 1. Cor . 7.12. ) of the ...

Side 270

D of the

part of the cylinder . Let these be the segments upon AE , EB , BF , FC , CG , GD ,

DH ...

D of the

**cone**, and so on , there must at length remain some segments of the**cone**, which together shall be less than the excess of the**cone**above the thirdpart of the cylinder . Let these be the segments upon AE , EB , BF , FC , CG , GD ,

DH ...

Side 271

tex with the

circumscribed about it , because they are to one another as their bases ( 6. 12. ) :

but the

which ...

tex with the

**cone**, * the pyramid inscribed in the**cone**is half of the pyramidcircumscribed about it , because they are to one another as their bases ( 6. 12. ) :

but the

**cone**is less than the circumscribed pyramid ; therefore the pyramid ofwhich ...

Side 273

than the pyramid in the

therefore the circle ABCD is not to the circle EFGH , as the

which is less than the

...

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 solidwhich is less than the

**cone**EN . In the same manner it may be denionstrated that...

Side 277

triplicate ratio of that which EG has to AC : but as the solid Z is to the

, so is the

ABCDL , because the solid Z is greater than the

triplicate ratio of that which EG has to AC : but as the solid Z is to the

**cone**ABCDL, so is the

**cone**EFGHN to some solid , which must be less ( 14. 5. ) than the**cone**ABCDL , because the solid Z is greater than the

**cone**EFGHN : therefore the ...### Hva folk mener - Skriv en omtale

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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.