## 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 273

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

solid greater than the cone EN : and it has been

circle ABCD to the circle EFGH , as the cone AL to any solid less than the cone

EN ...

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

solid greater than the cone EN : and it has been

**demonstrated**that neither is thecircle ABCD to the circle EFGH , as the cone AL to any solid less than the cone

EN ...

Side 313

this book : the author of it designed to

F , H be proportionals , they are also ... its

because it is

this book : the author of it designed to

**demonstrate**, that if four magnitudes E , G ,F , H be proportionals , they are also ... its

**demonstration**: for , when he says , “because it is

**demonstrated**that if K be greater than M , L is greater than N , ” & c . Side 318

Wherefore the 10th proposition is not sufficiently

he who has given the

instead of that which Eudoxus or Euclid had given , has been deceived in ...

Wherefore the 10th proposition is not sufficiently

**demonstrated**. And it seems thathe who has given the

**demonstration**of the 10th proposition as we now have it ,instead of that which Eudoxus or Euclid had given , has been deceived in ...

Side 320

B. V. The

depends upon this hypothesis , that to any ... be

propositions preceding this : so far is it from deserving to be reckoned an axiom ,

as Clavius ...

B. V. The

**demonstration**of this is none of Euclid's , nor is it legi . timate ; for itdepends upon this hypothesis , that to any ... be

**demonstrated**by thepropositions preceding this : so far is it from deserving to be reckoned an axiom ,

as Clavius ...

Side 325

To this a case is added which occurs not unfrequently in

VIII . B. VI . It seems plain that some editor has changed the

Euclid gave of this proposition : for , after he has

...

To this a case is added which occurs not unfrequently in

**demonstration**. PROP .VIII . B. VI . It seems plain that some editor has changed the

**demonstration**thatEuclid gave of this proposition : for , after he has

**demonstrated**, that the triangles...

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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.