## 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 vi

Also the

explicit, and a more general Demonstration is given, instead of that which was in

the

Also the

**Note**on the 29th Proposition, Book 1st, is altered, and made moreexplicit, and a more general Demonstration is given, instead of that which was in

the

**Note**on the 10th Definition of Book 11th ; besides, the Translation is much ... Side 260

But it is also less , which is impossible . There• See

explained the same way as at the

base ABC is not to the base DEF 260 BOOK XII . THE ELEMENTS OF EUCLID .

But it is also less , which is impossible . There• See

**Note**. + This may beexplained the same way as at the

**note**t in proposition 2 in the like case . fore thebase ABC is not to the base DEF 260 BOOK XII . THE ELEMENTS OF EUCLID .

Side 273

For , if the cone ABCDL has not to the cone EFGHN the triplicate ratio of that

which AC has to EG , the cone ABCDL shall have the triplicate of that ratio to

some solid which is less or • See

Mm 1 ...

For , if the cone ABCDL has not to the cone EFGHN the triplicate ratio of that

which AC has to EG , the cone ABCDL shall have the triplicate of that ratio to

some solid which is less or • See

**Note**. greater than the cone EFGHN . First , let itMm 1 ...

Side 315

See the

geometers , and is necessary to the 5th and 6th propositions of the 10th book :

Clavius , in his

See the

**note**on that corollary . PROP . C. B. V. This is frequently made use of bygeometers , and is necessary to the 5th and 6th propositions of the 10th book :

Clavius , in his

**notes**subjoined to the 8th def . of book 5. demonstrates it only in ... Side 346

Mr. Thomas Simpson , in his

Geometry , p . 262 , after repeating the words of this

possibly show any want of skill in an editor ( he means Euclid or Theon ) to refer

to ...

Mr. Thomas Simpson , in his

**notes**at the end of the 2d edition of his Elements ofGeometry , p . 262 , after repeating the words of this

**note**, adds , “ Now , can itpossibly show any want of skill in an editor ( he means Euclid or Theon ) to refer

to ...

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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.