## 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 46

D Let AB be the given straight line ; it is required to

... the figure ADEB is rectangular , and it has been demonstrated that it is

equilateral ; it is therefore a square , and it is

line AB .

D Let AB be the given straight line ; it is required to

**describe**a square upon AB .... the figure ADEB is rectangular , and it has been demonstrated that it is

equilateral ; it is therefore a square , and it is

**described**upon the given straightline AB .

Side 289

... line AZ consequently greater than the straight line AG . COR . And if in the

lesser sphere there be

betwixt the points in which the straight lines from the centre of the sphere drawn ...

... line AZ consequently greater than the straight line AG . COR . And if in the

lesser sphere there be

**described**a solid polyhedron , by drawing straight linesbetwixt the points in which the straight lines from the centre of the sphere drawn ...

Side 405

If two rectilineal figures given in species be

, they shall have a given ratio to one another . * Let any two rectilineal figures

ABCDE , ABFG , which are given in species , be

straight ...

If two rectilineal figures given in species be

**described**upon the same straight line, they shall have a given ratio to one another . * Let any two rectilineal figures

ABCDE , ABFG , which are given in species , be

**described**upon the samestraight ...

Side 407

To find the ratio of two similar rectilineal figures , E , F , similarly

straight lines AB , CD which have a given ratio to one another : let G be a third

proportional to AB , CD . Take a straight line H given in magnitude ; and because

...

To find the ratio of two similar rectilineal figures , E , F , similarly

**described**uponstraight lines AB , CD which have a given ratio to one another : let G be a third

proportional to AB , CD . Take a straight line H given in magnitude ; and because

...

Side 408

If a rectilineal figure given in species be

magnitude , the figure is given in magnitude . Let the rectilineal figure ABCDE

given in species be

If a rectilineal figure given in species be

**described**upon a straight line given inmagnitude , the figure is given in magnitude . Let the rectilineal figure ABCDE

given in species be

**described**upon the straight line AB given in magnitude ; 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.