## 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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Resultat 1-5 av 6

Side 395

In like manner EF also is given in position ; wherefore the point F is given : and

the points D , E are given ; therefore each of the straight lines DE , EF , FD is

given ( 29. dat . ) in magnitude ; wherefore the triangle DEF is

42.

In like manner EF also is given in position ; wherefore the point F is given : and

the points D , E are given ; therefore each of the straight lines DE , EF , FD is

given ( 29. dat . ) in magnitude ; wherefore the triangle DEF is

**given in species**(42.

Side 400

And the triangles DEF , DEK are

triangles ABC , ABL are H ... in this third case there are always two triangles of a

different species , to which the things mentioned as given in the proposition can

agree .

And the triangles DEF , DEK are

**given in species**; thereE K fore also thetriangles ABC , ABL are H ... in this third case there are always two triangles of a

different species , to which the things mentioned as given in the proposition can

agree .

Side 403

IF from the vertex of a triangle ,

base in a given angle , it shall have a given ratio to the base . From the vertex A

of the triangle ABC which is

a ...

IF from the vertex of a triangle ,

**given in species**, a straight line be drawn to thebase in a given angle , it shall have a given ratio to the base . From the vertex A

of the triangle ABC which is

**given in species**, let AD be drawn to the base BC ina ...

Side 407

Take a straight line H given in magnitude ; and because the ratio of AB to CD is

given , make the ratio of H to K the same with ... If two straight lines have a given

ratio to one another ; the rectilineal figures

...

Take a straight line H given in magnitude ; and because the ratio of AB to CD is

given , make the ratio of H to K the same with ... If two straight lines have a given

ratio to one another ; the rectilineal figures

**given in species**described upon them...

Side 421

If two straight lines have a given ratio to one another , and upon one of them be

described a rectilineal figure

parallelogram having a given angle ; if the figure have a given ratio to the

parallelogram , the ...

If two straight lines have a given ratio to one another , and upon one of them be

described a rectilineal figure

**given in species**, and upon the other aparallelogram having a given angle ; if the figure have a given ratio to the

parallelogram , the ...

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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.