## 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 |

### Inni boken

Resultat 1-5 av 9

Side 177

RECTILINEAL figures which are

rectilineal figure C ; the figure A is

...

RECTILINEAL figures which are

**similar**to the same rectilineal figures , are also**similar**to one another . Let each of the rectilineal figures , A , B be**similar**to therectilineal figure C ; the figure A is

**similar**to the figure B. Because A is**similar**to C...

Side 180

1. ) , AB is ( 7.5 . ) to G AD , as AE to AG ; and DC to CB , as GF to FE ; and also

CD to DA , as FG to GA : therefore the sides of the L parallelograms ABCD ,

AEFG about DK the equal angles are proportionals ; and they are therefore

1. ) , AB is ( 7.5 . ) to G AD , as AE to AG ; and DC to CB , as GF to FE ; and also

CD to DA , as FG to GA : therefore the sides of the L parallelograms ABCD ,

AEFG about DK the equal angles are proportionals ; and they are therefore

**similar**to ... Side 185

To a given straight line to apply a parallelogram equal to a given rectilineal figure

, and deficient by a parallelogram

rectilineal figure to which the parallelogram to be applied is to be equal , must ...

To a given straight line to apply a parallelogram equal to a given rectilineal figure

, and deficient by a parallelogram

**similar**to a given parallelogram : but the givenrectilineal figure to which the parallelogram to be applied is to be equal , must ...

Side 256

and

and

which meet one another , are parallel to KD , DL that meet one another , and are

not in ...

and

**similar**to the triangle HKD : for the same reason , the triangle AGH is equaland

**similar**to the triangle HLD : and because the two straight lines EH , HGwhich meet one another , are parallel to KD , DL that meet one another , and are

not in ...

Side 265

cause the pyramid ABCG is

( 11. def . ... angles are proportionals ; wherefore the parallelogram BM is

to EP : for the same reason , the parallelogram BN is

cause the pyramid ABCG is

**similar**to the pyramid DEFH , the angle ABC is equal( 11. def . ... angles are proportionals ; wherefore the parallelogram BM is

**similar**to EP : for the same reason , the parallelogram BN is

**similar**to ER , and BK to ...### Hva folk mener - Skriv en omtale

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### Andre utgaver - Vis alle

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.