## 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 7

Side 220

to one another : and in the same manner it may be demonstrated , that the other

planes in which the equal angles are , have ... Let there be two

and B , of which the

...

to one another : and in the same manner it may be demonstrated , that the other

planes in which the equal angles are , have ... Let there be two

**solid angles**at Aand B , of which the

**solid angle**at A is contained by the three plane angles CAD...

Side 221

Solid figures contained by the same number of equal and similar planes alike

situated , and having none of their solid ... Because the

contained by the three plane angles BAD , BAE , EAD , which , by the hypothesis

, are ...

Solid figures contained by the same number of equal and similar planes alike

situated , and having none of their solid ... Because the

**solid angle**at A iscontained by the three plane angles BAD , BAE , EAD , which , by the hypothesis

, are ...

Side 224

is of the base AF , the same multiple is the solid LV of the solid AV : for the same

reason , whatever multiple the base NF is of ... At a given point in a given straight

line , to make a

...

is of the base AF , the same multiple is the solid LV of the solid AV : for the same

reason , whatever multiple the base NF is of ... At a given point in a given straight

line , to make a

**solid angle**equal to a given**solid angle**contained by three plane...

Side 225

same at right angles to the plane BAL ; and make KH equal to GF , and join AH :

then the

BAH , HAL , is equal to the

same at right angles to the plane BAL ; and make KH equal to GF , and join AH :

then the

**solid angle**at A , which is contained by the three plane angles BAL ,BAH , HAL , is equal to the

**solid angle**at D contained by the three plane angles ... Side 289

And if in the lesser sphere there be described a solid polyhedron , by drawing

straight lines betwixt the points in which the ... sphere the same in each pyramid ,

and their other

11. ) ...

And if in the lesser sphere there be described a solid polyhedron , by drawing

straight lines betwixt the points in which the ... sphere the same in each pyramid ,

and their other

**solid angle**at the bases equal to one another , each to each ( B.11. ) ...

### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### 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.