## 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 8

Side 20

C Because AC is equal to CB , and CD

the two sides AC , CD are equal to BC , CD , each to each ; and the angle ACD is

equal to the angle BCD ; therefore the base AD is equal to the base ( 4. 1. ) ...

C Because AC is equal to CB , and CD

**common**to the two triangles ACD , BCD ;the two sides AC , CD are equal to BC , CD , each to each ; and the angle ACD is

equal to the angle BCD ; therefore the base AD is equal to the base ( 4. 1. ) ...

Side 210

and any straight line FG in the plane DE , which is at right angles to CE the

plane CK ; therefore the plane DE is at right angles to the plane CK . In like

manner , it ...

and any straight line FG in the plane DE , which is at right angles to CE the

**common**section of the planes , has been proved to be perpendicular to the otherplane CK ; therefore the plane DE is at right angles to the plane CK . In like

manner , it ...

Side 289

... the pyramids shall be similar to one another , each to each ; because they have

the solid angles at their

each pyramid , and their other solid angle at the bases equal to one another ,

each ...

... the pyramids shall be similar to one another , each to each ; because they have

the solid angles at their

**common**vertex , the centre of the sphere the same ineach pyramid , and their other solid angle at the bases equal to one another ,

each ...

Side 295

The boundary of a superficies is called a line , or a line is the

of two superficies that are contiguous , or which divides one superficies into two

contiguous parts : thus , if BC be one of the boundaries which contain the ...

The boundary of a superficies is called a line , or a line is the

**common**boundaryof two superficies that are contiguous , or which divides one superficies into two

contiguous parts : thus , if BC be one of the boundaries which contain the ...

Side 296

... and that a superficies has no thickness , as was shown ; therefore a line has

neither breadth nor thickness , but only length . The boundary of a line is called a

point , or a point is the

...

... and that a superficies has no thickness , as was shown ; therefore a line has

neither breadth nor thickness , but only length . The boundary of a line is called a

point , or a point is the

**common**boundary or extremity of H G M two lines that are...

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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.