## 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

AC at

angles ABE , BED is a

and it has been demonstrated that it is equilateral ; it is therefore a square , and it

is ...

AC at

**right angles**to AB ; and make ( 3. 1. ) ... therefore each of the oppositeangles ABE , BED is a

**right angle**; wherefore the figure ADEB is rectangular ,and it has been demonstrated that it is equilateral ; it is therefore a square , and it

is ...

Side 58

to the squares of AE , EF , because AEF is a

AF is double of the squares of AC , CD : but the squares of AD , DF are equal to

the square of AF , because the angle ADF is a

...

to the squares of AE , EF , because AEF is a

**right angle**; therefore the square ofAF is double of the squares of AC , CD : but the squares of AD , DF are equal to

the square of AF , because the angle ADF is a

**right angle**; therefore the squares...

Side 91

1 In a circle , the angle in a semicircle is a

greater than a semicircle is less than a

less than a semicircle is greater than a

1 In a circle , the angle in a semicircle is a

**right angle**; but the angle in a segmentgreater than a semicircle is less than a

**right angle**; and the angle in a segmentless than a semicircle is greater than a

**right angle**. Let ABCD be a circle , of ... Side 202

In the plane to which AB is at

make DE equal to AB , and join BE , AE , AD ... therefore each of the angles ABD ,

ABE is a

...

In the plane to which AB is at

**right angles**, draw DE at**right angles**to BD , andmake DE equal to AB , and join BE , AE , AD ... therefore each of the angles ABD ,

ABE is a

**right angle**; and because the straight line BD meets the parallel straight...

Side 304

the angle AGF is equal to CHF , and AFG to B the angle CFH : to these last add

the common angles AFH ; therefore the two angles AFG , AFH are equal to the

two angles CFH , HFA , which two last are equal together to two

1. ) ...

the angle AGF is equal to CHF , and AFG to B the angle CFH : to these last add

the common angles AFH ; therefore the two angles AFG , AFH are equal to the

two angles CFH , HFA , which two last are equal together to two

**right angles**( 13.1. ) ...

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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.