## The Elements of Euclid: 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. viz. the first six books, together with the eleventh and twelfth |

### Inni boken

Side 11

From the

AB and C be the two given straight lines , whereof AB is the

to cut off from AB , the

From the

**greater**of two given straight lines to cut off a part equal to the less . LetAB and C be the two given straight lines , whereof AB is the

**greater**. It is requiredto cut off from AB , the

**greater**, a part equal to C , the less . Ç B A From the point ... Side 14

to the angle ADC : but the angle ACD is

the angle ADC is

is ...

to the angle ADC : but the angle ACD is

**greater**than the angle BCD ; thereforethe angle ADC is

**greater**also than BCD ; much more then is the angle BDC**greater**than the angle BCD . Again , because CB is equal to DB , the angle BDCis ...

Side 19

If one side of a triangle be produced , the exterior angle is

the interior opposite angles . Let ABC be a triangle , and let its side BC be

produced to D , the exterior angle ACD is

opposite ...

If one side of a triangle be produced , the exterior angle is

**greater**than either ofthe interior opposite angles . Let ABC be a triangle , and let its side BC be

produced to D , the exterior angle ACD is

**greater**than either of the interioropposite ...

Side 20

Produce BC to D ; and because ACD is the exterior angle of the triangle ABC ,

ACD is

these add the angle ACB ; therefore the angles ACD , ACB are

angles ...

Produce BC to D ; and because ACD is the exterior angle of the triangle ABC ,

ACD is

**greater**( 16. 1. ) than the interior and opposite angle ABC ; to each ofthese add the angle ACB ; therefore the angles ACD , ACB are

**greater**than theangles ...

Side 21

For , if it be not

equal , because then the angle ABC would be equal ( 5. 1. ) to the angle ACB ;

but it is not ; therefore AC is not equal to AB ; neither is it less ; because then the ...

For , if it be not

**greater**, AC must A either be , equal to AB , or less than it ; it is notequal , because then the angle ABC would be equal ( 5. 1. ) to the angle ACB ;

but it is not ; therefore AC is not equal to AB ; neither is it less ; because then the ...

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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1810 |

The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |

### Vanlige uttrykk og setninger

added altitude angle ABC angle BAC base centre circle circle ABCD circumference common cone contained 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 gles greater Greek half join less likewise 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 45 - Ir a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Side 41 - 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 54 - Ir any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two points in the circumference ; the straight line drawn from A to B shall fall within the circle.

Side 18 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC.

Side 10 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line: it is required to draw from the point A a straight line equal to BC.

Side 8 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 256 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.

Side 129 - 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 23 - At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A...

Side 20 - ANY two angles of a triangle are together less than two right angles.