## 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

Resultat 1-5 av 13

Side 89

angle FLC : and because KC is equal to CL , KL is double of KC : in the same

manner , it may be

KC , as was demonstrated , and that KL is double of KC , and HK double of BK ,

HK ...

angle FLC : and because KC is equal to CL , KL is double of KC : in the same

manner , it may be

**shown**that HK is double of BK : and because BK is equal toKC , as was demonstrated , and that KL is double of KC , and HK double of BK ,

HK ...

Side 105

2 .

greater than D ; FA therefore the whole A EG is greater than K and D together ;

but , K together with D , is equal to L ; therefore F EG is greater than L ; but FG is

not ...

2 .

**shown**, that FG was E E not less than K , and , by the construction , EF isgreater than D ; FA therefore the whole A EG is greater than K and D together ;

but , K together with D , is equal to L ; therefore F EG is greater than L ; but FG is

not ...

Side 113

but it was

GK is the same multiple of AE , that LN is D of CF ; that is , GK , LN are equimulE

F tiples of AE , CF : and because KO , NP are equimultiples of BE , DF , if G A С ...

but it was

**shown**that LM is the same multiple of CD , B that GK is of AE ; thereforeGK is the same multiple of AE , that LN is D of CF ; that is , GK , LN are equimulE

F tiples of AE , CF : and because KO , NP are equimultiples of BE , DF , if G A С ...

Side 154

BAE to the angle BDC , the triangle ABE is equiangular E to the triangle BCD : as

therefore BA to AE , so is BD to DC ; wherefore the rectangle BA , DC is equal to

the rectan A A gle BD , AE : but the rectangle BC , AD has been

BAE to the angle BDC , the triangle ABE is equiangular E to the triangle BCD : as

therefore BA to AE , so is BD to DC ; wherefore the rectangle BA , DC is equal to

the rectan A A gle BD , AE : but the rectangle BC , AD has been

**shown**equal to ... Side 241

262 of the second edition of his Elements of Geometry , printed anno 1760 ,

observes in his notes , that it ought to have been

below the line EG . This probably Euclid omitted , as G it is very easy to perceive ,

that DG ...

262 of the second edition of his Elements of Geometry , printed anno 1760 ,

observes in his notes , that it ought to have been

**shown**that the point F fallsbelow the line EG . This probably Euclid omitted , as G it is very easy to perceive ,

that DG ...

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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: Viz. the First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1892 |

### 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.