## 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 5

Side 48

EG is double of the

of EG is double of the

EA is double of the

...

EG is double of the

**square**of EF : and EF is equal to CD ; wherefore the**square**of EG is double of the

**square**of CD : but it was de monstrated , that the**square**ofEA is double of the

**square**of AC ; therefore the squares of AE , EG are double of...

Side 78

to the

together with the

ED is equal ( 47. 1. ) to the squares of EB , BD because EBD is a right angle : E ...

to the

**square**С of ED , and CE is equal to EB : therefore the rectangle AD , DC ,together with the

**square**of В. EB , is equal to the**square**of ED : but the**square**ofED is equal ( 47. 1. ) to the squares of EB , BD because EBD is a right angle : E ...

Side 357

Also, the Book of Euclid's Data, in Like Manner Corrected. viz. the first six books,

together with the eleventh and t Euclid, Robert Simson. of rectangle CB , BD is

given , being the given excess of the

...

Also, the Book of Euclid's Data, in Like Manner Corrected. viz. the first six books,

together with the eleventh and t Euclid, Robert Simson. of rectangle CB , BD is

given , being the given excess of the

**square**BC , BA ; therefore the**square**of BC...

Side 361

The excess of the

rectangle BC , CD is given , for it is equal ( 3. 2. ) to the given rectangle CB , BD ;

therefore , because the rectangle contained by the straight lines FB , BC is given ,

and ...

The excess of the

**square**of BC above the**square**of BF , that is , above therectangle BC , CD is given , for it is equal ( 3. 2. ) to the given rectangle CB , BD ;

therefore , because the rectangle contained by the straight lines FB , BC is given ,

and ...

Side 379

magnitude of AC is exhibited by making the rectangle EG , GH equal to it ; and

the given excess of the

the rectangle CB , BL is equal , is exhibited by the rectangle HG , GL : then , in the

...

magnitude of AC is exhibited by making the rectangle EG , GH equal to it ; and

the given excess of the

**square**of BC above the**square**of BA , to which excessthe rectangle CB , BL is equal , is exhibited by the rectangle HG , GL : then , in the

...

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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.