## 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 |

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Resultat 1-5 av 5

Side 42

to the angle ABD , because BA is equal to AD , being sides of a square ;

side BC is equal ( 6. 1. ) to the side CG ; but CB is equal ( 34. 1. ) also to GK , and

CG to BK ...

to the angle ABD , because BA is equal to AD , being sides of a square ;

**wherefore**the angle CGB is equal to the A C B angle GBC ; and therefore theside BC is equal ( 6. 1. ) to the side CG ; but CB is equal ( 34. 1. ) also to GK , and

CG to BK ...

Side 129

À BCA ;

EGF ( 32. 1. ) , and the triangle ABC is therefore ES F equiangular to the triangle

GEF ; and consequently they have their sides opposite to the B с equal angles ...

À BCA ;

**wherefore**the remaining A D angle BAC is equal to the remaining angleEGF ( 32. 1. ) , and the triangle ABC is therefore ES F equiangular to the triangle

GEF ; and consequently they have their sides opposite to the B с equal angles ...

Side 300

Because the ratio of AE to CD is given , as AE to CD , so make BE to FD ;

therefore the ratio of BE to FD is given , and BE is given ;

A B E ( 2. dat . ) : and because as AE to CD , so is BE to FD , the remainder AB is (

19. 5. ) ...

Because the ratio of AE to CD is given , as AE to CD , so make BE to FD ;

therefore the ratio of BE to FD is given , and BE is given ;

**wherefore**FD is givenA B E ( 2. dat . ) : and because as AE to CD , so is BE to FD , the remainder AB is (

19. 5. ) ...

Side 317

In like manner EF also is given in po . sition ;

the points D , E are given ; therefore each of the straight lines DE , EF , FD is

given ( 29 . dat . ) in magnitude ;

42.

In like manner EF also is given in po . sition ;

**wherefore**the point F is given : andthe points D , E are given ; therefore each of the straight lines DE , EF , FD is

given ( 29 . dat . ) in magnitude ;

**wherefore**the triangle DEF is given in species (42.

Side 359

AC , BE is equal to AB , BC ; and the rectangle AB , BC is given ,

BE is given : and because the sum of the squares of AB , BC is given , the square

of AC which is equal ( 47. 1. ) to that sum is given ; and AC itself is therefore ...

AC , BE is equal to AB , BC ; and the rectangle AB , BC is given ,

**wherefore**AC ,BE is given : and because the sum of the squares of AB , BC is given , the square

of AC which is equal ( 47. 1. ) to that sum is given ; and AC itself is therefore ...

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

The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2017 |

### 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.