## 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 44

H draw KLM parallel to AD or EF , and also through A draw AK parallel to CL or

DM : and be A C B D cause

the

CB ...

H draw KLM parallel to AD or EF , and also through A draw AK parallel to CL or

DM : and be A C B D cause

**AC**is ... add to each of these LG , which is equal tothe

**square**of CB , therefore the rectangle AD , DB , together with the**square**ofCB ...

Side 46

CE at right angles to AB , and make it equal to AC or CB , and join EA , EB ;

through D draw ( 31. 1. ) DF parallel to ... the side DB : and because AC is equal

to CE , the

AC ...

CE at right angles to AB , and make it equal to AC or CB , and join EA , EB ;

through D draw ( 31. 1. ) DF parallel to ... the side DB : and because AC is equal

to CE , the

**square of AC**is equal to the square of CE ; there . fore the squares ofAC ...

Side 48

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 of

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 of

EA is double of the

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

Side 50

to the squares of BD , DA , because the angle BDA is a right angle , and the

square B D C of AC is equal to the squares of AD , DC : therefore the squares of

CB , BA are equal to the

the ...

to the squares of BD , DA , because the angle BDA is a right angle , and the

square B D C of AC is equal to the squares of AD , DC : therefore the squares of

CB , BA are equal to the

**square of AC**, and twice the rectangle CB , BD , that is ,the ...

Side 359

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

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 ...### Hva folk mener - Skriv en omtale

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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.