## 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 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 ...

Side 106

proposition , there are some equimultiples of A and B , and some multiple of C

such , that the multiple of A is

is not

proposition , there are some equimultiples of A and B , and some multiple of C

such , that the multiple of A is

**greater**than the multiple of C , but the multiple of Bis not

**greater**than that of C. Let such multiples be taken , and let D , E , be the ... Side 109

N. KL of E is not

and of C , E let G , H be equimultiples , and K , L equimultiples of D , F , so that G

be

take ...

N. KL of E is not

**greater**than the multiple of F ( 7. def . 5. ) ; let such be taken ,and of C , E let G , H be equimultiples , and K , L equimultiples of D , F , so that G

be

**greater**than K , but H not**greater**than L ; and whatever multiple G is of C ,take ...

Side 115

so is D to E ; and as B to C , so is E to F. If A be

than F ; and if equal , equal ; and if less , less . Because A is

B is any other magnitude , and that the

so is D to E ; and as B to C , so is E to F. If A be

**greater**than C , D shall be**greater**than F ; and if equal , equal ; and if less , less . Because A is

**greater**than C , andB is any other magnitude , and that the

**greater**has to the same magnitude a ... Side 274

Three magnitudes , A , B , C being given , to find a fourth such , that every three

shall be

less than A , B , C together : of the three , A , B , C , let A be that which is not less ...

Three magnitudes , A , B , C being given , to find a fourth such , that every three

shall be

**greater**than the remaining one . Let D be the fourth : therefore D must beless than A , B , C together : of the three , A , B , C , let A be that which is not less ...

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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.