## 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 101

First , let GB be equal to E , HD is equal A to F : make CK equal to F ; and

because K AG is the same

E , and CK to F ; therefore AB is the same

by the G.

First , let GB be equal to E , HD is equal A to F : make CK equal to F ; and

because K AG is the same

**multiple**of E , that CH is of F , and that GB is equal toE , and CK to F ; therefore AB is the same

**multiple**of E , that KH is of F. But AB ,by the G.

Side 106

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

such , that the

is not greater than that of C. Let such

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

**multiple**of Csuch , 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 255

Therefore A is not equal to B. ” The force of which reasoning is this ; if A had to C

the same ratio that B has to C ; then if any equimultiples whatever of A and B be

taken , and any

Therefore A is not equal to B. ” The force of which reasoning is this ; if A had to C

the same ratio that B has to C ; then if any equimultiples whatever of A and B be

taken , and any

**multiple**whatever of C ; if the**multiple**of A be greater than the ... Side 256

The above mentioned proposition , viz . If A have to C a greater ratio than B to C :

and if of A and B there be taken certain equimultiples , and some

then if the

...

The above mentioned proposition , viz . If A have to C a greater ratio than B to C :

and if of A and B there be taken certain equimultiples , and some

**multiple**I of C ;then if the

**multiple**of B be greater than the**multiple**of C , the**multiple**of A is also...

Side 258

T T -Н 11 GE equal to one another ; and also , in the same case , some one

equality is no where to be found . If the rst case happen [ i . e . if such equality is

to be found ) ...

T T -Н 11 GE equal to one another ; and also , in the same case , some one

**multiple**GH of the third C equal to LM the**multiple**of the fourth D , or suchequality is no where to be found . If the rst case happen [ i . e . if such equality is

to be found ) ...

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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.