## The Elements of Euclid |

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Side 101

Euclid Robert Simson. First, let GB be equal to E, HD is equal A to F : make CK

equal to F; and because AG is the same

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

Euclid Robert Simson. First, let GB be equal to E, HD is equal A to F : make CK

equal to F; and because AG is the same

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

**multiple**of E, that KH is of F. Side 106

Euclid Robert Simson. proposition, there are some equimultiples of A and B, and

some

but the

...

Euclid Robert Simson. 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 B is not greater than that of C. Let such**multiples**be taken, and...

Side 255

... any

then, by the 5th def. of book 5, the

from the hypothesis that A has a greater ratio to C, than B has to C, there must, ...

... any

**multiple**whatever of C; if the**multiple**of A be greater than the**multiple**of C,then, by the 5th def. of book 5, the

**multiple**of B is also greater than that of C ; but,from the hypothesis that A has a greater ratio to C, than B has to C, there must, ...

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**| of C;then if the

**multiple**of B be greater than the**multiple**of C, the**multiple**of A is also ... Side 257

... possible equimultiples of the second B, and of the fourth D, there can be found

some One

one another; and also, in the same case, 33 BOOK W. NOTEs. 257 PROP. XVIII.

... possible equimultiples of the second B, and of the fourth D, there can be found

some One

**multiple**EF of the first A, and one IK of the second B, that are equal toone another; and also, in the same case, 33 BOOK W. NOTEs. 257 PROP. XVIII.

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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1834 |

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

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

### Vanlige uttrykk og setninger

altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given point given ratio given straight line gles gnomon join less Let ABC meet multiple parallel parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third three plane angles triangle ABC triplicate ratio vertex wherefore

### 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.