## The Elements of Euclid |

### Inni boken

Resultat 1-5 av 12

Side 57

Let ABCD be a circle, and AD its diameter, in which let any

which is not the centre; let the centre be E; of all the straight lines FB, FC, FG, &c.

that can be drawn from F to the circumference, FA is the greatest, and FD, the

other ...

Let ABCD be a circle, and AD its diameter, in which let any

**point F**be takenwhich is not the centre; let the centre be E; of all the straight lines FB, FC, FG, &c.

that can be drawn from F to the circumference, FA is the greatest, and FD, the

other ...

Side 76

point B, and at the point B, in the straight line BF, make (23. ... to one another: and

because the straight line BD is cut into two equal parts in the

unequal in the point E, the F rectangle BE ED, together with the square of BF, ...

point B, and at the point B, in the straight line BF, make (23. ... to one another: and

because the straight line BD is cut into two equal parts in the

**point F**, and into twounequal in the point E, the F rectangle BE ED, together with the square of BF, ...

Side 89

the angles BCD, CDE by the straight lines CF, DF, and from the

they meet, draw the straight lines FB, FA, FE; therefore, since BC is equal to CD,

and CF common to the triangles BCF, DCF, the two sides BC, CF, are equal to ...

the angles BCD, CDE by the straight lines CF, DF, and from the

**point F**, in whichthey meet, draw the straight lines FB, FA, FE; therefore, since BC is equal to CD,

and CF common to the triangles BCF, DCF, the two sides BC, CF, are equal to ...

Side 177

... PL; and the

coincides with the figure KR, and the straight line DH with NR, and the

with the

...

... PL; and the

**points**E,**F**, with the**points**O, P. In the same manner, the figure AHcoincides with the figure KR, and the straight line DH with NR, and the

**point**Hwith the

**point**R : and because the solid angle at B is equal to the solid angle at L,...

Side 185

A S H T But if the insisting straight lines AG, HK, BE, LM ; CN, RS, DF, OP, be not

at right angles to the bases AB, CD; in this case likewise the solid AE, is equal to

the solid CF: from the

...

A S H T But if the insisting straight lines AG, HK, BE, LM ; CN, RS, DF, OP, be not

at right angles to the bases AB, CD; in this case likewise the solid AE, is equal to

the solid CF: from the

**points**G, K, E, M ; N, S,**F**, P, draw the straight lines GQ, KT...

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### Andre utgaver - Vis alle

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.