## The Elements of Euclid |

### Inni boken

Resultat 1-5 av 18

Side 16

DB and the

was to be done. - - A. D B PROP. XI. PROB. To draw a straight line at right angles

to a given straight line, from a given point in the same. Let AB be a given straight

...

DB and the

**straight line AB**is divided into two equal parts in the point / D. Whichwas to be done. - - A. D B PROP. XI. PROB. To draw a straight line at right angles

to a given straight line, from a given point in the same. Let AB be a given straight

...

Side 36

Then, because the straight line HF falls upon the parallels AH, EF, the ahgles

AHF, HFE are together equal (29. ... is applied to the

the triangle C, and has the angle ABM equal to the angle D. Which was to be

done.

Then, because the straight line HF falls upon the parallels AH, EF, the ahgles

AHF, HFE are together equal (29. ... is applied to the

**straight line**,**AB**, is equal tothe triangle C, and has the angle ABM equal to the angle D. Which was to be

done.

Side 86

Take any

AB, BC be equal to the square of CA; and from the centre A, at the distance AB,

describe the circle BDE, in which place (1. 4.) the straight line BD is equal to AC,

...

Take any

**straight line AB**, and divide (11. 2.) it in the point C, so that the rectangleAB, BC be equal to the square of CA; and from the centre A, at the distance AB,

describe the circle BDE, in which place (1. 4.) the straight line BD is equal to AC,

...

Side 89

, and the right angle FHC equal to C K D the right angle FKC; in the triangles -

FHC, FKC there are two angles of one equal to two angles of the other, and the ...

**straight lines AB**, BC, CD, DE, EA ; A and because the angle HCF is equal to KCF, and the right angle FHC equal to C K D the right angle FKC; in the triangles -

FHC, FKC there are two angles of one equal to two angles of the other, and the ...

Side 177

being applied to the H G R Q. plane figure KM: - Y the

coinciding with KL P the figure AC must C. N M coincide with the fi- D N *N gure

KM, because - they are equal and A B K L similar: therefore the straight lines AD,

DC, ...

being applied to the H G R Q. plane figure KM: - Y the

**straight line AB**E. F Qcoinciding with KL P the figure AC must C. N M coincide with the fi- D N *N gure

KM, because - they are equal and A B K L similar: therefore the straight lines AD,

DC, ...

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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.