## The Elements of Euclid |

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Resultat 1-5 av 7

Side 143

BCD equal to the angle ECG : the ratio of the

parallelogram CF, is the same with the ratio which is compounded of the ratios of

their sides. Let BG, CG, be placed in a straight line; therefore DC and CE are also

in a ...

BCD equal to the angle ECG : the ratio of the

**parallelogram AC**to theparallelogram CF, is the same with the ratio which is compounded of the ratios of

their sides. Let BG, CG, be placed in a straight line; therefore DC and CE are also

in a ...

Side 177

being applied to the H G R Q. plane figure KM: - Y the straight line AB E. F Q

coinciding with KL P the figure

two of which are parallel; the opposite planes are similar and equal

being applied to the H G R Q. plane figure KM: - Y the straight line AB E. F Q

coinciding with KL P the figure

**AC**must C. ... be contained by six planes, two andtwo of which are parallel; the opposite planes are similar and equal

**parallelograms**. Side 332

may be found by making the angle FGH equal to the given angle ABC, and

drawing from any point F in one of its sides, FK perpendicular to the other GH: for

GF is to FK, as BA to AE, that is, as the rectangle AB, BC to the

may be found by making the angle FGH equal to the given angle ABC, and

drawing from any point F in one of its sides, FK perpendicular to the other GH: for

GF is to FK, as BA to AE, that is, as the rectangle AB, BC to the

**parallelogram AC**. Side 333

And if the ratio of the

straight line AB to BG is given; and if the ratio of ... If two parallelograms have

unequal but given angles, and if as a side of the first to a side of the second, so

the other ...

And if the ratio of the

**parallelogram AC**to DF be given, then the ratio of thestraight line AB to BG is given; and if the ratio of ... If two parallelograms have

unequal but given angles, and if as a side of the first to a side of the second, so

the other ...

Side 355

Because the

is given; and E G - C BK is similar (24. 6.) to

species. And since the parallelo- | gram AK given in magnitude is applied to F the

...

Because the

**parallelogram**AK is equal (43. 1.) to BC which is given, therefore AKis given; and E G - C BK is similar (24. 6.) to

**AC**, therefore BK ^ 1– is given inspecies. And since the parallelo- | gram AK given in magnitude is applied to F the

...

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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.