## The Elements of Euclid |

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Side 43

to DB, and E G F DF together with CH is the

CMG is equal to the rectangle AD, DB : to each of these add LG, which is equal (

43. 1.) to the square of CD; therefore the

to DB, and E G F DF together with CH is the

**gnomon**CMG ; therefore the**gnomon**CMG is equal to the rectangle AD, DB : to each of these add LG, which is equal (

43. 1.) to the square of CD; therefore the

**gnomon**CMG, together with LG, ... Side 44

to HF ; therefore also AL is equal to HF: to each of these add CM; therefore the

whole AM is equal to the |

contained by AD, DB, for DM is equal (Cor. 4. 2.) to DB : therefore the

CMG is ...

to HF ; therefore also AL is equal to HF: to each of these add CM; therefore the

whole AM is equal to the |

**gnomon**CMG : and DM is the E G F rectanglecontained by AD, DB, for DM is equal (Cor. 4. 2.) to DB : therefore the

**gnomon**CMG is ...

Side 45

And it was demonstrated that the four CK, BN, GR, and RN are quadruple to CK:

therefore the eight rectangles which contain the

AK; and because AK is the rectangle contained by AB, BC, for BK is equal to BC,

...

And it was demonstrated that the four CK, BN, GR, and RN are quadruple to CK:

therefore the eight rectangles which contain the

**gnomon**AOH are quadruple ofAK; and because AK is the rectangle contained by AB, BC, for BK is equal to BC,

...

Side 353

First, let the parallelogram AB given in species and magnitude be increased by

the given

AB is given in species and magnitude, and that the

First, let the parallelogram AB given in species and magnitude be increased by

the given

**gnomon**ECBDFG, each of the straight lines CE, DF is given. BecauseAB is given in species and magnitude, and that the

**gnomon**ECBDFG is given, ... Side 354

A E D B dat.) in magnitude, and the

given figure AC: therefore (82. dat.) since EF is diminished by the given

ELH, the sides BK. FH of the

...

A E D B dat.) in magnitude, and the

**gnomon**ELH is equal (36. and 43. 1.) to thegiven figure AC: therefore (82. dat.) since EF is diminished by the given

**gnomon**ELH, the sides BK. FH of the

**gnomon**are given; but EK is equal to DC, and FH to...

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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.