## The Elements of Euclid |

### Inni boken

Resultat 1-5 av 12

Side 141

Wherefore,

, that

the duplicate ratio of their homologous sides, and it has already been proved in ...

Wherefore,

**similar**polygons, &c. Q. E. D. CoR. 1. In like manner, it may be proved, that

**similar**four sided figures, or of any number of sides, are one to another inthe duplicate ratio of their homologous sides, and it has already been proved in ...

Side 147

To a given straight line to apply a parallelogram equal to a given rectilineal figure

, and deficient by a parallelogram

rectilineal figure to which the parallelogram to be applied is to be equal, must not

...

To a given straight line to apply a parallelogram equal to a given rectilineal figure

, and deficient by a parallelogram

**similar**to a given parallelogram: but the givenrectilineal figure to which the parallelogram to be applied is to be equal, must not

...

Side 148

the parallelogram EL

parallelogram GH equal to EL and C together, and

to D ; wherefore GH is

...

the parallelogram EL

**similar**and similarly situated to D: and glake (25. 6.) theparallelogram GH equal to EL and C together, and

**similar**and similarly situatedto D ; wherefore GH is

**similar**to EL (21. 6); let KH be the side homologous to FL,...

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 AC must C. N M coincide with the fi- D N *N gure

KM, because - they are equal and A B K L

DC, ...

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. 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, ...

Side 181

For the same N reason, the parallelogram A B CTE KH is

FE. Wherefore three parallelograms of the solid AL are

CD; and the three opposite ones in each solid are equal (24. 11.) and

For the same N reason, the parallelogram A B CTE KH is

**similar**to GF, and HB toFE. Wherefore three parallelograms of the solid AL are

**similar**to three of the solidCD; and the three opposite ones in each solid are equal (24. 11.) and

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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.