## The Elements of Euclid |

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Side 95

“Geometers make use of the following technical words to signify cer. tain ways of

changing either the order or magnitude of

still to be

“Geometers make use of the following technical words to signify cer. tain ways of

changing either the order or magnitude of

**proportionals**, so as that they continuestill to be

**proportionals**.' XIII. Permutando, or alternando, by permutation, ... Side 136

IF four straight lines be

equal to the rectangle contained by the means: and if the rectangle contained by

the extremes be equal to the rectangle contained by the means, the four straight ...

IF four straight lines be

**proportionals**, the rectangle contained by the extremes isequal to the rectangle contained by the means: and if the rectangle contained by

the extremes be equal to the rectangle contained by the means, the four straight ...

Side 137

If three straight lines be

equal to the square of the mean: and if the rectangle contained by the extremes

be equal to the square of the mean, the three straight lines are

If three straight lines be

**proportionals**, the rectangle contained by the extremes isequal to the square of the mean: and if the rectangle contained by the extremes

be equal to the square of the mean, the three straight lines are

**proportionals**. Side 141

And if to AB, FG, two of the homologous sides, a third

has (10, def 5,) to M the duplicate ratio ... that if three straight lines be

a similar ...

And if to AB, FG, two of the homologous sides, a third

**proportional**M be taken ABhas (10, def 5,) to M the duplicate ratio ... that if three straight lines be

**proportionals**, as the first is to the third, so is any rectilineal figure upon the first toa similar ...

Side 181

F-N gles ECG, BAK are

lar to EG. For the same N reason, the parallelogram A B CTE KH is similar to GF,

and HB to FE. Wherefore three parallelograms of the solid AL are similar to ...

F-N gles ECG, BAK are

**proportionals**: therefore the | parallelogram BK is simi- - Glar to EG. For the same N reason, the parallelogram A B CTE KH is similar to GF,

and HB to FE. Wherefore three parallelograms of the solid AL are similar 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.