## The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored ; Also the Book of Euclid's Data, in Like Manner Corrected |

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Side 313

Viz, the First Six Books, Together

which Theon, Or Others, Have Long Ago ... this book : the author of it designed to

demonstrate , that if four

Viz, the First Six Books, Together

**with**the Eleventh and Twelfth ; the Errors, bywhich Theon, Or Others, Have Long Ago ... this book : the author of it designed to

demonstrate , that if four

**magnitudes**E , G , F , H be proportionals , they are also ... Side 373

Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by

which Theon, Or Others, Have Long Ago ... A. If a magnitude together with a

...

Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by

which Theon, Or Others, Have Long Ago ... A. If a magnitude together with a

**given magnitude**has a given ratio to another magnitude ; the excess of this other...

Side 375

Let the excess of the magnitude AB above a

to the magnitude BC ; the excess of AC , both of them together , above the

Let the excess of the magnitude AB above a

**given magnitude**, have a given ratioto the magnitude BC ; the excess of AC , both of them together , above the

**given****magnitude**, has a given ratio to BC . Let AD be the**given magnitude**, the ... Side 379

above the

XXI . C. IF two magnitudes have a given ratio to one another , if a

above the

**given magnitude**EG , has a given ratio to the remainder FD . ! PROP .XXI . C. IF two magnitudes have a given ratio to one another , if a

**given****magnitude**be added to one of them , and the other be taken from a**given****magnitude**; the ... Side 383

1 ELet AB , CD , EF be three magnitudes , and let GD the excess of one of them

CD above the

excess of the same CD above the

1 ELet AB , CD , EF be three magnitudes , and let GD the excess of one of them

CD above the

**given magnitude**CG have a given ratio to AB ; and also let KD theexcess of the same CD above the

**given magnitude**CK have a given ratio to EF ...### Hva folk mener - Skriv en omtale

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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1825 |

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Euclid,Robert Simson Uten tilgangsbegrensning - 1838 |

### Vanlige uttrykk og setninger

added altitude angle ABC angle BAC base centre circle circle ABCD circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples Euclid excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid Q. E. D. PROP radius reason rectangle rectangle contained rectilineal figure remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole

### Populære avsnitt

Side 9 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 81 - The angles in the same segment of a circle are equal to one another.

Side 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Side 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 49 - 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 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

Side 155 - 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 22 - ANY two angles of a triangle are together less than two right angles.

Side 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.

Side 24 - Any two sides of a triangle are together greater than the third side.