## 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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Resultat 1-5 av 9

Side vi

In this edition, Ptolemy's Proposition concerning a property of quadrilateral

figures in a circle, is

Proposition, Book 1st, is altered, and made more explicit, and a more general ...

In this edition, Ptolemy's Proposition concerning a property of quadrilateral

figures in a circle, is

**added**at the end of the sixth Book. Also the Note on the 29thProposition, Book 1st, is altered, and made more explicit, and a more general ...

Side 297

... on which account , especially since they are quite useless , these definitions

are distinguished from the rest by inverted double commas . DEF . XVII . B. I. The

words , “ which also divides the circle into two equal parts , " are

...

... on which account , especially since they are quite useless , these definitions

are distinguished from the rest by inverted double commas . DEF . XVII . B. I. The

words , “ which also divides the circle into two equal parts , " are

**added**at the end...

Side 298

This part must therefore have been

proposition betwixt the 5th and 13th , but none of these stand in need of it except

the 7th proposition , on account of which it has been

translation ...

This part must therefore have been

**added**to prop . 5. upon account of someproposition betwixt the 5th and 13th , but none of these stand in need of it except

the 7th proposition , on account of which it has been

**added**: besides , thetranslation ...

Side 319

There is a corollary

prop . of this book , and is as useful as the proposition . rest PROP . XIV . B. V.

The two cases of this , which are not in the Greek , are

of ...

There is a corollary

**added**to prop . 13. as it is necessary to the 20th and 21stprop . of this book , and is as useful as the proposition . rest PROP . XIV . B. V.

The two cases of this , which are not in the Greek , are

**added**; the demonstrationof ...

Side 353

... as it was probably

manner we may demonstrate , are not inserted except when the demonstration is

not given , or when it is something different from the other , if it be given , as in

prop .

... as it was probably

**added**to the text by some editor ; for the words , “ in likemanner we may demonstrate , are not inserted except when the demonstration is

not given , or when it is something different from the other , if it be given , as in

prop .

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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.