## 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 |

### Inni boken

Resultat 1-5 av 9

Side 296

B. I. Instead of this definition as it is in the

given from a property of a plane superficies , which is manifestly supposed in the

Elements , viz . that a straight line drawn from any point in a plane to any other in

it ...

B. I. Instead of this definition as it is in the

**Greek**copies , a more distinct one isgiven from a property of a plane superficies , which is manifestly supposed in the

Elements , viz . that a straight line drawn from any point in a plane to any other in

it ...

Side 329

And these two enunciations , the first especially , agree to the demonstration

which is now in the

as Candalla does , thus : let ABCD , CEFG , be two equiangular parallelograms ,

and ...

And these two enunciations , the first especially , agree to the demonstration

which is now in the

**Greek**. The proposition may be more briefly demonstrated ,as Candalla does , thus : let ABCD , CEFG , be two equiangular parallelograms ,

and ...

Side 353

The angles ABH , DEM are demonstrated to be right angles in a shorter way than

in the

angles : also the repetition of the same demonstration , which begins with “ in the

...

The angles ABH , DEM are demonstrated to be right angles in a shorter way than

in the

**Greek**; and in the same way ACH , DFM may be demonstrated to be rightangles : also the repetition of the same demonstration , which begins with “ in the

...

Side 461

THIS is made more explicit than in the

author of the second demonstration of the 24th proposition in the

has fallen into , of thinking that a ratio is given to which another ratio is shown to ...

THIS is made more explicit than in the

**Greek**text , to prevent a mistake which theauthor of the second demonstration of the 24th proposition in the

**Greek**editionhas fallen into , of thinking that a ratio is given to which another ratio is shown to ...

Side 464

In the 23d prop . in the

avres ds , ” are wrong translated by Claud . Hardy , in his edition of Euclid's Data ,

printed at Paris , anno 1625 , which was the first edition of the

In the 23d prop . in the

**Greek**text , which here is the 12th , the words , “ un tosavres ds , ” are wrong translated by Claud . Hardy , in his edition of Euclid's Data ,

printed at Paris , anno 1625 , which was the first edition of the

**Greek**text ; and Dr.### 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.