## 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 7

Side 335

and the

AL , the half of AB ; wherefore the

of AL , that is of KG : add to each the square of KE ; therefore the square ( 6 . 2. ) ...

and the

**rectangle**C , D , from the determination , is not greater than the square ofAL , the half of AB ; wherefore the

**rectangle**EA , All is not greater than the squareof AL , that is of KG : add to each the square of KE ; therefore the square ( 6 . 2. ) ...

Side 444

Because as CB to BD , so is OG to GL , the square of CB is to the

BD as ( 1. 6. ) the

CB is equal to the rect . angle HG , GO , because GO , BC , GH are proportionals

...

Because as CB to BD , so is OG to GL , the square of CB is to the

**rectangle**CB ,BD as ( 1. 6. ) the

**rectangle**HIG , GO to the**rectangle**HG , GL : and the square ofCB is equal to the rect . angle HG , GO , because GO , BC , GH are proportionals

...

Side 446

to AEB , as AC to CB , so is AB to BE ; therefore the

AB , BC ; and the

because the sum of the squares of AB , BC is given , the square of AC which is ...

to AEB , as AC to CB , so is AB to BE ; therefore the

**rectangle**AC , BE is equal toAB , BC ; and the

**rectangle**AB , BC is given , wherefore AC , BE is given : andbecause the sum of the squares of AB , BC is given , the square of AC which is ...

Side 447

E But if the given angle ABC of the parallelogram AC be not a right angle , in this

case , because ABC is a given angle , the ratio of the

sides AB , BC to the parallelogram AC is given ( 62. dat . ) ; and AC is given ...

E But if the given angle ABC of the parallelogram AC be not a right angle , in this

case , because ABC is a given angle , the ratio of the

**rectangle**contained by thesides AB , BC to the parallelogram AC is given ( 62. dat . ) ; and AC is given ...

Side 448

Because the excess of the square of BC above a given space has a given ratio to

the square of BA , let the

square of BC ; the remainder , to wit , the

Because the excess of the square of BC above a given space has a given ratio to

the square of BA , let the

**rectangle**CB , BD be the given space ; take this from thesquare of BC ; the remainder , to wit , the

**rectangle**( 2. 2. ) BC , CB has a given ...### 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.