## 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 59

1. ) to the opposite angle ECD , the remaining angle FEG is half a C B right angle

, and equal to the A D angle EGF ; wherefore also the side GF is equal ( 6. 1. ) to

the side FE . And because EC is G equal to CA , the

...

1. ) to the opposite angle ECD , the remaining angle FEG is half a C B right angle

, and equal to the A D angle EGF ; wherefore also the side GF is equal ( 6. 1. ) to

the side FE . And because EC is G equal to CA , the

**square**of EC is equal to the...

Side 60

1. ) the

and make ( 3. 1. ) EF equal to EB , and upon AF describe ( 46. 1. ) the

FGHA ; AB is divided in H , so that the rectangle AB , BH is equal to the

AH .

1. ) the

**square**ABDC ; bisect ( 10. 1. ) AC in E , and join BE ; produce CA to F ,and make ( 3. 1. ) EF equal to EB , and upon AF describe ( 46. 1. ) the

**square**FGHA ; AB is divided in H , so that the rectangle AB , BH is equal to the

**square**ofAH .

Side 97

angle : and D because the straight line AC is bisected in E , and produced to the

point D , the rectangle AD , DC , together with the

) to the

...

angle : and D because the straight line AC is bisected in E , and produced to the

point D , the rectangle AD , DC , together with the

**square**of С EC , is equal ( 6. 2.) to the

**square**of ED , and CE is equal to EB : therefore the rectВ. angle AD , DC...

Side 289

... and the

the

that is , to the squares of AZ , ZB ; but the

... and the

**square**of GU than the**square**of BZ , and AU is equal to AB ; thereforethe

**square**of AU , that is , the squares of AG , GU are equal to the**square**of AB ,that is , to the squares of AZ , ZB ; but the

**square**of BZ is less than the**square**of ... Side 444

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

BD as ( 1. 6. ) the rectangle HIG , GO to the rectangle HG , GL : and 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

...

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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.