## 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 6

Side 57

If a straight line be divided into two equal , and also into two unequal parts ; the

squares of the two unequal parts are together double of the square of

, and of the square of the line between the points of section . Let the straight line ...

If a straight line be divided into two equal , and also into two unequal parts ; the

squares of the two unequal parts are together double of the square of

**half**the line, and of the square of the line between the points of section . Let the straight line ...

Side 472

ML is to LG , as BC together with CD is to BD ; and , by composition , ML and LG

together , that is , producing GL to N , so that ML be equal to LN , the straight line

NG is to GL , as twice BC is to BD ; and by taking GO equal to the

...

ML is to LG , as BC together with CD is to BD ; and , by composition , ML and LG

together , that is , producing GL to N , so that ML be equal to LN , the straight line

NG is to GL , as twice BC is to BD ; and by taking GO equal to the

**half**of NG , GO...

Side 483

S. In a plane triangle , the sum of any two sides is to their difference , as the

tangent of

difference . Let ABC be a plane triangle ; the sum of any two sides , AB , AC will

be to their ...

S. In a plane triangle , the sum of any two sides is to their difference , as the

tangent of

**half**the sum of the angles at the base , to the tangent of**half**theirdifference . Let ABC be a plane triangle ; the sum of any two sides , AB , AC will

be to their ...

Side 487

the given sum , AC the greater , and BC the less . Let AD be

and ...

**Half**the given sum added to**half**the given difference , will be the greater , and**half**the difference subtracted from**half**the sum , will be the less . For , let AB bethe given sum , AC the greater , and BC the less . Let AD be

**half**the given sum ;and ...

Side 512

The rectangle contained by

of two arches , is equal to the rectangle contained by the sines of

and

...

The rectangle contained by

**half**of the radius , and the excess of the versed sinesof two arches , is equal to the rectangle contained by the sines of

**half**the sum ,and

**half**the difference of the same arches .. Let AB , AC be any two arches , and...

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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.