## 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 6

Side 342

But if B and C together be less than A ; then , because it is required that B , C , D

together be greater than A , from each of these taking away B , C , the remaining

one D must be greater than the

But if B and C together be less than A ; then , because it is required that B , C , D

together be greater than A , from each of these taking away B , C , the remaining

one D must be greater than the

**excess**of A above B and C ; take therefore any ... Side 375

Let the

to the magnitude BC ; the

magnitude , has a given ratio to BC . Let AD be the given magnitude , the ...

Let the

**excess**of the magnitude AB above a given magnitude , have a given ratioto the magnitude BC ; the

**excess**of AC , both of them together , above the givenmagnitude , has a given ratio to BC . Let AD be the given magnitude , the ...

Side 381

EG to FD ; the ratio of EG to FE is given : and GB is given ; therefore EG , the

case is shown in the same way . PROP . XXIV . 13 . If there be three magnitudes ,

the ...

EG to FD ; the ratio of EG to FE is given : and GB is given ; therefore EG , the

**excess**of EB above a given magnitude GB , has a given ratio to FD . The othercase is shown in the same way . PROP . XXIV . 13 . If there be three magnitudes ,

the ...

Side 382

Also , if the first have a given ratio to the second , and the

above a given magnitude have also a given ratio to the second , the same

shall have a given ratio to the first ; as is evident from the 9th dat . 17 . PROP .

XXV .

Also , if the first have a given ratio to the second , and the

**excess**of the thirdabove a given magnitude have also a given ratio to the second , the same

**excess**shall have a given ratio to the first ; as is evident from the 9th dat . 17 . PROP .

XXV .

Side 384

If there be three magnitudes , the

magnitude has a given ratio to the second ; and the

a given magnitude has also a given ratio to the third ; the

a ...

If there be three magnitudes , the

**excess**of the first of which above a givenmagnitude has a given ratio to the second ; and the

**excess**of the second abovea given magnitude has also a given ratio to the third ; the

**excess**of the first abovea ...

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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.