## 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 5

Side 91

B С

a right angle . And because the two angles ABC , BAC , of the triangle ABC are

together less ( 17. 1. ) than two right angles , and that BAC is a right angle , ABC ...

B С

**fore**a right ( 10. def . 1. ) angle : whereE**fore**the angle BAC in a semicircle isa right angle . And because the two angles ABC , BAC , of the triangle ABC are

together less ( 17. 1. ) than two right angles , and that BAC is a right angle , ABC ...

Side 206

thereE

that is , they are parallel ( 8. def . 11. ) . Therefore , planes , & c . Q. E. D. B PROP .

XV . THEOR . If two straight lines 206 BOOK XI . THE ELEMENTS OF EUCLID . a

.

thereE

**fore**the planes CD , EF though producD ed , do not meet one another ;that is , they are parallel ( 8. def . 11. ) . Therefore , planes , & c . Q. E. D. B PROP .

XV . THEOR . If two straight lines 206 BOOK XI . THE ELEMENTS OF EUCLID . a

.

Side 384

B

" Otherwise , Let AB , C , D , be three magnitudes , the excess EB of the first of

which AB above the given magnitude AE has a given ratio to C , and the excess

of ...

B

**fore**HB , the excess of AB above a given magnitude AH , has a given ratio to E." Otherwise , Let AB , C , D , be three magnitudes , the excess EB of the first of

which AB above the given magnitude AE has a given ratio to C , and the excess

of ...

Side 417

... whereM

to the parallelogram EG , as the straight line K to the . See Note . straight line M ,

as is demonstrated in the 23d 3G 1 EUCLID'S DATA . 417 B ...

... whereM

**fore**( 1. dat . ) the ratio of K to M is given : but the parallelogram AC isto the parallelogram EG , as the straight line K to the . See Note . straight line M ,

as is demonstrated in the 23d 3G 1 EUCLID'S DATA . 417 B ...

Side 489

... except when the three angles are given ; in which case the ratios of the sides

are only given , being the same with the ratios of the sines of the angles opposite

to them . GIVEN . SOUGHT . A , B , and there- BC , AC .

...

... except when the three angles are given ; in which case the ratios of the sides

are only given , being the same with the ratios of the sines of the angles opposite

to them . GIVEN . SOUGHT . A , B , and there- BC , AC .

**fore**C , and the side 1 AB...

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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.