## 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 388

to the angle ADC ; and ADC is given , wherefore also the angle EAD is given :

therefore , because the straight line DA is drawn to the given point A in the

straight line EF

given ( 32.

to the angle ADC ; and ADC is given , wherefore also the angle EAD is given :

therefore , because the straight line DA is drawn to the given point A in the

straight line EF

**given in position**, and makes with it a given angle EAD , AD isgiven ( 32.

Side 391

line BC

given angle ADC ; HG is

magnitude , because it is equal to ( 34. 1. ) AD which is given in magnitude ;

therefore ...

line BC

**given in position**, in a given angle HGC , for it is equal ( 29. 1. ) to thegiven angle ADC ; HG is

**given in position**( 32 . dat . ) ; but it is given also inmagnitude , because it is equal to ( 34. 1. ) AD which is given in magnitude ;

therefore ...

Side 392

From the given point A , let the straight line AED be drawn to the two parallel

straight lines FG , BC , and let the ratio of the segments AE , AD be given ; if one

of the parallels BC be

From the given point A , let the straight line AED be drawn to the two parallel

straight lines FG , BC , and let the ratio of the segments AE , AD be given ; if one

of the parallels BC be

**given in position**, the other FG is also**given in position**. Side 393

ments GE , GF into which the straight line GEF is cut by the three parallels , be

given ; the third parallel HK is

draw LM perpendicular to CD , meeting HK in N ; because LM is drawn from the ...

ments GE , GF into which the straight line GEF is cut by the three parallels , be

given ; the third parallel HK is

**given in position**. In AB take a given point L , anddraw LM perpendicular to CD , meeting HK in N ; because LM is drawn from the ...

Side 453

given , the angle BDC is given ( 20. 3. ) , therefore because the straight line DC is

drawn to the given point D in the straight line BD

angle BDC , DC is given ( 32. dat . ) in position : and the circumference ABC is ...

given , the angle BDC is given ( 20. 3. ) , therefore because the straight line DC is

drawn to the given point D in the straight line BD

**given in position**in the givenangle BDC , DC is given ( 32. dat . ) in position : and the circumference ABC is ...

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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.