## The Elements of Euclid: 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. viz. the first six books, together with the eleventh and twelfth |

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Resultat 1-5 av 5

Side 16

Because DC is equal to CE , and FC

two sides , DC , CF , are equal A D С to the two EC , CF , each to each ; and B the

base DF is equal to the base EF ; therefore the angle DCF is equal ( 8. 1. ) ...

Because DC is equal to CE , and FC

**common**to the two triangles DCF , ECF ; thetwo sides , DC , CF , are equal A D С to the two EC , CF , each to each ; and B the

base DF is equal to the base EF ; therefore the angle DCF is equal ( 8. 1. ) ...

Side 167

KL , MN are cut by the plane EBDX , the

16. 11. ) . For the same reason , because the two parallel planes GH , KL are cut

by С H the plane AXFC , the

KL , MN are cut by the plane EBDX , the

**common**sections EX , BD , are parallel (16. 11. ) . For the same reason , because the two parallel planes GH , KL are cut

by С H the plane AXFC , the

**common**G A sections AC , XF , are parallel : and ... Side 168

IF two planes cutting one another be each of them perpendicular to a third plane ;

their

planes AB , BC be each of them perpendicular to a third plane , and let BD be the

...

IF two planes cutting one another be each of them perpendicular to a third plane ;

their

**common**section shall be perpendicular to the same plane . Let the twoplanes AB , BC be each of them perpendicular to a third plane , and let BD be the

...

Side 273

in the same manner the triangle EBC is similar to the triangle FBC , F and the

triangle EAC to FAC ; therefore there are two solid figures , each of which is

contained by six triangles , one of them by three triangles , the

which is ...

in the same manner the triangle EBC is similar to the triangle FBC , F and the

triangle EAC to FAC ; therefore there are two solid figures , each of which is

contained by six triangles , one of them by three triangles , the

**common**vertex ofwhich is ...

Side 396

... and is the same with the inclination of the planes of these great circles . PROP .

I. GREAT circles bisect one another . As they have a

. 1 .

... and is the same with the inclination of the planes of these great circles . PROP .

I. GREAT circles bisect one another . As they have a

**common**centre , their**common**section will be a diameter of each which will bisect them . PROP . II . FIG. 1 .

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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: Viz. the First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1892 |

### Vanlige uttrykk og setninger

added altitude angle ABC angle BAC base centre circle circle ABCD circumference common cone contained 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 gles greater Greek half join less likewise 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 45 - Ir a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Side 41 - 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 54 - Ir any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two points in the circumference ; the straight line drawn from A to B shall fall within the circle.

Side 18 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC.

Side 10 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line: it is required to draw from the point A a straight line equal to BC.

Side 8 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 256 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.

Side 129 - 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 23 - At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A...

Side 20 - ANY two angles of a triangle are together less than two right angles.