## 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 15

Side 28

STRAIGHT lines which are

another . Let AB , CD , be each of them

Let the straight line GHK cut AB , EF , CD ; and because GHK cuts the

STRAIGHT lines which are

**parallel**to the same straight line are**parallel**to oneanother . Let AB , CD , be each of them

**parallel**to EF , AB is also**parallel**to CD ,Let the straight line GHK cut AB , EF , CD ; and because GHK cuts the

**parallel**... Side 33

7 AN between the same

triangle DEF . Produce AD both ways to the points G , H , and through B draw BG

7 AN between the same

**parallels**BF , AD ; the triangle ABC is equal to thetriangle DEF . Produce AD both ways to the points G , H , and through B draw BG

**parallel**( 31. 1. ) to CA , and through F draw FH**parallel**to ED : then each of the ... Side 36

AH

upon the

two right angles : wherefore the angles BHF , HFE are less than two right angles

...

AH

**parallel**to BG or EF , and join HB . Then , because the straight line HF fallsupon the

**parallels**AH , EF , the angles AHF , HFE are together equal ( 29. 1. ) totwo right angles : wherefore the angles BHF , HFE are less than two right angles

...

Side 163

Let the two straight lines AB , BC which meet one another be

straight lines DE , EF that meet one another , and are not in the same plane with

AB , BC . The angle ABC is equal to the angle DEF . Take BA , BC , ED , EF all ...

Let the two straight lines AB , BC which meet one another be

**parallel**to the twostraight lines DE , EF that meet one another , and are not in the same plane with

AB , BC . The angle ABC is equal to the angle DEF . Take BA , BC , ED , EF all ...

Side 166

to one another : therefore the plane through AB , BC is

through DE , EF . Wherefore , if two straight ... If two

another plane , their common sections with it are

planes AB ...

to one another : therefore the plane through AB , BC is

**parallel**to the planethrough DE , EF . Wherefore , if two straight ... If two

**parallel**planes be cut byanother plane , their common sections with it are

**parallels**. * Let the**parallel**planes 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: 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.