## 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 |

### Inni boken

Side 12

... and join FC , GB . Because AF is equal to AG , and AB to AC , the two sides FA

, AC , are equal to the two GA , AB , each to each ; and they contain the angle

FAG

4.

... and join FC , GB . Because AF is equal to AG , and AB to AC , the two sides FA

, AC , are equal to the two GA , AB , each to each ; and they contain the angle

FAG

**common**to the two А triangles AFC , AGB ; therefore the base FC is equal (4.

Side 13

off DB equal to AC the less , and join DC ; therefore , because A in the triangles

DBC , ACB , DB is equal to AC , and BC

D are equal to the two AC , CB , each to each ; and the angle DBC is equal to the

...

off DB equal to AC the less , and join DC ; therefore , because A in the triangles

DBC , ACB , DB is equal to AC , and BC

**common**to both , the two sides DB , BCD are equal to the two AC , CB , each to each ; and the angle DBC is equal to the

...

Side 15

Because AD is equal to AE , and AF is

the two sides DA , AF , are equal to the two sides , EA , AF each to each ; and the

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

Because AD is equal to AE , and AF is

**common**to the two triangles DAF , EAF ; Dthe two sides DA , AF , are equal to the two sides , EA , AF each to each ; and the

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

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 17

FG in H , and join A G B CF , CH , CG ; the straight line CH , D drawn from the

given point C , is perpendicular to the given straight line AB . Because FH is

equal to HG , and HC ,

, HC ...

FG in H , and join A G B CF , CH , CG ; the straight line CH , D drawn from the

given point C , is perpendicular to the given straight line AB . Because FH is

equal to HG , and HC ,

**common**to the two triangles FHC , GHC , the two sides FH, HC ...

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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1810 |

The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |

### 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.