## 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

Resultat 1-5 av 12

Side 84

to the base AD ; and for the same

BA , or AD ; therefore the quadrilateral fiB D gure ABCD is equilateral . It is also

rectangular ; for the straight line BD , being the diameter of the circle ABCD , BAD

is ...

to the base AD ; and for the same

**reason**, BC , CD are each of them equal to EBA , or AD ; therefore the quadrilateral fiB D gure ABCD is equilateral . It is also

rectangular ; for the straight line BD , being the diameter of the circle ABCD , BAD

is ...

Side 88

to the angle AED : for the same

equal to the angle BAE , or AED : therefore the pentagon ABCDE is equiangular ;

and it has been shown that it is equilateral . Wherefore , in the given circle , an ...

to the angle AED : for the same

**reason**, each of the angles ABC , BCD , CDE isequal to the angle BAE , or AED : therefore the pentagon ABCDE is equiangular ;

and it has been shown that it is equilateral . Wherefore , in the given circle , an ...

Side 138

... the whole angle AGH is equal to the whole CFE : for the same

angle ABH is equal to the angle CDE ; also the angle at A is equal to the angle at

C , and the angle GHB to FED ; therefore the rectilineal figure ABHG is

equiangular ...

... the whole angle AGH is equal to the whole CFE : for the same

**reason**, theangle ABH is equal to the angle CDE ; also the angle at A is equal to the angle at

C , and the angle GHB to FED ; therefore the rectilineal figure ABHG is

equiangular ...

Side 169

than the third ; therefore the angles CBA , ABD , are greater than the angle DBC ;

for the same

the angles CDA , ADB , greater than BDC : wherefore the six angles CBA ...

than the third ; therefore the angles CBA , ABD , are greater than the angle DBC ;

for the same

**reason**, the angles BCA , ACD are greater than the angle DCB ; andthe angles CDA , ADB , greater than BDC : wherefore the six angles CBA ...

Side 180

G. 1 44 L it in that plane : therefore each of the angles FGD , FGE is a right angle :

for the same

equal to GD , DE , each to each , and contain equal angles , therefore the base

BK ...

G. 1 44 L it in that plane : therefore each of the angles FGD , FGE is a right angle :

for the same

**reason**, HKA , HKB , are right angles : and because KA , AB areequal to GD , DE , each to each , and contain equal angles , therefore the base

BK ...

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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.