## 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 25

to

also the third angle of the one to the third angle of the other . Let ABC , DEF be

two triangles which have the angles ABC , BCA equal to the angles DEF , EFD ,

viz ...

to

**equal angles**in each ; then shall the other sides be equal , each to each ; andalso the third angle of the one to the third angle of the other . Let ABC , DEF be

two triangles which have the angles ABC , BCA equal to the angles DEF , EFD ,

viz ...

Side 126

If the angle of a triangle be divided into two

also cuts the base ; the segments of the base shall have the same ratio which the

other sides of the triangle have to one another : and if the segments of the ...

If the angle of a triangle be divided into two

**equal angles**, by a straight line whichalso cuts the base ; the segments of the base shall have the same ratio which the

other sides of the triangle have to one another : and if the segments of the ...

Side 135

Wherefore the sides of the parallelograms AB , BC about their

reciprocally proporG C tional , But , let the sides about the

reciprocally proportional , viz . as DB to BE , so GB to BF ; the parallelogram AB is

...

Wherefore the sides of the parallelograms AB , BC about their

**equal angles**arereciprocally proporG C tional , But , let the sides about the

**equal angles**bereciprocally proportional , viz . as DB to BE , so GB to BF ; the parallelogram AB is

...

Side 175

N A mel If each of two solid

one another , each to each ; the ... Let there be two solid

; and let the

...

N A mel If each of two solid

**angles**be contained by three plane**angles equal**toone another , each to each ; the ... Let there be two solid

**angles**at the points A , B; and let the

**angle**at A be contained by the three plane**angles**CAD , CAE , EAD...

Side 194

equal to the angle DEF : and the right angle ABK is equal to the right angle DEN ,

whence the remaining angle CBK is ... in one equal to two angles in the other ,

each to each , and one side equal to one side adjacent to the

equal to the angle DEF : and the right angle ABK is equal to the right angle DEN ,

whence the remaining angle CBK is ... in one equal to two angles in the other ,

each to each , and one side equal to one side adjacent to the

**equal angles**in ...### Hva folk mener - Skriv en omtale

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

The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2017 |

### 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.